{"paper_id":"2ac16e0a-ee7d-4fe3-80ff-99323a3adebb","body_text":"Compression and k-mer based Approach For Anticancer Peptide\nAnalysis\nSarwan Ali * Tamkanat E Ali † Prakash Chourasia * Murray Patterson *\nAbstract\nOur research delves into the imperative realm of anti-cancer\npeptide sequence analysis, an essential domain for biologi-\ncal researchers. Presently, neural network-based methodolo-\ngies, while exhibiting precision, encounter challenges with a\nsubstantial parameter count and extensive data requirements.\nThe recently proposed method to compute the pairwise dis-\ntance between the sequences using the compression-based\napproach [26] focuses on compressing entire sequences, po-\ntentially overlooking intricate neighboring information for\nindividual characters (i.e., amino acids in the case of protein\nand nucleotide in the case of nucleotide) within a sequence.\nThe importance of neighboring information lies in its ability\nto provide context and enhance understanding at a finer level\nwithin the sequences being analyzed. Our study advocates\nan innovative paradigm, where we integrate classical com-\npression algorithms, such as Gzip, with a pioneeringk-mers-\nbased strategy in an incremental fashion. Diverging from\nconventional techniques, our method entails compressing in-\ndividual k-mers and incrementally constructing the compres-\nsion for subsequences, ensuring more careful consideration\nof neighboring information for each character. Our pro-\nposed method improves classification performance without\nnecessitating custom features or pre-trained models. Our ap-\nproach unifies compression, Normalized Compression Dis-\ntance, and k-mers-based techniques to generate embeddings,\nwhich are then used for classification. This synergy facili-\ntates a nuanced understanding of cancer sequences, surpass-\ning state-of-the-art methods in predictive accuracy on the\nAnti-Cancer Peptides dataset. Moreover, our methodology\nprovides a practical and efficient alternative to computation-\nally demanding Deep Neural Networks (DNNs), proving ef-\nfective even in low-resource environments.\n1 Introduction\nCancer is one of the leading contributors to global mor-\ntality trends [36]. Early and accurate detection of cancer\n*Georgia State University, Atlanta GA, USA\nemail: {sali85, pchourasia1}@student.gsu.edu, mpatterson30@gsu.edu\n†Lahore University of Management Sciences, Lahore, Pakistan\nemail: 20100159@lums.edu.pk\ncan lead to timely treatment and, in turn, can save precious\nhuman lives. Sequence analyses help improve our under-\nstanding of cancer biology, including tumorigenesis, metas-\ntasis, and drug resistance mechanisms, driving further re-\nsearch and innovation in cancer prevention, diagnosis, and\ntreatment [32]. The development of advanced computational\ntechniques leads to the effective use of Anticancer peptides\n(ACPs) in the treatment of cancer. ACPs belong to the an-\ntimicrobial peptide (AMP) group that exhibits anticancer ac-\ntivity [14]. Analyzing ACPs properties identifies potent can-\ndidates for new treatments. Insights into ACP mechanisms\nof action, including cell interaction and immune modulation,\nare crucial for optimizing efficacy and minimizing side ef-\nfects [10]. By analyzing ACPs and understanding their phar-\nmacokinetics (how the body processes them), pharmacody-\nnamics (how they exert their effects), and tissue distribution,\nresearchers can optimize treatment strategies such as dosing\nregimens and combination therapies [14]. The analysis of\nanti-cancer peptides is crucial for advancing our understand-\ning of their therapeutic potential, optimizing their efficacy\nand safety profiles, and ultimately developing effective can-\ncer treatments.\nPerforming underlying ML tasks requires converting\nvariable-length peptide sequences to numerical vectors using\na sequence encoding technique, such as Amino Acid Com-\nposition (AAC) [1] involving frequency vector generation\nand/or di-peptide AAC (DAAC) based on the frequency of\npeptide pairs, etc. As a solution, CKSAAP [13] was pro-\nposed, which concatenates the DAAC feature vectors of K-\nspaced amino acid pairs and has been successfully used in\nAnti Cancer peptide classification tasks [19]. The k-spaced\namino acid group pairs (CKSAAGP) [37] is also used for\nrepresenting ACPs based on the frequency of amino acid\ngroup pairs separated by k residues. However, such meth-\nods either do not generalize on different types of data (e.g.,\ndue to sub-optimal feature selection approach in [1, 13, 37]\nor struggle to capture complex relationships and interactions\nbetween features due to sparse representations [19]) or could\nbe computationally expensive to learn the optimal embed-\nding representations for the ACPs, hence limiting the predic-\ntive performance.\nString kernels are a class of kernel methods that have\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint \n\ngained increasing popularity in biological sequence analysis.\nMany string kernels have been proposed such as spectrum\nkernel, mismatch kernel [29], sparse representation classi-\nfication [19], and local alignment kernel [39]. These string\nkernels have shown promising results in Anti-Cancer Peptide\nclassification for example, an ML method involving Chou’s\npseudo-amino acid composition (PseAAC) and local align-\nment kernel [22] successfully predicted ACPs similarly Ker-\nnel Sparse Representation Classifier [19] was also used in\nACP classification. Although these methods provide accu-\nrate results they could cause an overfitting problem along\nwith scalability issues making them memory intensive.\nDeep Learning, especially Natural Language Processing\nmethods have been used in forming numeric representations\nof antimicrobial peptides for example in [11] the sequence\ninformation is converted into digital vectors using a combi-\nnation of BiLSTM, attention-residual algorithm, and BERT\nEncoder. The transfer learning-based pretrained biological\nlanguage models along with CNN successfully generate anti-\ncancer peptide embeddings [18]. Despite the widespread use\nof these Neural Networks (NNs) and language models, de-\nmand a substantial number of parameters and extended train-\ning times, and are computationally expensive. Moreover,\nthey heavily rely on large-scale training data, often unavail-\nable for certain biological datasets.\nTo address these challenges we propose a novel\ncompression-based approach involving k-mer strategy and\nNLP-based encoding to classify anti-cancer peptides using\nk-mers. Traditional methods, including NNs, predominantly\nfocus on compressing entire sequences, potentially neglect-\ning nuanced neighboring information for individual charac-\nters within a sequence. Inspired by recent advancements in\ncompression-based approaches [26] our innovative method\nintegrates the classical compression algorithm Gzip to com-\npress individual encoded k-mers generated by NLP-based\nembedding and incrementally construct the compression for\nsubsequences, ensuring a meticulous consideration of neigh-\nboring information for each character (Amino Acid). Gzip\nis a lossless data compression technique that gained popu-\nlarity in Computational biology due to its easy integration\nwith biological sequence analysis tools. Some prominent\nCompression-based distances include Normalized Compres-\nsion Distance (NCD) [7], Normalized Information Distance\n(NID) [31], etc. Pairwise NCD is a parameter-free, feature-\nfree, alignment-free, similarity metric based on compression.\nIn our proposed method, we calculate NCD for each k-mer\npair in the sequence data, which is further used to compute\nthe distance matrix. To generate a low-dimensional numeri-\ncal representation, we convert the distance matrix into a ker-\nnel matrix. Our proposed compression-based model not only\novercomes the limitations of existing methods by eliminat-\ning the computational intensity associated with deep neural\nnetworks but also demonstrates efficiency in handling low-\nresource biological datasets where labeled data is scarce.\nThe contributions of our study include:\n1. A novel approach for identifying cancer by analyz-\ning and classifying Anti-Cancer Peptides (ACPs) using\ncompression-based models.\n2. Our innovative approach integrates the classical Gzip\ncompression algorithm with a pioneering k-mers-based\nstrategy. It involves compressing individualk-mers and\nincrementally constructing the compression for subse-\nquences, ensuring a meticulous consideration of neigh-\nboring information of each amino acid in a sequence.\n3. We develop an algorithm for Distance Matrix computa-\ntion, where we take a set of sequences as input and out-\nput a non-symmetric Distance matrix using Normalized\nCompression Distance (NCD) and Gzip compressor.\n4. The proposed compression-based model eliminates the\ncomputational intensity associated with deep neural\nnetworks.\n5. Leveraging Gzip compression, our approach becomes\nparticularly advantageous in scenarios where labeled\ndata is scarce demonstrating efficiency in handling low-\nresource datasets.\n6. Our method addresses limitations observed in prior\nwork related to Anti-Cancer Peptide classification,\nshowcasing its applicability to a broader range of clas-\nsification tasks.\n2 Related Work\nAnti-cancer peptides (ACPs) can be reconstructed or modi-\nfied to increase their anti-cancer activity while lowering cy-\ntotoxicity as demonstrated in [41]. Usually, this entails ACP\nside chain modification and main chain reconstruction [16].\nHowever, this work delves into recent advancements in their\nreconstruction and modification, which is not applicable in\nour case. In another work, ACP\nMS is proposed in [44],\nwhich makes use of the monoMonoKGap technique to ex-\ntract properties from anticancer peptide sequences and cre-\nate digital features. Sequential features or patterns or motifs\nand Physicochemical properties which encompass various\nmolecular properties are used in [24]. The g-gap dipeptide\ncomponents were optimized to create the sequence-based\npredictor known as iACP, which is presented by the au-\nthors of [12]. A lot of research has been conducted on the\nuse of Neural Networks (NNs) in predicting anticancer pep-\ntides, for example, DeepACP a sequence-based deep learn-\ning tool [43], a Long Short-Term Neural Network model [42]\nwith integrated binary profile features and a k-mer sparse\nmatrix of the reduced amino-acid alphabet, convolutional\nneural network-recurrent neural network (CNN-RNN) [43].\nAlthough these NN-based methods exhibit accurate perfor-\nmance, they are computationally expensive.\nNatural Language Processing methods have made a\nsignificant mark in Anti Cancer Peptide (ACPs) classifica-\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint \n\ntion including pre-trained language models such as Protein-\nBERT [25]. In another work [27] Protein-based transform-\ners such as ESM, ProtBert, BioBERT, and SciBERT, have\nshown promising results in identifying ACPs. In a recent\nresearch [2] a FastText-based word embedding method in-\nvolving a skip-gram model has been used to represent each\npeptide for forming the embedding on which a deep neu-\nral network (DNN) model is employed to accurately classify\nthe ACPs. CancerGram [9] uses n-grams and random forests\nfor predicting ACPs. UniRep [30], a Language model-based\nembedding is also used as a feature representation for anti-\ncancer peptides leading to improved ACP prediction. These\nLanguage model-based methods have shown improved clas-\nsification results but have high memory requirements.\n3 Proposed Approach\nOur proposed approach consists of generating embedding\nfor the ACP sequences based on k-mer compression and\nincremental NCD computation. Given a set of Sequences\n(S) we process each pair of these sequences represented as\ns1 and s2 in every iteration ultimately covering all possible\npairs. The overall flow diagram of the proposed method is\nshown in Figure 1. Moreover, the pseudocode of our method\nis given in Algorithm 1.\nWe first compute thek-mers of each sequence as shown\nin step (b) of Figure 1 and the line numbers 10 and 15 of\nAlgorithm 1 for s1 and s2 respectively. This is followed\nby encoding these k-mers using the function Encode in line\nnumbers 11 and 16 which is presented in Algorithm 1 and\nalso shown in step (d) of Figure 1, it takes in a sequence\nin our case k-mer and uses NLP based method involving\ntokenization of k-mers followed by Count Vectorization of\nthe tokens as shown in line number 2 and 3 of Algorithm 2\nto form numerical representation of thek-mers which is then\nflattened in line number 4 of Algorithm 2 and converted into\na string forming the encoded version of k-mers. It can also\nbe noticed in line numbers 11 and 16 of Algorithm 1 and\nincremental stage of step(d) in Figure 1 that the encoded\nforms of k-mers keep adding up in each iteration leading to\nincremental encoding. These incrementally encoded k-mers\nare further compressed using Gzip as shown in Algorithm 3\nand step (e) of Figure 1. This is followed by calculating\nthe lengths of these compressed incrementally encoded k-\nmers in line numbers 13 and 18 for s1 and s2 respectively.\nTo finally calculate the NCD values we need lengths of\ncompressed concatenated sequences. In our algorithm, we\nadopt a unique method for concatenating by first segmenting\nthe s1 and s2 into portions with increased length after\nevery iteration and then concatenate in line number 19 of\nAlgorithm 1, a detailed view of this technique is shown in\nstep (c) of Figure 1 where the black lines show the formation\nof first concatenated fragments for each successive amino\nacid followed by red and blue lines that clearly show the\nincreasing length of the fragments. These concatenated\nsequence fragments, also referred to as sub-sequences are\nfurther encoded as shown in step (d) of Figure 1 but this\ntime without incremental stage as can be seen in line number\n20 of Algorithm 1. Followed by compression and length\ncomputation stages in step(e) and step(f) of Figure 1. We\nthen calculate NCD values using Equation 3.1.\n(3.1) N CD(s1, s2) = L(.) − min{Lks1 , Lks2 }\nmax{Lks1 , Lks2 }\nwhere Lks1 and Lks2 represent the lengths of the com-\npressed incrementally encoded k-mers of sequences s1 and\ns2 respectively, and L(.) denotes the length of the com-\npressed form of the concatenated fragments of sequence s1\nand s2. Finally, the NCD values are aggregated using the\nmean function to obtain a scalar value. These Scalar NCD\nvalues are appended in Distance Matrix (D) in line number\n26 of Algorithm 1. This process is repeated for all pairs of se-\nquences, resulting in the incremental encoding distance ma-\ntrix, which contains the pairwise similarity values between\nsequences.\nAlgorithm 1 Incremental Encoding Distance Matrix\nInput:Set of Sequences (S)\nOutput: Distance Matrix (D)\n1: function INCENCOD DIST MAT(S)\n2: D ← []\n3: k val ← 3 ▷ Length of k-mer\n4: for s1 ← S do\n5: initialize(Eks1 , Cks1 , Lks1 )\n6: D local 1, D local 2 ← []\n7: for s2 ← S do\n8: initialize(Eks2 , Cks2 , Lks2 )\n9: for i ← range (len(s1) - k val + 1) do\n10: kmers1 ← s1[i:i+k val]\n11: Eks1 += ENCODE(kmers1 )\n12: Cks1 ← COMPRESS(Eks1 )\n13: Lks1 ← len(Cks1 )\n14: for j ← range (len(s2) - k val + 1) do\n15: kmers2 ← s2[j:j+k val]\n16: Eks2 += ENCODE(kmers2 )\n17: Cks2 ← COMPRESS(Eks2 )\n18: Lks2 ← len(Cks2 )\n19: concatSeq ← s1[:i+1] + s2[:j+1]\n20: E(.) ← ENCODE(concatSeq)\n21: C(.) ← COMPRESS(E(.))\n22: L(.) ← len(C(.))\n23: NCD ←\nL(.) −min(Lks1 ,Lks2 )\nmax(Lks1 ,Lks2 )\n24: D local 1.append(NCD)\n25: end for\n26: scalar value ← mean(D local 1)\n27: D local 2.append(scalar value)\n28: end for\n29: end for\n30: D.append(D local 2)\n31: end for\n32: return D\n33: end function\nREMARK 1. NCD Lower Bound: NCD values are bounded\nby 0 when two sequences are identical. In this case,\nthe compressed concatenation of the sequences will be\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint \n\nFigure 1: Flow diagram for the proposed approach. The figure is best seen in color.\nAlgorithm 2 Encoding\nInput: Sequence (seq)\nOutput: Encoded Sequence (E)\n1: function ENCODE (seq)\n2: tokens ← Tokenize(seq)\n3: Vector ← CountVectorizer(tokens)\n4: E ← GetString(Vector) ▷ Flatten and convert to string\n5: return E\n6: end function\nAlgorithm 3 Gzip compression\nInput: Encoded Sequence (E)\nOutput: Compressed Sequence (C)\n1: function COMPRESS (E)\n2: C ← Gzip(E) ▷ Encoded to utf-8 then compressed using Gzip\n3: return C\n4: end function\nthe same as the compressed length of each sequence, i.e.\nN CD(s1, s2) = 0 if s1 = s2.\nREMARK 2. NCD Upper Bound: The NCD value is upper-\nbounded by 1 in the case where two sequences are com-\npletely dissimilar, as the compressed concatenated sequence\nwill not provide any significant compression advantage, i.e.\nN CD(s1, s2) ≤ 1.\nREMARK 3. Compression Efficiency Guarantees: The pro-\nposed algorithm’s performance depends on the efficiency of\nthe compression algorithm (i.e. Gzip). Some key properties\nto note are the following:\n1. Optimality in Compression: The Gzip compression\nalgorithm ensures that common substrings or patterns\nwithin a sequence or concatenation are compressed\nefficiently, leading to shorter compressed lengths.\n2. Monotonicity of Compression: The compression length\nfor the concatenation of two sequences s1 + s2 will\nnever exceed the sum of their individual compressed\nlengths, i.e. L(s1 + s2) ≤ L(s1) + L(s2).\nThis ensures that the NCD is always well-defined.\nREMARK 4. Incremental Encoding Stability: The incre-\nmental encoding approach adds k-mers to the existing se-\nquence encoding. To ensure the stability of the algorithm,\nwe can say the following:\n1. Monotonic Growth in Encoding: The length of the\nencoded sequence grows monotonically as k-mers are\nadded, which means the size of the encoded sequence\nafter each iteration will never decrease. This guaran-\ntees that the compression length also grows or remains\nconstant.\n2. Asymptotic Compression Convergence: As the k-mer\nsequences are incrementally encoded and compressed,\nthe compression lengths for large enough sequences\nshould converge to a stable value, reflecting the overall\nsequence similarity.\n3.1 Distance Matrix Symmetry The Distance matrix (D)\nobtained is of size n × n, where n represents the number of\nsequences in set S. Note that D is non-symmetric, so we\nconvert it into a symmetric matrix by taking the average of\nupper and lower triangle values and replacing the original\nvalues of the matrix with the average values.\n3.2 Kernel Matrix Computation Then we generate a\nKernel matrix from the symmetric distance matrix using a\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint \n\nGaussian Kernel. First, we calculate Euclidean Distance\n(W ) between two pairs of distances using the equation:\n(3.2) Wblm,blt = ||blm − blt||\nwhere blm and blt represent any two values of the symmetric\nDistance matrix.\nThe Gaussian Kernel (G) is defined as a measure of\nsimilarity between blm and blt :\n(3.3) G(blm, blt) = exp( −Wblm,blt\n2\nσ2 )\nwhere σ2 represents the bandwidth of the kernel.\nThe kernel value is computed for each pair of distances\nin the symmetric distance matrix to get n × n dimensional\nkernel matrix using the following theory:\n(\nG = 1, if blm and blt are identical\nG − →0, b lm and blt move further apart\nAfter computing the kernel matrix, we apply ker-\nnel Principal Component Analysis (PCA) to get a lower-\ndimensional embedding of the data. It preserves the es-\nsential information while retaining the relationships among\nthe anti-cancer peptide sequences, including non-linear rela-\ntions. This representation proves valuable for various tasks,\nincluding classification.\n4 Experimental Setup\nThis section outlines the experimental setup, including de-\ntails on the dataset, visualization techniques, baseline mod-\nels, and metrics used for evaluation. All experiments were\nconducted on a computing system equipped with an In-\ntel(R) Xeon(R) CPU E7-4850 v4 running at a clock speed\nof 2.10GHz and operating on a 64-bit Ubuntu OS (version\n16.04.7 LTS Xenial Xerus), with a total memory capacity of\n3023 GB. The algorithms were implemented using Python.\nThe dataset was partitioned into training and testing sets us-\ning a 70 − 30% split ratio. To account for variability, experi-\nments were conducted with5 different random initializations\nfor the train-test splits, and the results reported include both\naverage values and standard deviations. For hyperparameter\ntuning, a 5-fold cross-validation strategy was employed.\n4.1 Dataset Statistics The dataset on Membranolytic anti-\ncancer peptides (ACPs) [21] provides details regarding pep-\ntide sequences and their corresponding anticancer effective-\nness against breast and lung cancer cell lines. The target\nlabels are classified into four groups: “very active,” “moder-\nately active,” “experimental inactive,” and “virtual inactive.”\nIn total, the dataset comprises 949 and 901 peptide sequences\nfor breast and lung cancer, respectively. Table 1 shows the\ndistribution.\nA\nCPs Category Count Min. Max. Average\nInacti\nve-Virtual 750 8 30 16.64\nModerate Active 98 10 38 18.44\nInactive-Experimental 83 5 38 15.02\nVery Active 18 13 28 19.33\nT\notal 949 - - -\nBreast cancer data\nA\nCPs Category Count Min. Max. Average\nInacti\nve-Virtual 750 8 30 16.64\nModerate Active 75 11 38 17.76\nInactive-Experimental 52 5 38 14.5\nVery Active 24 13 28 20.70\nT\notal 901 - - -\nLung cancer data\nTable 1: Dataset statistics for the Breast cancer and Lung\ncancer data. Columns represent the min., max., and average\nlengths of the peptide sequence.\n4.2 Data Visualization A widely used visualization tech-\nnique, namely t-stochastic distributed neighborhood embed-\nding (t-SNE) [15, 38], is employed to visualize the feature\nvectors from different embedding methods. The t-SNE plots\nare presented in Figure 2 and Figure 3 (in the appendix) for\nBreast Cancer and Lung Cancer, respectively. These plots\nshowcase the distribution and grouping patterns of the em-\nbeddings and facilitate the qualitative assessment of how\nwell the embeddings capture the inherent structure and re-\nlationships within the data. We can observe in Figure 2 that\nthe proposed k-mers compression-based method can group\nsimilar classes reasonably well.\n4.3 Baseline Models Detail We selected the baseline and\nstate-of-the-art (SOTA) methods that represent different cat-\negories of sequence classification. These categories in-\nclude feature engineering, kernel methods, neural networks,\nand pre-trained large language models. The feature engi-\nneering approache include One-Hot encoding (OHE) [28],\nSpike2Vec [4], Minimizers [20], Spaced k-mer [35], and\nPWM2Vec [5]. The kernel method includes String kernel [6]\nand Sinkhorn-Knopp Algorithm [3]. The neural network\nmethods include WDGRL [34] and AutoEncoder [40]. Fi-\nnally, the pre-trained large language models (LLMs) include\nSeqVec [23], Protein Bert [8], and TAPE [33]. Each method\nis summarized in Table 2.\n4.4 Evaluation Metrics And Classifiers For classifica-\ntion tasks, we employ several classifiers including Support\nVector Machine (SVM), Naive Bayes (NB), Multi-Layer\nPerceptron (MLP), K-Nearest Neighbors (KNN) withK = 5\n(selected through the standard validation set approach [17]),\nRandom Forest (RF), and Logistic Regression (LR). To as-\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint \n\n(a) OHE\n (b) Spike2Vec\n (c) Minimizer\n (d) Spaced k-mer\n (e) PWM2Vec\n(f) String kernel\n (g) WDGRL\n (h) AutoEncoder\n (i) SeqVec\n (j) Ours\nFigure 2: t-SNE plots for (Breast Cancer Data) for different structure embeddings. The figure is best seen in color.\nMethod\nDescription Source\nOHE\nThis\nmethod is introduced for generating fixed-length nu-\nmerical feature vectors. It creates a binary vector (0-1) by\nassigning positions to characters in the sequence.\n[28]\nSpik\ne2Vec\nThis approach utilizes the concept of k-mers to generate\nnumerical embeddings. k-mers are contiguous substrings\nof length k derived from a spike sequence.\n[4]\nMinimizer\nThe\nminimizer-based feature vector approach involves\ncomputing a ”minimizer” of length m (where m < k )\nfor a given k-mer. This ”m-mer” is the lexicographically\nsmallest in both forward and reverse order of the k-mer.\n[20]\nSpaced\nK-mers\nSpaced k-mers, also known as g-mers, represent non-\ncontiguous substrings of length k, resulting in smaller and\nless sparse feature vectors.\n[35]\nPWM2V\nec This method takes a biological sequence as input and\ngenerates fixed-length numerical embeddings. [5]\nString\nKernel\nThis approach designs an n × n kernel matrix that can be\nused with kernel classifiers or kernel PCA to obtain feature\nvectors based on principal components.\n[6]\nWDGRL\nWDGRL\naims to optimize the network by minimizing the\nWasserstein distance (WD) between the source and target\nnetworks. The input is one-hot encoded (OHE) vectors, and\nit produces the corresponding embeddings\n[34]\nAutoEncoder The\nautoencoder technique leverages an encoder-decoder\narchitecture to derive feature embeddings. [40]\nSeqV\nec\nA large language model (LLM) that takes biological se-\nquences as input and fine-tunes the weights based on a pre-\ntrained model to obtain the final embeddings.\n[23]\nProteinBER\nT\nThis is a pre-trained LLM protein sequence model that\nutilizes the Transformer/Bert architecture to classify the\ngiven biological sequences.\n[8]\nT\nAPE\nTAPE is a semi-supervised LLM, protein representation\nlearning method that works by training a protein large lan-\nguage model and then generating numerical embeddings.\n[33]\nSKA\nThe\nSinkhorn-Knopp Algorithm (SKA) uses the idea of\ngenerating a kernel matrix using the Sinkhorn-Knopp ap-\nproach, which can then be used with kernel PCA to gener-\nate low-dimensional embeddings.\n[3]\nTable 2: Description of different baseline models.\nsess the effectiveness, we utilize a range of evaluation met-\nrics, including average accuracy, precision, recall, weighted\nmetrics, and the area under the Receiver Operating Charac-\nteristic (ROC) curve (AUC).\n5 Results And Discussion\nWe discuss the results of the proposed method and its com-\nparisons with the baselines and SOTA in this section.\n5.1 Classification Results The classification results aver-\naged over 5 runs for both datasets are reported in Table 3\nand 4. Breast Cancer classification results show our pro-\nposed Gzip-based representation outperformed all baselines\naccording to accuracy, precision, recall, weighted F1 score,\nand ROC-AUC. Even after fine-tuning the Large language\nmodels (LLM) such as SeqVec, Protein Bert, and TAPE, the\nproposed parameter-free method significantly outperforms\nthe LLMs for all evaluation metrics. TAPE has better ROC-\nAUC but it is very marginal and for other metrics our pro-\nposed method still outperforms. For classification training\nruntime, WDGRL with Naive Bayes performs the best due\nto the smaller embedding size. We observe similar results for\nLung Cancer classification, where our Gzip-based method\noutperforms all baselines in the majority of the metrics ex-\ncept for ROC-AUC and F1 Macro score.\n5.2 Class-Wise Analysis Using Heatmaps We employ\nheat maps to delve deeper into the effectiveness of our pro-\nposed approach in distinguishing between various classes.\nThese maps are created by initially calculating the pairwise\ncosine similarity between embeddings of different classes\nand then averaging the similarity values to derive a singu-\nlar value for each class pair. Heatmaps are shown in Figure 4\nand Figure 5 (in the appendix) for Breast Cancer and Lung\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint \n\nEmbedding\nMethod\nML\nAlgo. Acc. ↑ Prec. ↑ Recall ↑\nF1\n(W\neig.)\n↑\nF1\n(Macro)\n↑\nROC\nAUC\n↑\nTraining\nTime\n(sec.) ↓OHE\nSVM\n0.882 0.883 0.882\n0.880 0.568 0.764 0.247\nNB\n0.844 0.842 0.844 0.834 0.451 0.686 0.028\nMLP\n0.849 0.868 0.849 0.857 0.521 0.742 7.933\nKNN 0.609 0.853 0.609 0.676 0.395 0.678 0.069\nRF 0.880 0.864 0.880 0.867 0.554 0.726 0.720\nLR 0.888\n0.880\n0.888 0.881 0.575 0.755\n0.052\nSpik\ne2Vec\nSVM 0.878 0.870 0.878 0.868 0.534 0.727 8.342\nNB 0.855 0.844 0.855 0.842 0.470 0.695 0.181\nMLP 0.756 0.834 0.756 0.788 0.441 0.700 27.214\nKNN 0.241 0.298 0.241 0.212 0.200 0.550 0.133\nRF\n0.893 0.885 0.893 0.883 0.606 0.752 1.812\nLR\n0.890 0.876 0.890 0.878 0.557 0.733 0.092\nMinimizer\nSVM\n0.773 0.808 0.773 0.784 0.424 0.668 3.788\nNB 0.733 0.806 0.733 0.762 0.355 0.653 0.315\nMLP 0.766 0.822 0.766 0.788 0.441 0.689 28.805\nKNN 0.577 0.807 0.577 0.635 0.332 0.616 0.149\nRF 0.731 0.817 0.731 0.761 0.410 0.660 2.832\nLR 0.843\n0.836 0.843 0.833 0.483 0.690 0.109\nSpaced\nk-mer\nSVM\n0.865 0.842 0.865 0.845 0.465 0.674 127.502\nNB 0.469 0.865 0.469\n0.599 0.359 0.607 4.302\nMLP 0.420 0.851 0.420 0.497 0.341 0.624 204.755\nKNN 0.276 0.460 0.276 0.253 0.216 0.559 1.036\nRF\n0.348 0.864 0.348 0.363 0.304 0.598 38.087\nLR 0.869 0.848\n0.869 0.851 0.480 0.682 1.445\nPWM2V\nec\nSVM 0.804 0.834 0.804 0.811 0.434 0.687 132.720\nNB 0.826 0.846 0.826 0.823 0.408 0.670 0.887\nMLP 0.764 0.841 0.764 0.791 0.462 0.720 36.824\nKNN\n0.199 0.808 0.199 0.221 0.190 0.541 0.618\nRF\n0.754 0.857 0.754\n0.788 0.460 0.717 6.479\nLR 0.839 0.819\n0.839 0.824 0.434\n0.670 16.056\nString\nK\nernel\nSVM 0.808 0.865 0.808 0.829 0.503 0.730 0.316\nNB 0.874 0.880 0.874 0.873\n0.545 0.746 0.011\nMLP\n0.634 0.789 0.634 0.684 0.358 0.648 5.259\nKNN 0.881 0.860\n0.881 0.862\n0.494 0.705 0.030\nRF 0.879 0.862 0.879\n0.861 0.498 0.697 1.133\nLR 0.790 0.843 0.790 0.812 0.464 0.707 0.398\nWDGRL\nSVM\n0.804 0.646 0.804 0.716 0.223 0.500 0.026\nNB 0.779 0.718 0.779 0.735 0.305 0.535 0.002\nMLP\n0.778 0.714 0.778 0.735 0.301 0.536 3.588\nKNN\n0.794 0.715 0.794 0.730 0.270 0.518 0.016\nRF 0.667 0.689 0.667 0.672 0.301 0.532 0.021\nLR 0.818\n0.825 0.818 0.749 0.301\n0.531 0.006\nAuto-\nEncoder\nSVM\n0.816 0.813 0.816 0.813 0.443 0.678 0.109\nNB 0.735 0.754 0.735 0.738 0.360 0.630 0.009\nMLP\n0.806 0.808 0.806 0.806 0.451 0.675 15.740\nKNN 0.832 0.802 0.832 0.804 0.431 0.645 0.067\nRF 0.846\n0.805\n0.846 0.817\n0.439 0.648 2.210\nLR 0.834 0.820 0.834\n0.826 0.464 0.684 0.693\nSeqV\nec\nSVM 0.886 0.881 0.886\n0.882 0.531\n0.735 80.105\nNB 0.625 0.757 0.625 0.665 0.244 0.607 4.691\nMLP\n0.848 0.872 0.848 0.856 0.516 0.743 160.886\nKNN\n0.674 0.819 0.674 0.725 0.389 0.651 22.253\nRF 0.887 0.874\n0.887 0.876\n0.551 0.725\n11.360\nLR 0.769 0.872 0.769 0.813 0.465 0.725 1816.404\nProtein\nBert 0.893\n0.893 0.893 0.893 0.602 0.779 64.849\nT\nAPE\nSVM 0.890 0.892 0.890 0.890 0.579 0.774 0.042\nNB 0.859 0.888 0.859 0.870 0.584 0.795\n0.022\nMLP\n0.886 0.893 0.886 0.889 0.592 0.781\n0.926\nKNN 0.886 0.875 0.886 0.879 0.551 0.745 0.021\nRF\n0.885 0.863 0.885 0.871 0.523 0.724 3.141\nLR 0.893 0.894 0.893 0.894 0.592 0.778\n0.530\nSKA\nSVM\n0.840 0.808 0.840 0.799 0.425 0.613 0.347\nNB 0.884 0.881 0.884 0.873 0.547 0.752 0.011\nMLP\n0.542 0.681 0.542 0.588 0.280 0.545 11.433\nKNN 0.236 0.226 0.236 0.213 0.199 0.546 0.080\nRF 0.875 0.848 0.875 0.858 0.483 0.708 1.412\nLR 0.793 0.629 0.793 0.702 0.221 0.500 0.084\nOurs\nSVM\n0.783 0.614 0.783 0.688 0.220 0.500 0.247\nNB 0.587 0.880 0.587 0.694 0.453 0.679 0.018\nMLP 0.752 0.662 0.752 0.696 0.263 0.518 2.201\nKNN 0.783 0.614 0.783 0.688 0.220 0.500 0.271\nRF 0.915 0.910 0.915 0.910 0.579 0.784 0.728\nLR\n0.783 0.614 0.783 0.688 0.220 0.500 0.055\nTable 3: Average classification results for Breast Cancer\ndataset. The best values for each metric are underlined.\nOverall best values are shown in bold\nCancer data, respectively. These figures show the inter-class\nand intra-class similarity. The light color diagonals in all fig-\nEmbedding\nMethod\nML\nAlgo. Acc. ↑ Prec. ↑ Recall ↑\nF1\n(W\neig.)\n↑\nF1\n(Macro)\n↑\nROC\nAUC\n↑\nTraining\nTime\n(sec.) ↓\nOHE\nSVM\n0.917 0.922 0.917\n0.917 0.639\n0.808 0.142\nNB\n0.904 0.899 0.904 0.896 0.585 0.742 0.022\nMLP\n0.864 0.894 0.864 0.876 0.573 0.784 15.337\nKNN 0.804 0.907 0.804 0.835 0.537 0.781 0.117\nRF 0.921 0.916\n0.921 0.913\n0.667 0.778\n0.457\nLR 0.895 0.909 0.895 0.900 0.629 0.805 0.637\nSpik\ne2Vec\nSVM 0.893 0.888 0.893 0.884 0.546 0.734 218.389\nNB 0.894 0.884 0.894 0.881 0.571 0.731 0.498\nMLP\n0.834 0.889 0.834 0.854 0.554 0.773 70.784\nKNN 0.877 0.919 0.877\n0.883 0.590 0.790 0.590\nRF\n0.918 0.914\n0.918 0.912 0.657 0.789\n3.141\nLR 0.897 0.905 0.897 0.899 0.587 0.786 19.848\nMinimizer\nSVM\n0.832 0.851 0.832 0.837 0.508 0.711 65.717\nNB 0.821 0.860 0.821 0.832 0.532 0.765 0.632\nMLP\n0.835 0.870 0.835 0.847 0.565 0.767 110.362\nKNN\n0.858 0.835 0.858 0.840 0.455 0.681 0.837\nRF 0.872 0.871 0.872 0.865 0.546\n0.723 8.444\nLR 0.861 0.862 0.861 0.858 0.562 0.735 6.078\nSpaced\nk-mer\nSVM\n0.886 0.874 0.886 0.871 0.540 0.706 210.539\nNB 0.506 0.862 0.506 0.604 0.441 0.706 43.705\nMLP 0.846 0.882 0.846 0.856 0.556 0.752 2567.545\nKNN 0.883 0.871 0.883 0.862 0.530 0.699 21.594\nRF\n0.796 0.887 0.796 0.804 0.550 0.727 317.588\nLR 0.900 0.895 0.900 0.890 0.590 0.756 56.141\nPWM2V\nec\nSVM 0.853 0.864 0.853 0.852 0.544 0.738 105.862\nNB 0.886 0.891 0.886 0.880 0.539\n0.743 1.328\nMLP 0.790 0.845 0.790 0.811 0.487 0.725 119.903\nKNN 0.452 0.842 0.452 0.511 0.335 0.614 0.931\nRF\n0.878 0.885 0.878 0.878 0.578 0.761 14.993\nLR\n0.877 0.871 0.877 0.870 0.584 0.736\n26.217\nString\nK\nernel\nSVM 0.867 0.884 0.867 0.871 0.519 0.731 0.203\nNB 0.889 0.903 0.889 0.889 0.561 0.761\n0.009\nMLP\n0.647 0.823 0.647 0.709 0.378 0.658 5.243\nKNN 0.909 0.906 0.909 0.899 0.592 0.752\n0.035\nRF 0.878 0.834 0.878 0.851 0.424 0.638 0.900\nLR 0.874 0.886 0.874 0.878 0.566 0.757 0.290WDGRL\nSVM\n0.843 0.729 0.843 0.775 0.259 0.514 0.062\nNB 0.125 0.738 0.125 0.126 0.115 0.525 0.005\nMLP\n0.831 0.799 0.831 0.813 0.363 0.598 7.815\nKNN\n0.862 0.820 0.862 0.822\n0.360 0.583 0.050\nRF 0.858 0.812 0.858 0.823 0.366 0.587\n0.968\nLR 0.849 0.769 0.849 0.789 0.301 0.536 0.021\nAuto-\nEncoder\nSVM\n0.911 0.918 0.911 0.912 0.619 0.800 0.078\nNB 0.870 0.887 0.870 0.871 0.560 0.780 0.012\nMLP\n0.910 0.920 0.910 0.911 0.603 0.799 5.965\nKNN 0.910 0.908 0.910 0.906 0.602 0.771 0.090\nRF 0.917\n0.912\n0.917 0.913\n0.627 0.780 1.303\nLR 0.917 0.921 0.917 0.918 0.629 0.806 0.933\nSeqV\nec\nSVM 0.927 0.925 0.927 0.923 0.689 0.822\n159.204\nNB 0.361 0.800 0.361 0.366 0.183 0.587 5.130\nMLP\n0.897 0.896 0.897 0.894 0.621 0.792 264.274\nKNN 0.886 0.882 0.886 0.878 0.604 0.761 33.326\nRF 0.912 0.906 0.912 0.902 0.660 0.774 11.063\nLR 0.789 0.900 0.789 0.828 0.566 0.829\n1635.13\nProtein\nBert 0.923\n0.936 0.923 0.923 0.639 0.803 63.599\nT\nAPE\nSVM 0.900 0.903 0.900 0.900 0.602 0.782 0.045\nNB 0.893 0.911 0.893 0.898 0.639 0.823\n0.032\nMLP\n0.902 0.908 0.902 0.903 0.636 0.800 1.274\nKNN 0.906 0.915 0.906 0.906 0.637 0.797 0.091\nRF 0.897 0.886 0.897 0.884 0.574 0.731 3.199\nLR 0.913\n0.920 0.913 0.912 0.655 0.802\n0.521\nSKA\nSVM\n0.852 0.889 0.852 0.864 0.510 0.727 0.155\nNB 0.886 0.901 0.886\n0.888 0.580 0.771 0.019\nMLP\n0.680 0.826 0.680 0.735 0.378 0.662 1.475\nKNN 0.907 0.896\n0.907 0.894 0.536\n0.732 0.012\nRF\n0.890 0.858 0.890 0.865 0.471 0.665 2.973\nLR 0.842 0.709 0.842 0.770 0.229 0.500 0.064\nOurs\nSVM\n0.830 0.688 0.830 0.752 0.227 0.500 0.042\nNB 0.573 0.863 0.573 0.659 0.392 0.722 0.007\nMLP 0.788 0.710 0.788 0.744 0.248 0.508 5.629\nKNN 0.830 0.688 0.830 0.752 0.227 0.500 0.038\nRF 0.931\n0.938 0.931 0.932 0.661 0.827 0.636\nLR\n0.830 0.688 0.830 0.752 0.227 0.500 0.048\nTable 4: Average classification results for Lung Cancer\ndataset. The best values for each metric are underlined.\nOverall best values are shown in bold\nures show a high positive intra-class similarity, depicting a\nstrong resemblance of the ACP sequences belonging to the\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint \n\nsame category. The portions other than the diagonals in the\nheatmap represent inter-class similarity. The heatmaps for\nthe proposed k-mer compression-based method are given in\nFigure 4j and Figure 5j. It can be observed that the similar-\nity between different classes is very low, showing that our\nproposed embedding differentiates between classes. While\nthe heatmaps for baselines, especially WDGRL and SeqVec,\nshown in Figure (4g-4i) and Figure (5g-5i) mostly have pos-\nitive high similarity between all the classes showing zero to\nvery weak differentiation between different classes of ACPs\nin the embedding feature space as they are very close to each\nother.\n5.3 Class-Wise Analysis Using Bar Plots We use bar\nplots to analyze the values in different embeddings and com-\npute their kernel values to observe which ones have better\nclass-wise separations. An example of a pair of embeddings\n(using the Spike2Vec approach) belonging to the same class\nand a pair of embeddings belonging to a different class is\nshown in Figure 6 for randomly selected pairs for the breast\ncancer dataset (in the appendix). In Figure 6 (a) and (b),\nwe can observe the Spike2Vec-based k-mers spectrum for\nthe “mod. active” label. As they belong to the same class,\nwe expect the pairwise Gaussian kernel value to be as big\nas possible. The Gaussian kernel value for Figure 6 (a)\nand (b) is 0.98412732 using k-mers spectrum embedding,\nwhile for our proposed k-mer Compression-based embed-\nding, the Gaussian kernel value is 0.99999999, hence show-\ning that the proposed method captures the similarity among\nsame class better. Similarly, Figure 6 (c) and (d) represent\nk-mers spectrum embeddings for different classes (selected\nrandomly), and we can expect the Gaussian kernel value to\nbe smaller, which we observed in the case of the proposedk-\nmers compression-based approach compared to Spike2Vec-\nbased k-mers spectrum.\nFor the Lung cancer ACP dataset, we can observe sim-\nilar behavior in Figure 7 (in the appendix). The Gaussian\nkernel value for Figure 7 (a) and (b), which represents the\nlabel “very active”, is 0.9884221 for Spike2Vec, while for\nk-mer Compression, it is 0.9999999 (larger value is better).\nSimilarly, the Gaussian kernel value for Figure 7 (c) and\n(d) is 0.9999060 for Spike2Vec, which represents the label\n“inactive-exp” and “very active”, while for the k-mer Com-\npression, the Gaussian kernel value is0.99989160 (a smaller\nkernel value is better). This behavior also shows that the em-\nbeddings generated using the proposed k-mers compression-\nbased approach better show the inter-class-based separations\nand intra-class-based closeness.\n5.4 Statistical Significance We conducted a student t-test,\nthe p-values were derived from the average and standard\ndeviations obtained from five independent random runs. It\nis noteworthy that all computed p-values were below 0.05,\nindicating the statistical significance of the results. This\nobservation can be attributed to the generally low standard\ndeviation (SD) values across the data. The SD results for\nbreast cancer and lung cancer datasets are in Table 5 and\nTable 6 (in the appendix), respectively. We can observe that\nthe SD values of our method and most of the baselines are\nvery small, which shows that the results are stable.\nFrom the overall average and SD results, we can see\nthat our method outperforms the SOTA for predictive per-\nformance on the real-world Anti-Cancer Peptides (ACPs)\nsequence datasets. The results demonstrate the effective-\nness of our Gzip-based representation method over various\nbaselines across multiple evaluation metrics. This superi-\nority is particularly notable in terms of accuracy, precision,\nrecall, weighted F1 score, and ROC-AUC. Such consistent\noutperformance indicates the robustness and reliability of\nour approach across different classification tasks. Despite\nfine-tuning large language models (LLMs) like SeqVec and\nProtein Bert, our parameter-free method outperforms them\nacross all evaluation metrics. This observation is particularly\nintriguing given the complexity and expressiveness of LLMs,\nsuggesting that domain-specific representations, such as the\nGzip-based method proposed, can provide more tailored and\neffective solutions for sequence analysis. Also, it can help bi-\nologists better understand Cancer Biology and come up with\nimproved cancer prediction and treatment methods.\nWhile the proposed method excels in classification ac-\ncuracy, computational efficiency is crucial for large-scale ap-\nplications. Despite competitive performance, methods like\nSeqVec and Spacedk-mers may require more computational\nresources, posing practical limitations. Class-wise similar-\nity plots reveal strong intra-class similarities and low inter-\nclass similarities, indicating effective differentiation and val-\nidating the discriminative power of the proposed embedding\nmethod. These promising results open up avenues for its ap-\nplication in various bioinformatics and medical domains be-\nyond cancer classification. Such as facilitating the develop-\nment of diagnostic tools, drug discovery pipelines, and per-\nsonalized medicine approaches.\n6 Conclusion\nWe propose a lightweight and efficient compression-based\nmethod involving k-mer strategy and NLP-based encoding\nfor classifying Anti-Cancer Peptide sequences. Our method\nachieves SOTA performance without the need for parameter\ntuning or pre-trained models. 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