A Novel Algorithm to Spatio-Temporal Data Clustering on Indian Earthquake Dataset

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Wagh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3068567/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The seismic map of India displays the Himalayas, the North-East and the Andaman-Nicobar Islands are highly seismically active regions. The characteristics of the seismicity of Indian sub-continent needs to analyzed. This paper presents a novel algorithm to analyse data through partitioning by forming clusters. The clusters of spatial and spatio-temporal data are generated by distributing the data in spatial buckets or bins, finding the neighbouring buckets, and reducing the computation of distance. Moreover, centroid selection method focuses on randomly selecting centroids, based on the density of data in the spatial region. The advantage of the algorithm is, it is simpler in design and one parameter settings required. The result indicates that the approach is effective in detecting spatio-temporal patterns as clusters on the earthquake catalogue dataset. The experiments demonstrate the regions with higher occurrence of earthquake events, have more clusters formed depicting the earthquake prone areas. The clustering quality measured by Silhouette index is in the range of 0.88 to 0.93, which reflects good clusters are formed. pattern mining neighbourhood centroid seismology Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 I. Introduction The recent advancements in machine learning have opened new possibilities and challenges in spatio-temporal computing. The use of machine learning models is a critical tool in solving spatio-temporal problems. Spatial refers to geographical coordinates and temporal is the time when the event occurred or data is recorded. Spatio-temporal data is a collection of events recorded with spatio-temporal attributes and other non-spatio-temporal features. The spatial-temporal data is generated from variety of sources such as satellites, GPS, lidar, drones and other sensors. The voluminous and complex spatio-temporal data makes it challenging to extract meaningful insights and patterns from it. To overcome these problems, machine learning can be used to process and analyze spatio-temporal data, identifying patterns, making predictions and forecasting. One of the advantages of using machine learning on spatio-temporal data analysis is its ability to automate time-consuming and repetitive tasks such as trying various possibilities of data arrangements and discovering meaning patterns. This helps in drawing important insights about the data with accuracy and support. The approach that can be used for the process of pattern mining, is the classification technique. Clustering is an unsupervised classification technique that forms groups or clusters of data which are highly similar to members of the group as outlined in [ 1 ], [ 2 ]. In Fig. 1 , clustering process requires to read the input dataset and setting of distance metric. The data is processed using clustering algorithm and clusters are generated. Further, clusters are validated to obtain optimal clusters. Here the clusters are validated for its goodness from the internal information about the clustering objects. Externally, comparing with external result or relative evaluation by varying different parameters. The Fig. 1 presents the flow of processing in clustering applications. The similarity or closeness between the members of the clusters is determined by the distance or similarity measure.[ 3 ]. Some widely used distance metric are Euclidean, Manhattan, Minkowski, Cosine etc.[ 4 ] Clustering is useful in various applications of pattern recognition like in market research and recommendation systems by grouping similar customer reviews and computing the popularity of the product. Classifying spam mails, dynamic trend detection, image processing, in land use to identify areas of similar use. Cluster web usage to identify similar access patterns etc. Clustering or data segmentation identifies the objects that not similar to any groups as outliers. Outliers’ detection is useful in applications to determine online credit card and insurance frauds. To identify spending behaviour of extremely high or extremely low-income group. Spatio-temporal data clustering is a process of discovering interesting correlations across spatial and temporal features.[ 5 ] Spatio-temporal clustering analysis assists in the applications like agricultural monitoring, climate modelling, crime hot spot detection, event modelling to name a few. An example of Spatio-temporal pattern discovery has an application viz, Station = Andheri \(\to\) Airport Station = CSMT \(\to\) Outstation trains. station = Santacruz \(\wedge\) time 5.00pm \(\to\) Beach. Seismic Zone : Earthquakes are the sudden shaking of the ground caused due release of energy from the crust of the Earth[ 6 ]. The Indian sub-continent experiences heterogeneous seismic characteristics. The seismic map of India displays the Himalayas, the North-East also known as Assam syntaxis and the Andaman-Nicobar Islands are highly active regions than the Central and Peninsular India[ 7 ].The North-West region of Himalayan mountain known as Hazara syntaxis. The structure and tectonics of this region is unknown. The North-East and Himalayan belt are susceptible to earthquakes with magnitude greater than 8.0 by the tectonic disturbance due to the movement of Indian plate under Eurasian plate by 45 to 50 mm per year[ 8 ].Earthquake data analysis is important in understanding the seismic hazard assessment. Contribution of our paper is : We propose a clustering algorithm for spatio-temporal data. Clustering as an unsupervised classification tool on Indian earthquake dataset to infer the vulnerable regions. Our main idea for clustering is forming of spatial buckets based on spatial coordinates boundaries. We bring forth the concept of centroid selection as an efficient process as random datapoints are choosen as centroids from spatial bucket based on the density of the spatial bucket. Denser the spatial bucket, more centroids are selected, moderate density bucket would obtain fewer centroids and no centroids from the buckets with few to no datapoints. There are one parameter settings of minPts required for the method and less computations are involved. The rest of this paper is organized as follows. In Section II, a literature review has been carried out. Then, proposed method is introduced in Section III. Next, experiments are implemented to research the performance of the proposed algorithms and discussion is performed in Section IV. Finally, conclusions are drawn in Section V II. Literature Review Spatio-temporal clustering is classified into techniques to identify moving objects, trajectories, geo-referenced time series. The recently carried out research in the area is discussed here. ST-DBSCAN[ 9 ] an extension of DBSCAN is based on core objects, noise objects and adjacent cluster identification. It requires many parameters setting like EPS1, EPS2, MinPts, \(\varDelta \in , \epsilon t\) which determines the cluster radius.The neighbours and the cluster radius are obtained by k-dist graph. NMAST (Neighbourhood Move Ability and Stay Time) density function and NT (Noise Tolerance) metrics have been conceptualized in the method to measure the spatio-temporal density of data to perform clustering[ 10 ].The Move ability evaluates the motion characteristic of the trajectory.In the paper[ 11 ], trajectory clustering to determine target behavioural pattern based on k-nearest spatial-temporal Hausdroff distance(STHD). Hidden-Markov models(HMM) is used to cluster the multivariate time series by requiring information on intital classes[ 12 ].An example of multivariate time series data is climate data collected from sensors for climate informatics. The spatial association and temporal association patterns are discovered to form clusters in [ 13 ]. ST-Grid[ 14 ] tends to partition spatio-temporal dimension into Grid cells. A density Cube-based spatio temporal clustering is proposed in [ 15 ] which uses distance threshold and density compensation calculation method. IMSTAGRID focuses on data partitioning along with interval expansion. A research is carried on earthquake time-series analysis based on declustering after sequences and regular background events which follows poisson process in the time domain. It relies on COV(T) and inter-event time statistics in sliding temporal window method[ 16 ]. K-means clustering has also been applied on the earthquake data pertaining to the Bengkulu Province, Indonesia dataset in [ 17 ]. In earthquake data analysis, Gutenberg and Richter law[ 18 ] describes the frequency and magnitude relationship given as \({log}_{10} N=a-bM\) , where N is the number of events having the magnitude greater than M. ‘a and b’ are the constants. ‘a’ is the regional seismicity level and ‘b’ is seismic b-value of the region in the range of 0.6 to 1.2 for India[ 4 ]. Gardner et.al[ 19 ] has proven sequence of earthquakes events observe Poissonian distribution. In the paper[ 20 ], the earthquake events that are inhomogeneous are declustered from the catalog using Gardner and Knopoff windowing method along with poissonian tests. In the paper[ 15 ], correlations of geomagnetic characteristics as precursors between the attributes amplitude, frequency, lead time, direction has been studied. Aftershocks are the smaller magnitude earthquakes occurring in the vicinity of larger magnitude mainshocks. Aftershocks organization is investigated focusing on interevent times and interevent distances[ 22 ]. The b-value varies with factors like stress accumulation, depth, plate tectonics and faulting style mechanism has been identified in [ 23 ]. Although some of the works have been carried out on earthquake data analysis using machine learning, a simple design based on clustering analysis is still lacking in this area. As such, the research will help decision makers in determining the regions that are highly seismic vulnerable in Indian subcontinent. III. Proposed Method The objective of the study is finding clustering patterns in Indian sub-continent on earthquake data. Acquire the Earthquake dataset and provide it as an input to the proposed algorithm. Find the number of records present in the earthquake catalogue. Determine the minimum and maximum latitude and longitude. The minimum and the maximum latitude longitude is used to determine the range of geographical coordinates. This range of geographical coordinates is divided into equal number of buckets(B) or bins. Further, determine each bucket minimum and maximum latitude and longitude. Find the neighboring buckets NB i for each bucket B i that are the adjacent buckets. Definition 1 Given a spatial bucket B i , a set NB i is a set of neighbouring buckets, if they are adjacent or immediate neighbors to the current bucket B i , in the directions viz North(N), South(S), East(E), West(W), North-East(NE), North-West(NW), South-East(SE), South-West(SW). Set NB i =Ø If B j is in either{N, S, E,W, NE, NW, SE, SW} directions of B i $${\{NB}_{i}\}\leftarrow {\{NB}_{i}\}\cup {B}_{j}$$ For the earthquake events, determine the bucket number into which they belong. Count the datapoints of every bucket. Compute the average number of datapoints per bucket. Compare the count of datapoints with average of datapoints per bucket and determine the buckets with more than average datapoints, less than average datapoints. The buckets with less than average datapoints are further considered the buckets less than minimum points, and buckets with zero points where minimum points is set to 10. These buckets less than minimum points and zero buckets are considered as discard bucket from which the centroid would not be selected. The bucket with more than average datapoints is sorted in descending order. Also find the bucket with maximum number of datapoints. Deciding the number of centroids for each bucket is carried out as follows. The Bucket count of datapoints is equal to zero than no centroid is chosen from the bucket. The Bucket count of datapoints is in the range of average bucket datapoint size to twice the average bucket datapoint size than one centroid is chosen from the bucket. The bucket count of datapoints is in the range of twice average bucket datapoint size to thrice the average bucket datapoint size than number of centroids for the bucket are chosen as log to the base 10 of Bucket count of datapoints. The bucket count of datapoints is greater than thrice the average bucket datapoint size and less than the maximum bucket count of datapoints than number of centroids for the bucket are chosen as log to the base 10 of bucket count of datapoints multiplied by 0.75. For, the bucket count of datapoints is equal to maximum bucket count of datapoints then the number of centroids for the bucket are chosen as log to the base 10 of bucket count of datapoints added by two. Thus, leads to more number of centroids selection in the region of the bucket with more than average number of datapoints. The principle of the centroid selection can be stated as follows. For each bucket with centroid count greater than 0, choose the datapoint as a centroid and append it to the centroid list, if the datapoint belongs to the bucket. This selection of centroid is performed randomly. To further append other centroids in the list, the new datapoint and all the existing centroids surface distance is computed. The new datapoint and all other previously chosen centroids distance must be greater than 500 km. This leads to not selecting centroids which are physically or surface distance closer to any other centroids. The surface distance is calculated with the Haversine formula as $$P=2*radius*arcsin\sqrt{{sin}^{2}+\text{cos}Lat1.cosLat2+{sin}^{2}(Long2-Long1)}$$ 1 where radius is the Earth radius equal to 6371 kms and Lat1, Lat2 are latitude coordinates and Long1, Long2 are longitude coordinates of two spatial datapoints.It computes the spatial distance of two datapoints.Further, for every centroid determine the neighbouring buckets. Use of this feature, eliminates distance computation with farthest centroid. The time difference between any two events is calculated.Convert the two timestamps into seconds. Compute the difference between these timestamps. Divide it with 3600 and 24 to get the time difference. Similarly, find the time difference between every consecutive event in the catalogue. Add these time differences and divide it by the size of catalogue, to obtain mean time between events as to normalize in further computations. The distance formula is the Euclidean distance and is computed for two datapoints as $$Euclidean Distance=\sqrt{{\varDelta S}^{2}+{\alpha \varDelta t}^{2}+{\Delta }{NS}^{2}}$$ 2 where S is the spatial distance between two locations, Δt is the time difference between two earthquake events. and NS is the non-spatial parameters like magnitude, depth etc. The time difference between the datapoint and centroid very large. So, normalize it with lambda which is set to 0.001. Proposed Algorithm for Clustering: X- Earthquake Catalogue or dataset. n- Total number of objects or datapoints in the catalogue. B - Bucket i – Bucket number. n Bi – total number of datapoints belonging to the bucket B i C k – Centroid k Step 1: Represent dataset X as a vector [x 1 , x 2 , x 3 ,..,x r ] where x 1 is a temporal attribute, x 2 , x 3 are spatial attributes and the rest are attributes related to the earthquake event. Step 2: Set each Bucket boundaries to map the entire geographical region. A bucket B i is logically represented as a conjunction of a range of values as [B i .minLat = Lat1] ^ [B i .maxLat = Lat2] ^ [B i .minLong = Long1] ^ [B i .maxLong = Long2] (3) where Lat1, Lat2 are latitudes and Long1, Long2 are Longitudes Step 3: For each bucket B i ,find the neighbouring buckets NB i list. Step 4: Assign each X j datapoint to the bucket B i as $$Bucket\left({X}_{j}\right) = \left\{i \right|\left({B}_{i} .minLat<{X}_{j}.Lat \le {B}_{i} .maxLat\right)\wedge \left({B}_{i}.minLong<{X}_{j}.Long \le {B}_{i}.maxLong\right)\}$$ 4 Step 5: Further, compute the count of datapoints for each bucket. \({n}_{Bi}={\forall }_{j}count\left( {X}_{j}\right)\) such that 1 \(\le j\le l\) and Bucket(X j )=i (5) Step 6: Compute the average count of datapoints for all the buckets. $$\mu =\frac{1}{b}\sum _{i=1}^{b}{n}_{Bi}$$ 6 where b is the total number of buckets. Step 7: Find the Buckets with more than average datapoints, less than average datapoints and more than minimum points, less than minimum datapoints and zero bucket. $$Bi\in \left\{\begin{array}{c}More\_than\_avg, if {n}_{Bi}\ge \mu \\ Less\_than\_avg, if {\text{m}\text{i}\text{n}\_pts<n}_{Bi}< \mu \\ zero\_buckets, if 0\le {n}_{Bi}\le min\_pts\end{array}\right.$$ 7 where More_than_avg is a list of buckets have the count of datapoints more than µ. The less_than_avg is a list of buckets that have datapoints count in the range of minimum points and µ. Step 8: Sort( \(More\_than\_avg )\) in descending order. Step 9: \({Bucket}_{max}=max{( n}_{Bi})\) (8) \(\text{S}\text{t}\text{e}\text{p} 10: \delta = \text{s}\text{u}\text{r}\text{f}\text{a}\text{c}\text{e}\_\text{d}\text{i}\text{s}\text{t}\text{a}\text{n}\text{c}\text{e}({B}_{i} .minLat, {B}_{i}.minLong\) , \({B}_{i} .maxLat\) , \({B}_{i} .maxLong)\) / 2 (9) Step 11: Compute the number of centroids as per the density of datapoints. $$Centroid\_count\left({B}_{i}\right)=\left\{\begin{array}{c}⌈{log}_{10}({n}_{Bi})+2⌉, if {n}_{Bi}\ge {Bucket}_{max}\\ ⌈{log}_{10}({n}_{Bi})*3/4⌉, {if 3*\mu <{n}_{Bi}<Bucket}_{max}\\ 1, {if \mu \le {n}_{Bi}\le 2*\mu }_{ }\\ 0, if 0\le {n}_{Bi}<\mu \end{array}\right.$$ 10 Step 12: Selection of the centroids Repeat for i = 1 to total_buckets. For k = 1 to \(Centroid\_count\left({B}_{i}\right)\) Start with num as a random number in the range from 1 to 1000. For j = num to n If (X[j] \(\in {B}_{i}\) and surface_distance(X[j], \(\left\{{C}_{k}\right\}\) )> \(\delta\) ) then //Determine the surface distance between X[j] and all previous centroids Append X[j] to { \({C}_{k}\}\) Step 13: Assign datapoints to the clusters For i = 1 to n For j = 1 to len( \({C}_{k}\) ) if(Bucket[i] = centroidBucket[j]) or (FindNeighbourBinCentroid(Bucket[i],neighbours_centroid[j]) = = 1) Euclidean Distance(X[i],Centroid[j]) And append X[i] to the closet clustered centroid which is at minimum euclidean distance. Step 14: Stop The proposed model is pictorial represented as follows in the Fig. 2 . The proposed algorithm is represented in a flowchart as : IV. Result and Discussion Dataset Description : The Earthquake data catalogue contains the earthquake data from the period 2019 to 2022. Capturing the events with details viz the timestamp, latitude and longitude as the geographical coordinates, depth, and magnitude of the earthquake events. The data about the earthquake is obtained from the National Centre of Seismology, Ministry of Earth Sciences, Government of India. The data catalogue is a collection of earthquake events occurred in India and its surrounded region bounded in 0 0 to 40 0 N and 60 0 to 100 0 N coordinates. The Earthquake data is chosen as the spatio-temporal data containing 4629 events records. Bucket assignments to the datapoints and the centroids assists in determining the points closer to buckets. The buckets are assigned as per the spatial coordinates as earthquake events are occasional occurring events. It might not occur at the same or nearby surrounding area repeatedly. There are not many events to be clustered for several intervals together. Thus, the distribution of buckets is on the spatial dimensions. The centroid selection method for clustering of data is the fundamental step of the algorithm. The proposed method, recommends to choose more datapoints as centroids from the region of higher rate of earthquakes. Selects a few number of centroids from the region of moderate rate of earthquakes. Whereas no centroids are selected from the region with less datapoints or no datapoints. These buckets are called discard buckets. It results into minimizing the error rate of clustering assignment of datapoints. Further, while centroid selection, if a centroid is already chosen from a region, then in order to choose the remaining centroids from the same bucket that are not very close by, the haversine distance formula and earths radius, in 6371km has been used. The two centroids are at least \(\delta\) as per the distance function. Thus, it yields clusters that are easily separable based on spatio-temporal Euclidean distance. Finding the neighbouring buckets of the centroids along with comparing the datapoints with the centroid or neighbouring buckets of centroids, gives the advantage that euclidean distance of centroids belonging to the buckets of datapoint and neighbours buckets of current centroid is only computed. The centroids which are not closer centroids neither are the neighbouring bucket centroids, are not considered for euclidean distance computation. Thus, it minimizes the Euclidean distance computation. The time difference between any two timestamps taken in seconds is very large, which results in distorted clustering. With inclusion of weight factor lambda, which is set to 0.001 gives expected clustering result. The lambda factor normalizes the data. The clusters formed are arbitrary in shape. Different clusters have different colors. The result shows (see figure.5) with lesser the minimum centroid-centroid distance such as less than 300km, more clusters are formed as 25. If the minimum distance between centroids is increased, the number of clusters formed are less in number as here it is 19(see figure.4). Mostly, the cluster density is higher than the average density of datapoints for buckets. The outlier ratio is very small, as those are the points where very few earthquakes have occurred. With increase in minpts, more outliers would be formed. As number of cluster centroids increase the computational complexity also increases. If the cluster centroids are not appropriately chosen, it may result into cluster centroids selected which are very close to each other. that results into distinct, non overlapping clusters generated. To measure the quality of clustering, Silhouette index for the clusters is computed which is stated as $$Silhoutt{eindex}_{i}=\frac{u\left(i\right)-v\left(i\right)}{\text{max}\left(v\left(i\right),u\left(i\right)\right)}$$ 11 where v - within the cluster, mean distance from datapoint ‘i’ to all other datapoints. u - mean distance with all datapoints of any other cluster. For our experiment the Silhouette index is in the range of 0.88 to 0.93, which reflects good clustering quality on the Spatio-temporal Indian Earthquake dataset. Table 1: Clustering Result with Datapopulation Characteristics of the clusters of earthquakes in Indian subcontinent: The high active zones are identified in the study area as given in Table 1 . The cluster 0, 1 and 2 are the clusters in Andaman and Nicobar islands having the cluster size as 76, 123 and 74 events respectively. Cluster 3, Longitude range of 70.03° to 77.69°, Latitude range of 16.77° to 23.63°. The centroid selected is 93km NW of Mumbai, Maharashtra, India, towards the Gujarat state. The number of earthquake events in the cluster are 216. The mean time difference between the earthquake events is 5.29 days. Mostly, 81 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 5.3 M L and on average 2.94 M L . Mean depth is 8km. Cluster 5 Longitude range of 91.79° to 96.77°, Latitude range of 21.7° to 26.7°. The centroid selected is 35km SE of Imphal, Manipur, India. The number of earthquake events in the cluster are 443. The mean time difference between the earthquake events is 2.34days. Mostly, 155 events have occurred in the time difference of 0 days. And 87 events have occurred with the time difference of 1 day. Mostly the 346 events have occurred with 0,1,2,3 days of time difference. The maximum magnitude earthquake is 5.3 M L and on average 3.52 M L . Mean depth is 42.28 km. 23 events in the 7th month of 2020, and 22 events in the 11th month of 2021 have occurred in the cluster. Cluster 8, Longitude range of 76.6° to 84.52°, Latitude range of 27.07° to 33.85°. The centroid selected is 46km NW of Pithoragarh, Uttarakhand, India. The number of earthquake events in the cluster are 224. The mean time difference between the earthquake events is 5.00 days. Mostly, 57 events have occurred in the time difference of 0 days. Mostly the 138 events have occurred with 0,1,2,3 days of time difference. The maximum magnitude earthquake is 6.3 M L and on average 3.14 M L . Mean depth is 11.5 km Cluster 12, Longitude range of 90° to 94.42°, Latitude range of 24.2° to 28.9°. The centroid selected is 29km W of Tezpur, Assam, India. The number of earthquake events in the cluster are 315. The mean time difference between the earthquake events is 3.52 days. Mostly, 113 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 6.4 M L and on average 3.16 M L . Mean depth is 18 km, 58 events have occurred from the time period from 4th April 2021 to 22nd may 2021 in this cluster. Cluster 19, Longitude range of 75.23° to 84.13°, Latitude range of 31.33° to 38.2°. The centroid selected is 53km NNE of Leh, Laddakh, India. The number of earthquake events in the cluster are 378. The mean time difference between the earthquake events is 2.88 days. Mostly, 144 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 6.1 M L and on average 3.99 M L . Mean depth is 20km Cluster 21, the mean time difference between the earthquake events is 2.32 days. Mostly, 166 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 5.5 M L and on average 3.95 M L . longitude range 68.06° to 72.03°, Latitude range of 35.53° to 40°, with the centroid as 69.9° long, 37.2° lat. The centroid selected is 58km west of Fazyabad, Afghanistan. Mean depth is 103.89km. The number of earthquake events in the cluster are 431. Cluster 23 is the cluster near to Fazyabad, Afghanistan with maximum magnitude of 6.3 M L and depth at 220km.The longitude range 69.79° to 73.58°, Latitude range of 35.3° to 39.5°. The mean time difference between the earthquake events is 1.697 days. The pattern identified in the cluster 23 is time difference between the events is mostly less than 2 days. With the centroid as 71.3° long, 36.6° lat. The number of earthquake events in the cluster are 579. Mostly, 233 events have occurred in the time difference of 0 days. Mostly, 145 events have occurred in the time difference of 1 days. Cluster 24, the mean time difference between the earthquake events is 3.77 days. The maximum magnitude earthquake is 6 M L and on average 4.01 M L . longitude range 71.84° to 77.25°, Latitude range of 35.26° to 40°, with the centroid as 74.3° long, 38.1° lat. The number of earthquake events in the cluster are 248.Mostly the events have occurred with 0,1,2,3,4 days of time difference.66 events have occurred with 0 days’ time difference. The regions with the longitude 65° to 80°, latitude 30° to 40° and the longitude 85° to 97°, latitude 30° to 40° are prone to more occurrence of earthquakes. So, more clusters are formed in the area. V. Conclusion Machine-Learning, tackles variety of problems by developing data-driven models by identifying the problems and infer to provide feasible solutions. Clustering has been one of the main tools in knowledge discovery in spatial and spatio-temporal datasets. Seismic events like earthquakes are a good example of spatio-temporal data as it includes location and time of events occurrence. The proposed method required few iterations to compute the clusters. The method is based on neighbourhood bucket searching and Euclidean distance metric.Our method also formulates the number of clusters to be formed based on the density of earthquakes in the region. In clustering we consider the isolated datapoints, far away from all clusters as noise or outliers. These outliers have extremely large spatial distance from any clusters. Outliers have no influence on the inliers, in the proposed method. The clustering result show distinct and non overlapping clusters are formed.The clustering quality measured by Silhouette index is in the range of 0.88 to 0.93, which reflects good clusters are formed. Declarations It is Ph.D research work contributed by Ms Swati Meshram under the supervision of Dr Kishor Wagh. Both the authors have contributed in preparation of manuscript. This research has not received financial support from third party. As per my understanding authors have no conflict of interest with third person/party. 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Pattern Anal Applic 26(1):19–37. 10.1007/s10044-022-01092-1 Novianti P, Setyorini D, Rafflesia U (2017) “K-Means cluster analysis in earthquake epicenter clustering,” International Journal of Advances in Intelligent Informatics , vol. 3, no. 2, Art. no. 2, Jul. doi: 10.26555/ijain.v3i2.100 Gutenberg B, Richter CF (1954) Seismicity of the Earth and Associated Phenomena. ” Princeton University Press, Princeton Gardner JK, Knopoff L (1974) “Is the sequence of earthquakes in Southern California, with aftershocks removed, Poissonian?,” Bulletin of the Seismological Society of America , vol. 64, no. 5, pp. 1363–1367, Oct. doi: 10.1785/BSSA0640051363 Brad Luen PB, Stark (April 2012) Poisson tests of declustered catalogues. Geophys J Int 189(1):691–700. https://doi.org/10.1111/j.1365-246X.2012.05400.x Yusof KA, Abdullah M, Hamid NSA, Ahadi S, Yoshikawa A (2021) “Correlations between Earthquake Properties and Characteristics of Possible ULF Geomagnetic Precursor over Multiple Earthquakes,” Universe , vol. 7, no. 1, Art. no. 1, Jan. doi: 10.3390/universe7010020 Bottiglieri M, Lippiello E, Godano C, de Arcangelis L (2009) Identification and spatiotemporal organization of aftershocks. J Geophys Research: Solid Earth 114(B3). 10.1029/2008JB005941 Sarma V, Bora DK, Biswas R (2022) “Spatio-temporal analysis of b-value prior to 28 April 2021 Assam Earthquake and implications thereof,” Annals of Geophysics , vol. 65, no. 5, Art. no. 5, Oct. doi: 10.4401/ag-8802 Additional Declarations No competing interests reported. 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Wagh","email":"","orcid":"","institution":"Government College of Engineering Amravati","correspondingAuthor":false,"prefix":"","firstName":"Kishor","middleName":"P.","lastName":"Wagh","suffix":""}],"badges":[],"createdAt":"2023-06-15 15:14:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3068567/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3068567/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":39102310,"identity":"3e7c7ca7-b152-4800-9bbe-b2f2c262023f","added_by":"auto","created_at":"2023-06-26 17:52:07","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":24552,"visible":true,"origin":"","legend":"\u003cp\u003eFlow of Processing in Clustering Application\u003c/p\u003e","description":"","filename":"Fig1.FlowofProcessinginClusteringApplications.png","url":"https://assets-eu.researchsquare.com/files/rs-3068567/v1/f42f6ea1b20128c5491333ce.png"},{"id":39102308,"identity":"092f69d5-cd90-49ec-8986-ea316ebb8e43","added_by":"auto","created_at":"2023-06-26 17:52:07","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":41877,"visible":true,"origin":"","legend":"\u003cp\u003eProposed Clustering Algorithm Process.\u003c/p\u003e","description":"","filename":"Fig2.ProposedClusteringAlgorithmProcess.png","url":"https://assets-eu.researchsquare.com/files/rs-3068567/v1/bdeab716bd2b5a9447eb7468.png"},{"id":39102309,"identity":"4d04afcd-1dff-4659-86fa-58f26ed95db1","added_by":"auto","created_at":"2023-06-26 17:52:07","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":121895,"visible":true,"origin":"","legend":"\u003cp\u003eFlowchart of the Proposed Clustering algorithm\u003c/p\u003e","description":"","filename":"Fig3.FlowchartoftheProposedclusteringAlgorithm.png","url":"https://assets-eu.researchsquare.com/files/rs-3068567/v1/1ac2cf4c47d01204775a86ac.png"},{"id":39102311,"identity":"fa281e81-8a9d-4a88-a2bf-338d91d3e0e7","added_by":"auto","created_at":"2023-06-26 17:52:08","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":288910,"visible":true,"origin":"","legend":"\u003cp\u003eResult of spatio-temporal clustering with number of clusters=19.\u003c/p\u003e","description":"","filename":"Fig4ResultofSpatioTemporalClusteringwith19clustersformed.png","url":"https://assets-eu.researchsquare.com/files/rs-3068567/v1/98fb3ededa74e07ee3ed5164.png"},{"id":39102312,"identity":"4cdc51c1-8097-4c9d-95e7-7a12f5eb7b5c","added_by":"auto","created_at":"2023-06-26 17:52:08","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":282475,"visible":true,"origin":"","legend":"\u003cp\u003eResult of spatio-temporal clustering with number of clusters=25\u003c/p\u003e","description":"","filename":"Fig5ResultofSpatioTemporalClusteringwith25clustersformed.png","url":"https://assets-eu.researchsquare.com/files/rs-3068567/v1/bee7df79ce46f8bf639befca.png"},{"id":39657597,"identity":"cd7961f4-6f6c-4844-9bc0-53f9da00e95d","added_by":"auto","created_at":"2023-07-06 19:59:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1028440,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3068567/v1/1827ae93-6acb-462e-9b7d-12ecbde19a37.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"A Novel Algorithm to Spatio-Temporal Data Clustering on Indian Earthquake Dataset","fulltext":[{"header":"I. Introduction","content":"\u003cp\u003eThe recent advancements in machine learning have opened new possibilities and challenges in spatio-temporal computing. The use of machine learning models is a critical tool in solving spatio-temporal problems. Spatial refers to geographical coordinates and temporal is the time when the event occurred or data is recorded. Spatio-temporal data is a collection of events recorded with spatio-temporal attributes and other non-spatio-temporal features. The spatial-temporal data is generated from variety of sources such as satellites, GPS, lidar, drones and other sensors. The voluminous and complex spatio-temporal data makes it challenging to extract meaningful insights and patterns from it. To overcome these problems, machine learning can be used to process and analyze spatio-temporal data, identifying patterns, making predictions and forecasting. One of the advantages of using machine learning on spatio-temporal data analysis is its ability to automate time-consuming and repetitive tasks such as trying various possibilities of data arrangements and discovering meaning patterns. This helps in drawing important insights about the data with accuracy and support. The approach that can be used for the process of pattern mining, is the classification technique. Clustering is an unsupervised classification technique that forms groups or clusters of data which are highly similar to members of the group as outlined in [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. In Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, clustering process requires to read the input dataset and setting of distance metric. The data is processed using clustering algorithm and clusters are generated. Further, clusters are validated to obtain optimal clusters. Here the clusters are validated for its goodness from the internal information about the clustering objects. Externally, comparing with external result or relative evaluation by varying different parameters. The Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e presents the flow of processing in clustering applications.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe similarity or closeness between the members of the clusters is determined by the distance or similarity measure.[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Some widely used distance metric are Euclidean, Manhattan, Minkowski, Cosine etc.[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eClustering is useful in various applications of pattern recognition like in market research and recommendation systems by grouping similar customer reviews and computing the popularity of the product. Classifying spam mails, dynamic trend detection, image processing, in land use to identify areas of similar use. Cluster web usage to identify similar access patterns etc. Clustering or data segmentation identifies the objects that not similar to any groups as outliers. Outliers\u0026rsquo; detection is useful in applications to determine online credit card and insurance frauds. To identify spending behaviour of extremely high or extremely low-income group.\u003c/p\u003e \u003cp\u003eSpatio-temporal data clustering is a process of discovering interesting correlations across spatial and temporal features.[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] Spatio-temporal clustering analysis assists in the applications like agricultural monitoring, climate modelling, crime hot spot detection, event modelling to name a few. An example of Spatio-temporal pattern discovery has an application viz,\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eStation\u0026thinsp;=\u0026thinsp;Andheri\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\to\\)\u003c/span\u003e\u003c/span\u003eAirport\u003c/p\u003e\u003cp\u003eStation\u0026thinsp;=\u0026thinsp;CSMT\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\to\\)\u003c/span\u003e\u003c/span\u003eOutstation trains.\u003c/p\u003e\u003cp\u003estation\u0026thinsp;=\u0026thinsp;Santacruz\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\wedge\\)\u003c/span\u003e\u003c/span\u003etime \u0026lt; 5.00pm \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\to\\)\u003c/span\u003e\u003c/span\u003e University\u003c/p\u003e\u003cp\u003estation\u0026thinsp;=\u0026thinsp;Santacruz \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\wedge\\)\u003c/span\u003e\u003c/span\u003etime\u0026thinsp;\u0026gt;\u0026thinsp;5.00pm \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\to\\)\u003c/span\u003e\u003c/span\u003e Beach.\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cb\u003eSeismic Zone\u003c/b\u003e:\u003c/p\u003e \u003cp\u003eEarthquakes are the sudden shaking of the ground caused due release of energy from the crust of the Earth[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe Indian sub-continent experiences heterogeneous seismic characteristics. The seismic map of India displays the Himalayas, the North-East also known as Assam syntaxis and the Andaman-Nicobar Islands are highly active regions than the Central and Peninsular India[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e].The North-West region of Himalayan mountain known as Hazara syntaxis. The structure and tectonics of this region is unknown. The North-East and Himalayan belt are susceptible to earthquakes with magnitude greater than 8.0 by the tectonic disturbance due to the movement of Indian plate under Eurasian plate by 45 to 50 mm per year[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].Earthquake data analysis is important in understanding the seismic hazard assessment.\u003c/p\u003e \u003cp\u003e \u003cb\u003eContribution of our paper is\u003c/b\u003e:\u003c/p\u003e \u003cp\u003eWe propose a clustering algorithm for spatio-temporal data.\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eClustering as an unsupervised classification tool on Indian earthquake dataset to infer the vulnerable regions.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eOur main idea for clustering is forming of spatial buckets based on spatial coordinates boundaries.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eWe bring forth the concept of centroid selection as an efficient process as random datapoints are choosen as centroids from spatial bucket based on the density of the spatial bucket. Denser the spatial bucket, more centroids are selected, moderate density bucket would obtain fewer centroids and no centroids from the buckets with few to no datapoints.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThere are one parameter settings of minPts required for the method and less computations are involved.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe rest of this paper is organized as follows. In Section II, a literature review has been carried out. Then, proposed method is introduced in Section III. Next, experiments are implemented to research the performance of the proposed algorithms and discussion is performed in Section IV. Finally, conclusions are drawn in Section V\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e"},{"header":"II. Literature Review","content":"\u003cp\u003eSpatio-temporal clustering is classified into techniques to identify moving objects, trajectories, geo-referenced time series. The recently carried out research in the area is discussed here. ST-DBSCAN[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] an extension of DBSCAN is based on core objects, noise objects and adjacent cluster identification. It requires many parameters setting like EPS1, EPS2, MinPts,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varDelta \\in , \\epsilon t\\)\u003c/span\u003e\u003c/span\u003e which determines the cluster radius.The neighbours and the cluster radius are obtained by k-dist graph.\u003c/p\u003e \u003cp\u003eNMAST (Neighbourhood Move Ability and Stay Time) density function and NT (Noise Tolerance) metrics have been conceptualized in the method to measure the spatio-temporal density of data to perform clustering[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e].The Move ability evaluates the motion characteristic of the trajectory.In the paper[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e], trajectory clustering to determine target behavioural pattern based on k-nearest spatial-temporal Hausdroff distance(STHD).\u003c/p\u003e \u003cp\u003eHidden-Markov models(HMM) is used to cluster the multivariate time series by requiring information on intital classes[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e].An example of multivariate time series data is climate data collected from sensors for climate informatics. The spatial association and temporal association patterns are discovered to form clusters in [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]. ST-Grid[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] tends to partition spatio-temporal dimension into Grid cells. A density Cube-based spatio temporal clustering is proposed in [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] which uses distance threshold and density compensation calculation method. IMSTAGRID focuses on data partitioning along with interval expansion. A research is carried on earthquake time-series analysis based on declustering after sequences and regular background events which follows poisson process in the time domain. It relies on COV(T) and inter-event time statistics in sliding temporal window method[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. K-means clustering has also been applied on the earthquake data pertaining to the Bengkulu Province, Indonesia dataset in [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eIn earthquake data analysis, Gutenberg and Richter law[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e] describes the frequency and magnitude relationship given as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({log}_{10} N=a-bM\\)\u003c/span\u003e\u003c/span\u003e, where N is the number of events having the magnitude greater than M. \u0026lsquo;a and b\u0026rsquo; are the constants. \u0026lsquo;a\u0026rsquo; is the regional seismicity level and \u0026lsquo;b\u0026rsquo; is seismic b-value of the region in the range of 0.6 to 1.2 for India[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Gardner et.al[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] has proven sequence of earthquakes events observe Poissonian distribution. In the paper[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], the earthquake events that are inhomogeneous are declustered from the catalog using Gardner and Knopoff windowing method along with poissonian tests. In the paper[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], correlations of geomagnetic characteristics as precursors between the attributes amplitude, frequency, lead time, direction has been studied. Aftershocks are the smaller magnitude earthquakes occurring in the vicinity of larger magnitude mainshocks. Aftershocks organization is investigated focusing on interevent times and interevent distances[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The b-value varies with factors like stress accumulation, depth, plate tectonics and faulting style mechanism has been identified in [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAlthough some of the works have been carried out on earthquake data analysis using machine learning, a simple design based on clustering analysis is still lacking in this area. As such, the research will help decision makers in determining the regions that are highly seismic vulnerable in Indian subcontinent.\u003c/p\u003e"},{"header":"III. Proposed Method","content":"\u003cp\u003eThe objective of the study is finding clustering patterns in Indian sub-continent on earthquake data. Acquire the Earthquake dataset and provide it as an input to the proposed algorithm.\u003c/p\u003e \u003cp\u003eFind the number of records present in the earthquake catalogue. Determine the minimum and maximum latitude and longitude. The minimum and the maximum latitude longitude is used to determine the range of geographical coordinates. This range of geographical coordinates is divided into equal number of buckets(B) or bins. Further, determine each bucket minimum and maximum latitude and longitude.\u003c/p\u003e \u003cp\u003eFind the neighboring buckets NB\u003csub\u003ei\u003c/sub\u003e for each bucket B\u003csub\u003ei\u003c/sub\u003e that are the adjacent buckets.\u003c/p\u003e \u003cp\u003e \u003cstrong\u003eDefinition 1\u003c/strong\u003e \u003cp\u003eGiven a spatial bucket B\u003csub\u003ei\u003c/sub\u003e, a set NB\u003csub\u003ei\u003c/sub\u003e is a set of neighbouring buckets, if they are adjacent or immediate neighbors to the current bucket B\u003csub\u003ei\u003c/sub\u003e, in the directions viz North(N), South(S), East(E), West(W), North-East(NE), North-West(NW), South-East(SE), South-West(SW).\u003c/p\u003e \u003c/p\u003e \u003cp\u003eSet NB\u003csub\u003ei\u003c/sub\u003e =\u0026Oslash;\u003c/p\u003e \u003cp\u003eIf B\u003csub\u003ej\u003c/sub\u003e is in either{N, S, E,W, NE, NW, SE, SW} directions of B\u003csub\u003ei\u003c/sub\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${\\{NB}_{i}\\}\\leftarrow {\\{NB}_{i}\\}\\cup {B}_{j}$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFor the earthquake events, determine the bucket number into which they belong. Count the datapoints of every bucket. Compute the average number of datapoints per bucket. Compare the count of datapoints with average of datapoints per bucket and determine the buckets with more than average datapoints, less than average datapoints. The buckets with less than average datapoints are further considered the buckets less than minimum points, and buckets with zero points where minimum points is set to 10. These buckets less than minimum points and zero buckets are considered as discard bucket from which the centroid would not be selected. The bucket with more than average datapoints is sorted in descending order. Also find the bucket with maximum number of datapoints.\u003c/p\u003e \u003cp\u003eDeciding the number of centroids for each bucket is carried out as follows. The Bucket count of datapoints is equal to zero than no centroid is chosen from the bucket. The Bucket count of datapoints is in the range of average bucket datapoint size to twice the average bucket datapoint size than one centroid is chosen from the bucket. The bucket count of datapoints is in the range of twice average bucket datapoint size to thrice the average bucket datapoint size than number of centroids for the bucket are chosen as log to the base 10 of Bucket count of datapoints. The bucket count of datapoints is greater than thrice the average bucket datapoint size and less than the maximum bucket count of datapoints than number of centroids for the bucket are chosen as log to the base 10 of bucket count of datapoints multiplied by 0.75. For, the bucket count of datapoints is equal to maximum bucket count of datapoints then the number of centroids for the bucket are chosen as log to the base 10 of bucket count of datapoints added by two. Thus, leads to more number of centroids selection in the region of the bucket with more than average number of datapoints.\u003c/p\u003e \u003cp\u003eThe principle of the centroid selection can be stated as follows. For each bucket with centroid count greater than 0, choose the datapoint as a centroid and append it to the centroid list, if the datapoint belongs to the bucket. This selection of centroid is performed randomly. To further append other centroids in the list, the new datapoint and all the existing centroids surface distance is computed. The new datapoint and all other previously chosen centroids distance must be greater than 500 km. This leads to not selecting centroids which are physically or surface distance closer to any other centroids. The surface distance is calculated with the Haversine formula as\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$P=2*radius*arcsin\\sqrt{{sin}^{2}+\\text{cos}Lat1.cosLat2+{sin}^{2}(Long2-Long1)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere radius is the Earth radius equal to 6371 kms and Lat1, Lat2 are latitude coordinates and Long1, Long2 are longitude coordinates of two spatial datapoints.It computes the spatial distance of two datapoints.Further, for every centroid determine the neighbouring buckets. Use of this feature, eliminates distance computation with farthest centroid.\u003c/p\u003e \u003cp\u003eThe time difference between any two events is calculated.Convert the two timestamps into seconds. Compute the difference between these timestamps. Divide it with 3600 and 24 to get the time difference. Similarly, find the time difference between every consecutive event in the catalogue. Add these time differences and divide it by the size of catalogue, to obtain mean time between events as to normalize in further computations.\u003c/p\u003e \u003cp\u003eThe distance formula is the Euclidean distance and is computed for two datapoints as\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$Euclidean Distance=\\sqrt{{\\varDelta S}^{2}+{\\alpha \\varDelta t}^{2}+{\\Delta }{NS}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere S is the spatial distance between two locations, Δt is the time difference between two earthquake events. and NS is the non-spatial parameters like magnitude, depth etc. The time difference between the datapoint and centroid very large. So, normalize it with lambda which is set to 0.001.\u003c/p\u003e \u003cp\u003eProposed Algorithm for Clustering:\u003c/p\u003e \u003cp\u003eX- Earthquake Catalogue or dataset.\u003c/p\u003e \u003cp\u003en- Total number of objects or datapoints in the catalogue.\u003c/p\u003e \u003cp\u003eB - Bucket\u003c/p\u003e \u003cp\u003ei \u0026ndash; Bucket number.\u003c/p\u003e \u003cp\u003en\u003csub\u003eBi\u003c/sub\u003e \u0026ndash; total number of datapoints belonging to the bucket B\u003csub\u003ei\u003c/sub\u003e\u003c/p\u003e \u003cp\u003eC\u003csub\u003ek\u003c/sub\u003e \u0026ndash; Centroid k\u003c/p\u003e \u003cp\u003eStep 1: Represent dataset X as a vector [x\u003csub\u003e1\u003c/sub\u003e, x\u003csub\u003e2\u003c/sub\u003e, x\u003csub\u003e3\u003c/sub\u003e,..,x\u003csub\u003er\u003c/sub\u003e]\u003c/p\u003e \u003cp\u003ewhere x\u003csub\u003e1\u003c/sub\u003e is a temporal attribute, x\u003csub\u003e2\u003c/sub\u003e, x\u003csub\u003e3\u003c/sub\u003e are spatial attributes and the rest are attributes related to the earthquake event.\u003c/p\u003e \u003cp\u003eStep 2: Set each Bucket boundaries to map the entire geographical region.\u003c/p\u003e \u003cp\u003eA bucket B\u003csub\u003ei\u003c/sub\u003e is logically represented as a conjunction of a range of values as\u003c/p\u003e \u003cp\u003e[B\u003csub\u003ei\u003c/sub\u003e .minLat\u0026thinsp;=\u0026thinsp;Lat1] ^ [B\u003csub\u003ei\u003c/sub\u003e .maxLat\u0026thinsp;=\u0026thinsp;Lat2] ^ [B\u003csub\u003ei\u003c/sub\u003e .minLong\u0026thinsp;=\u0026thinsp;Long1] ^ [B\u003csub\u003ei\u003c/sub\u003e .maxLong\u0026thinsp;=\u0026thinsp;Long2] (3)\u003c/p\u003e \u003cp\u003ewhere Lat1, Lat2 are latitudes and Long1, Long2 are Longitudes\u003c/p\u003e \u003cp\u003eStep 3: For each bucket B\u003csub\u003ei\u003c/sub\u003e ,find the neighbouring buckets NB\u003csub\u003ei\u003c/sub\u003e list.\u003c/p\u003e \u003cp\u003eStep 4: Assign each X\u003csub\u003ej\u003c/sub\u003e datapoint to the bucket B\u003csub\u003ei\u003c/sub\u003e as\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$Bucket\\left({X}_{j}\\right) = \\left\\{i \\right|\\left({B}_{i} .minLat\u0026lt;{X}_{j}.Lat \\le {B}_{i} .maxLat\\right)\\wedge \\left({B}_{i}.minLong\u0026lt;{X}_{j}.Long \\le {B}_{i}.maxLong\\right)\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eStep 5: Further, compute the count of datapoints for each bucket.\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({n}_{Bi}={\\forall }_{j}count\\left( {X}_{j}\\right)\\)\u003c/span\u003e\u003c/span\u003e such that 1\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\le j\\le l\\)\u003c/span\u003e\u003c/span\u003e and Bucket(X\u003csub\u003ej\u003c/sub\u003e)=i (5)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eStep 6: Compute the average count of datapoints for all the buckets.\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\mu =\\frac{1}{b}\\sum _{i=1}^{b}{n}_{Bi}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere b is the total number of buckets.\u003c/p\u003e \u003cp\u003eStep 7: Find the Buckets with more than average datapoints, less than average datapoints and more than minimum points, less than minimum datapoints and zero bucket.\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$Bi\\in \\left\\{\\begin{array}{c}More\\_than\\_avg, if {n}_{Bi}\\ge \\mu \\\\ Less\\_than\\_avg, if {\\text{m}\\text{i}\\text{n}\\_pts\u0026lt;n}_{Bi}\u0026lt; \\mu \\\\ zero\\_buckets, if 0\\le {n}_{Bi}\\le min\\_pts\\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere More_than_avg is a list of buckets have the count of datapoints more than \u0026micro;. The less_than_avg is a list of buckets that have datapoints count in the range of minimum points and \u0026micro;.\u003c/p\u003e \u003cp\u003eStep 8: Sort(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(More\\_than\\_avg )\\)\u003c/span\u003e\u003c/span\u003ein descending order.\u003c/p\u003e \u003cp\u003eStep 9: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Bucket}_{max}=max{( n}_{Bi})\\)\u003c/span\u003e\u003c/span\u003e (8)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\text{S}\\text{t}\\text{e}\\text{p} 10: \\delta = \\text{s}\\text{u}\\text{r}\\text{f}\\text{a}\\text{c}\\text{e}\\_\\text{d}\\text{i}\\text{s}\\text{t}\\text{a}\\text{n}\\text{c}\\text{e}({B}_{i} .minLat, {B}_{i}.minLong\\)\u003c/span\u003e \u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{i} .maxLat\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{i} .maxLong)\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e/\u003c/em\u003e 2 (9)\u003c/p\u003e \u003cp\u003eStep 11: Compute the number of centroids as per the density of datapoints.\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$Centroid\\_count\\left({B}_{i}\\right)=\\left\\{\\begin{array}{c}\u0026lceil;{log}_{10}({n}_{Bi})+2\u0026rceil;, if {n}_{Bi}\\ge {Bucket}_{max}\\\\ \u0026lceil;{log}_{10}({n}_{Bi})*3/4\u0026rceil;, {if 3*\\mu \u0026lt;{n}_{Bi}\u0026lt;Bucket}_{max}\\\\ 1, {if \\mu \\le {n}_{Bi}\\le 2*\\mu }_{ }\\\\ 0, if 0\\le {n}_{Bi}\u0026lt;\\mu \\end{array}\\right.$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eStep 12: Selection of the centroids\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eRepeat for i\u0026thinsp;=\u0026thinsp;1 to total_buckets.\u003c/p\u003e\u003cp\u003eFor k\u0026thinsp;=\u0026thinsp;1 to\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(Centroid\\_count\\left({B}_{i}\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003cp\u003eStart with num as a random number in the range from 1 to 1000.\u003c/p\u003e\u003cp\u003eFor j\u0026thinsp;=\u0026thinsp;num to n\u003c/p\u003e\u003cp\u003eIf (X[j]\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\in {B}_{i}\\)\u003c/span\u003e\u003c/span\u003e and surface_distance(X[j],\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left\\{{C}_{k}\\right\\}\\)\u003c/span\u003e\u003c/span\u003e)\u0026gt;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta\\)\u003c/span\u003e\u003c/span\u003e) then //Determine the surface distance between X[j] and all previous centroids\u003c/p\u003e\u003cp\u003eAppend X[j] to {\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({C}_{k}\\}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eStep 13: Assign datapoints to the clusters\u003cdiv class=\"BlockQuote\"\u003e\u003cp\u003eFor i\u0026thinsp;=\u0026thinsp;1 to n\u003c/p\u003e\u003cp\u003eFor j\u0026thinsp;=\u0026thinsp;1 to len(\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({C}_{k}\\)\u003c/span\u003e\u003c/span\u003e)\u003c/p\u003e\u003cp\u003eif(Bucket[i]\u0026thinsp;=\u0026thinsp;centroidBucket[j]) or (FindNeighbourBinCentroid(Bucket[i],neighbours_centroid[j])\u0026thinsp;=\u0026thinsp;=\u0026thinsp;1)\u003c/p\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEuclidean Distance(X[i],Centroid[j])\u003c/p\u003e \u003cp\u003eAnd append X[i] to the closet clustered centroid which is at minimum euclidean distance.\u003c/p\u003e \u003cp\u003eStep 14: Stop\u003c/p\u003e \u003cp\u003eThe proposed model is pictorial represented as follows in the Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe proposed algorithm is represented in a flowchart as :\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"IV. Result and Discussion","content":"\u003cdiv class=\"BlockQuote\"\u003e\n\u003cp\u003e\u003cstrong\u003eDataset Description\u003c/strong\u003e:\u003c/p\u003e\n\u003cp\u003eThe Earthquake data catalogue contains the earthquake data from the period 2019 to 2022. Capturing the events with details viz the timestamp, latitude and longitude as the geographical coordinates, depth, and magnitude of the earthquake events. The data about the earthquake is obtained from the National Centre of Seismology, Ministry of Earth Sciences, Government of India. The data catalogue is a collection of earthquake events occurred in India and its surrounded region bounded in 0\u003csup\u003e0\u003c/sup\u003e to 40\u003csup\u003e0\u003c/sup\u003e N and 60\u003csup\u003e0\u003c/sup\u003e to 100\u003csup\u003e0\u003c/sup\u003eN coordinates. The Earthquake data is chosen as the spatio-temporal data containing 4629 events records.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eBucket assignments to the datapoints and the centroids assists in determining the points closer to buckets. The buckets are assigned as per the spatial coordinates as earthquake events are occasional occurring events. It might not occur at the same or nearby surrounding area repeatedly. There are not many events to be clustered for several intervals together. Thus, the distribution of buckets is on the spatial dimensions.\u003c/p\u003e\n\u003cp\u003eThe centroid selection method for clustering of data is the fundamental step of the algorithm. The proposed method, recommends to choose more datapoints as centroids from the region of higher rate of earthquakes. Selects a few number of centroids from the region of moderate rate of earthquakes. Whereas no centroids are selected from the region with less datapoints or no datapoints. These buckets are called discard buckets. It results into minimizing the error rate of clustering assignment of datapoints. Further, while centroid selection, if a centroid is already chosen from a region, then in order to choose the remaining centroids from the same bucket that are not very close by, the haversine distance formula and earths radius, in 6371km has been used. The two centroids are at least \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\delta\\)\u003c/span\u003e\u003c/span\u003e as per the distance function. Thus, it yields clusters that are easily separable based on spatio-temporal Euclidean distance.\u003c/p\u003e\n\u003cp\u003eFinding the neighbouring buckets of the centroids along with comparing the datapoints with the centroid or neighbouring buckets of centroids, gives the advantage that euclidean distance of centroids belonging to the buckets of datapoint and neighbours buckets of current centroid is only computed. The centroids which are not closer centroids neither are the neighbouring bucket centroids, are not considered for euclidean distance computation. Thus, it minimizes the Euclidean distance computation.\u003c/p\u003e\n\u003cp\u003eThe time difference between any two timestamps taken in seconds is very large, which results in distorted clustering. With inclusion of weight factor lambda, which is set to 0.001 gives expected clustering result. The lambda factor normalizes the data.\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe clusters formed are arbitrary in shape. Different clusters have different colors. The result shows (see figure.5) with lesser the minimum centroid-centroid distance such as less than 300km, more clusters are formed as 25. If the minimum distance between centroids is increased, the number of clusters formed are less in number as here it is 19(see figure.4). Mostly, the cluster density is higher than the average density of datapoints for buckets. The outlier ratio is very small, as those are the points where very few earthquakes have occurred. With increase in minpts, more outliers would be formed. As number of cluster centroids increase the computational complexity also increases. If the cluster centroids are not appropriately chosen, it may result into cluster centroids selected which are very close to each other. that results into distinct, non overlapping clusters generated.\u003c/p\u003e\n\u003cp\u003eTo measure the quality of clustering, Silhouette index for the clusters is computed which is stated as\u003c/p\u003e\n\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\n\u003cdiv id=\"FileID_Equ7\" class=\"mathdisplay\"\u003e$$Silhoutt{eindex}_{i}=\\frac{u\\left(i\\right)-v\\left(i\\right)}{\\text{max}\\left(v\\left(i\\right),u\\left(i\\right)\\right)}$$\u003c/div\u003e\n\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere\u003c/p\u003e\n\u003cp\u003ev - within the cluster, mean distance from datapoint \u0026lsquo;i\u0026rsquo; to all other datapoints.\u003c/p\u003e\n\u003cp\u003eu - mean distance with all datapoints of any other cluster.\u003c/p\u003e\n\u003cp\u003eFor our experiment the Silhouette index is in the range of 0.88 to 0.93, which reflects good clustering quality on the Spatio-temporal Indian Earthquake dataset.\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\n\u003cdiv class=\"colspec\" align=\"left\"\u003e\n\u003cp\u003eTable 1: Clustering Result with Datapopulation\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\" alt=\"\" /\u003e\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;\u003c/p\u003e\n\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003eCharacteristics of the clusters of earthquakes in Indian subcontinent:\u003c/p\u003e\n\u003cp\u003eThe high active zones are identified in the study area as given in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e. The cluster 0, 1 and 2 are the clusters in Andaman and Nicobar islands having the cluster size as 76, 123 and 74 events respectively. Cluster 3, Longitude range of 70.03\u0026deg; to 77.69\u0026deg;, Latitude range of 16.77\u0026deg; to 23.63\u0026deg;. The centroid selected is 93km NW of Mumbai, Maharashtra, India, towards the Gujarat state. The number of earthquake events in the cluster are 216. The mean time difference between the earthquake events is 5.29 days. Mostly, 81 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 5.3 M\u003csub\u003eL\u003c/sub\u003e and on average 2.94 M\u003csub\u003eL\u003c/sub\u003e. Mean depth is 8km.\u003c/p\u003e\n\u003cp\u003eCluster 5 Longitude range of 91.79\u0026deg; to 96.77\u0026deg;, Latitude range of 21.7\u0026deg; to 26.7\u0026deg;. The centroid selected is 35km SE of Imphal, Manipur, India. The number of earthquake events in the cluster are 443. The mean time difference between the earthquake events is 2.34days. Mostly, 155 events have occurred in the time difference of 0 days. And 87 events have occurred with the time difference of 1 day. Mostly the 346 events have occurred with 0,1,2,3 days of time difference. The maximum magnitude earthquake is 5.3 M\u003csub\u003eL\u003c/sub\u003e and on average 3.52 M\u003csub\u003eL\u003c/sub\u003e. Mean depth is 42.28 km. 23 events in the 7th month of 2020, and 22 events in the 11th month of 2021 have occurred in the cluster.\u003c/p\u003e\n\u003cp\u003eCluster 8, Longitude range of 76.6\u0026deg; to 84.52\u0026deg;, Latitude range of 27.07\u0026deg; to 33.85\u0026deg;. The centroid selected is 46km NW of Pithoragarh, Uttarakhand, India. The number of earthquake events in the cluster are 224. The mean time difference between the earthquake events is 5.00 days. Mostly, 57 events have occurred in the time difference of 0 days. Mostly the 138 events have occurred with 0,1,2,3 days of time difference. The maximum magnitude earthquake is 6.3 M\u003csub\u003eL\u003c/sub\u003e and on average 3.14 M\u003csub\u003eL\u003c/sub\u003e. Mean depth is 11.5 km\u003c/p\u003e\n\u003cp\u003eCluster 12, Longitude range of 90\u0026deg; to 94.42\u0026deg;, Latitude range of 24.2\u0026deg; to 28.9\u0026deg;. The centroid selected is 29km W of Tezpur, Assam, India. The number of earthquake events in the cluster are 315. The mean time difference between the earthquake events is 3.52 days. Mostly, 113 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 6.4 M\u003csub\u003eL\u003c/sub\u003e and on average 3.16 M\u003csub\u003eL\u003c/sub\u003e. Mean depth is 18 km, 58 events have occurred from the time period from 4th April 2021 to 22nd may 2021\u003c/p\u003e\n\u003cp\u003ein this cluster.\u003c/p\u003e\n\u003cp\u003eCluster 19, Longitude range of 75.23\u0026deg; to 84.13\u0026deg;, Latitude range of 31.33\u0026deg; to 38.2\u0026deg;. The centroid selected is 53km NNE of Leh, Laddakh, India. The number of earthquake events in the cluster are 378. The mean time difference between the earthquake events is 2.88 days. Mostly, 144 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 6.1 M\u003csub\u003eL\u003c/sub\u003e and on average 3.99 M\u003csub\u003eL\u003c/sub\u003e. Mean depth is 20km\u003c/p\u003e\n\u003cp\u003eCluster 21, the mean time difference between the earthquake events is 2.32 days. Mostly, 166 events have occurred in the time difference of 0 days. The maximum magnitude earthquake is 5.5 M\u003csub\u003eL\u003c/sub\u003e and on average 3.95 M\u003csub\u003eL\u003c/sub\u003e. longitude range 68.06\u0026deg; to 72.03\u0026deg;, Latitude range of 35.53\u0026deg; to 40\u0026deg;, with the centroid as 69.9\u0026deg; long, 37.2\u0026deg; lat. The centroid selected is 58km west of Fazyabad, Afghanistan. Mean depth is 103.89km. The number of earthquake events in the cluster are 431.\u003c/p\u003e\n\u003cp\u003eCluster 23 is the cluster near to Fazyabad, Afghanistan with maximum magnitude of 6.3 M\u003csub\u003eL\u003c/sub\u003e and depth at 220km.The longitude range 69.79\u0026deg; to 73.58\u0026deg;, Latitude range of 35.3\u0026deg; to 39.5\u0026deg;. The mean time difference between the earthquake events is 1.697 days. The pattern identified in the cluster 23 is time difference between the events is mostly less than 2 days. With the centroid as 71.3\u0026deg; long, 36.6\u0026deg; lat. The number of earthquake events in the cluster are 579. Mostly, 233 events have occurred in the time difference of 0 days. Mostly, 145 events have occurred in the time difference of 1 days.\u003c/p\u003e\n\u003cp\u003eCluster 24, the mean time difference between the earthquake events is 3.77 days. The maximum magnitude earthquake is 6 M\u003csub\u003eL\u003c/sub\u003e and on average 4.01 M\u003csub\u003eL\u003c/sub\u003e. longitude range 71.84\u0026deg; to 77.25\u0026deg;, Latitude range of 35.26\u0026deg; to 40\u0026deg;, with the centroid as 74.3\u0026deg; long, 38.1\u0026deg; lat. The number of earthquake events in the cluster are 248.Mostly the events have occurred with 0,1,2,3,4 days of time difference.66 events have occurred with 0 days\u0026rsquo; time difference. The regions with the longitude 65\u0026deg; to 80\u0026deg;, latitude 30\u0026deg; to 40\u0026deg; and the longitude 85\u0026deg; to 97\u0026deg;, latitude 30\u0026deg; to 40\u0026deg; are prone to more occurrence of earthquakes. So, more clusters are formed in the area.\u003c/p\u003e"},{"header":"V. Conclusion","content":"\u003cp\u003eMachine-Learning, tackles variety of problems by developing data-driven models by identifying the problems and infer to provide feasible solutions. Clustering has been one of the main tools in knowledge discovery in spatial and spatio-temporal datasets. Seismic events like earthquakes are a good example of spatio-temporal data as it includes location and time of events occurrence. The proposed method required few iterations to compute the clusters. The method is based on neighbourhood bucket searching and Euclidean distance metric.Our method also formulates the number of clusters to be formed based on the density of earthquakes in the region. In clustering we consider the isolated datapoints, far away from all clusters as noise or outliers. These outliers have extremely large spatial distance from any clusters. Outliers have no influence on the inliers, in the proposed method. The clustering result show distinct and non overlapping clusters are formed.The clustering quality measured by Silhouette index is in the range of 0.88 to 0.93, which reflects good clusters are formed.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eIt is Ph.D research work contributed by Ms Swati Meshram under the supervision of Dr Kishor Wagh.\u003c/p\u003e\n\u003cp\u003eBoth the authors have contributed in preparation of manuscript. This research has not received financial support from third party. As per my understanding authors have no conflict of interest with third person/party.\u003c/p\u003e\n\u003cp\u003eThe dataset is available on https://seismo.gov.in/\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMeshram S, Wagh KP (2021) \u0026ldquo;Mining Intelligent Spatial Clustering Patterns: A Comparative Analysis of Different Approaches,\u0026rdquo; in \u003cem\u003e8th International Conference on Computing for Sustainable Global Development (INDIACom)\u003c/em\u003e, Mar. 2021, pp.\u0026nbsp;325\u0026ndash;330\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSibson R (Jan. 1973) SLINK: An optimally efficient algorithm for the single-link cluster method. 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J Geophys Research: Solid Earth 114(B3). \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1029/2008JB005941\u003c/span\u003e\u003cspan address=\"10.1029/2008JB005941\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSarma V, Bora DK, Biswas R (2022) \u0026ldquo;Spatio-temporal analysis of b-value prior to 28 April 2021 Assam Earthquake and implications thereof,\u0026rdquo; \u003cem\u003eAnnals of Geophysics\u003c/em\u003e, vol.\u0026nbsp;65, no. 5, Art. no. 5, Oct. doi: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.4401/ag-8802\u003c/span\u003e\u003cspan address=\"10.4401/ag-8802\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"pattern mining, neighbourhood, centroid, seismology","lastPublishedDoi":"10.21203/rs.3.rs-3068567/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3068567/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe seismic map of India displays the Himalayas, the North-East and the Andaman-Nicobar Islands are highly seismically active regions. The characteristics of the seismicity of Indian sub-continent needs to analyzed. This paper presents a novel algorithm to analyse data through partitioning by forming clusters. The clusters of spatial and spatio-temporal data are generated by distributing the data in spatial buckets or bins, finding the neighbouring buckets, and reducing the computation of distance. Moreover, centroid selection method focuses on randomly selecting centroids, based on the density of data in the spatial region. The advantage of the algorithm is, it is simpler in design and one parameter settings required. The result indicates that the approach is effective in detecting spatio-temporal patterns as clusters on the earthquake catalogue dataset. The experiments demonstrate the regions with higher occurrence of earthquake events, have more clusters formed depicting the earthquake prone areas. The clustering quality measured by Silhouette index is in the range of 0.88 to 0.93, which reflects good clusters are formed.\u003c/p\u003e","manuscriptTitle":"A Novel Algorithm to Spatio-Temporal Data Clustering on Indian Earthquake Dataset","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-06-26 17:52:03","doi":"10.21203/rs.3.rs-3068567/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"f29d34fc-17e2-40aa-97c4-3976cdaf8c09","owner":[],"postedDate":"June 26th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-07-06T19:59:07+00:00","versionOfRecord":[],"versionCreatedAt":"2023-06-26 17:52:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3068567","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3068567","identity":"rs-3068567","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}