Compression andk-mer based Approach For Anticancer Peptide Analysis

Our research delves into the imperative realm of anti-cancer peptide sequence analysis, an essential domain for biologi- cal researchers. Presently, neural network-based methodolo- gies, while exhibiting precision, encounter challenges with a substantial parameter count and extensive data requirements. The recently proposed method to compute the pairwise dis- tance between the sequences using the compression-based approach [26] focuses on compressing entire sequences, po- tentially overlooking intricate neighboring information for individual characters (i.e., amino acids in the case of protein and nucleotide in the case of nucleotide) within a sequence. The importance of neighboring information lies in its ability to provide context and enhance understanding at a finer level within the sequences being analyzed. Our study advocates an innovative paradigm, where we integrate classical com- pression algorithms, such as Gzip, with a pioneeringk-mers- based strategy in an incremental fashion. Diverging from conventional techniques, our method entails compressing in- dividual k-mers and incrementally constructing the compres- sion for subsequences, ensuring more careful consideration of neighboring information for each character. Our pro- posed method improves classification performance without necessitating custom features or pre-trained models. Our ap- proach unifies compression, Normalized Compression Dis- tance, and k-mers-based techniques to generate embeddings, which are then used for classification. This synergy facili- tates a nuanced understanding of cancer sequences, surpass- ing state-of-the-art methods in predictive accuracy on the Anti-Cancer Peptides dataset. Moreover, our methodology provides a practical and efficient alternative to computation- ally demanding Deep Neural Networks (DNNs), proving ef- fective even in low-resource environments. 1 Introduction Cancer is one of the leading contributors to global mor- tality trends [36]. Early and accurate detection of cancer *Georgia State University, Atlanta GA, USA email: {sali85, pchourasia1}@student.gsu.edu, [email protected] †Lahore University of Management Sciences, Lahore, Pakistan email: [email protected] can lead to timely treatment and, in turn, can save precious human lives. Sequence analyses help improve our under- standing of cancer biology, including tumorigenesis, metas- tasis, and drug resistance mechanisms, driving further re- search and innovation in cancer prevention, diagnosis, and treatment [32]. The development of advanced computational techniques leads to the effective use of Anticancer peptides (ACPs) in the treatment of cancer. ACPs belong to the an- timicrobial peptide (AMP) group that exhibits anticancer ac- tivity [14]. Analyzing ACPs properties identifies potent can- didates for new treatments. Insights into ACP mechanisms of action, including cell interaction and immune modulation, are crucial for optimizing efficacy and minimizing side ef- fects [10]. By analyzing ACPs and understanding their phar- macokinetics (how the body processes them), pharmacody- namics (how they exert their effects), and tissue distribution, researchers can optimize treatment strategies such as dosing regimens and combination therapies [14]. The analysis of anti-cancer peptides is crucial for advancing our understand- ing of their therapeutic potential, optimizing their efficacy and safety profiles, and ultimately developing effective can- cer treatments. Performing underlying ML tasks requires converting variable-length peptide sequences to numerical vectors using a sequence encoding technique, such as Amino Acid Com- position (AAC) [1] involving frequency vector generation and/or di-peptide AAC (DAAC) based on the frequency of peptide pairs, etc. As a solution, CKSAAP [13] was pro- posed, which concatenates the DAAC feature vectors of K- spaced amino acid pairs and has been successfully used in Anti Cancer peptide classification tasks [19]. The k-spaced amino acid group pairs (CKSAAGP) [37] is also used for representing ACPs based on the frequency of amino acid group pairs separated by k residues. However, such meth- ods either do not generalize on different types of data (e.g., due to sub-optimal feature selection approach in [1, 13, 37] or struggle to capture complex relationships and interactions between features due to sparse representations [19]) or could be computationally expensive to learn the optimal embed- ding representations for the ACPs, hence limiting the predic- tive performance. String kernels are a class of kernel methods that have .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint gained increasing popularity in biological sequence analysis. Many string kernels have been proposed such as spectrum kernel, mismatch kernel [29], sparse representation classi- fication [19], and local alignment kernel [39]. These string kernels have shown promising results in Anti-Cancer Peptide classification for example, an ML method involving Chou’s pseudo-amino acid composition (PseAAC) and local align- ment kernel [22] successfully predicted ACPs similarly Ker- nel Sparse Representation Classifier [19] was also used in ACP classification. Although these methods provide accu- rate results they could cause an overfitting problem along with scalability issues making them memory intensive. Deep Learning, especially Natural Language Processing

have been used in forming numeric representations of antimicrobial peptides for example in [11] the sequence information is converted into digital vectors using a combi- nation of BiLSTM, attention-residual algorithm, and BERT Encoder. The transfer learning-based pretrained biological language models along with CNN successfully generate anti- cancer peptide embeddings [18]. Despite the widespread use of these Neural Networks (NNs) and language models, de- mand a substantial number of parameters and extended train- ing times, and are computationally expensive. Moreover, they heavily rely on large-scale training data, often unavail- able for certain biological datasets. To address these challenges we propose a novel compression-based approach involving k-mer strategy and NLP-based encoding to classify anti-cancer peptides using k-mers. Traditional methods, including NNs, predominantly focus on compressing entire sequences, potentially neglect- ing nuanced neighboring information for individual charac- ters within a sequence. Inspired by recent advancements in compression-based approaches [26] our innovative method integrates the classical compression algorithm Gzip to com- press individual encoded k-mers generated by NLP-based embedding and incrementally construct the compression for subsequences, ensuring a meticulous consideration of neigh- boring information for each character (Amino Acid). Gzip is a lossless data compression technique that gained popu- larity in Computational biology due to its easy integration with biological sequence analysis tools. Some prominent Compression-based distances include Normalized Compres- sion Distance (NCD) [7], Normalized Information Distance (NID) [31], etc. Pairwise NCD is a parameter-free, feature- free, alignment-free, similarity metric based on compression. In our proposed method, we calculate NCD for each k-mer pair in the sequence data, which is further used to compute the distance matrix. To generate a low-dimensional numeri- cal representation, we convert the distance matrix into a ker- nel matrix. Our proposed compression-based model not only overcomes the limitations of existing methods by eliminat- ing the computational intensity associated with deep neural networks but also demonstrates efficiency in handling low- resource biological datasets where labeled data is scarce. The contributions of our study include: 1. A novel approach for identifying cancer by analyz- ing and classifying Anti-Cancer Peptides (ACPs) using compression-based models. 2. Our innovative approach integrates the classical Gzip compression algorithm with a pioneering k-mers-based strategy. It involves compressing individualk-mers and incrementally constructing the compression for subse- quences, ensuring a meticulous consideration of neigh- boring information of each amino acid in a sequence. 3. We develop an algorithm for Distance Matrix computa- tion, where we take a set of sequences as input and out- put a non-symmetric Distance matrix using Normalized Compression Distance (NCD) and Gzip compressor. 4. The proposed compression-based model eliminates the computational intensity associated with deep neural networks. 5. Leveraging Gzip compression, our approach becomes particularly advantageous in scenarios where labeled data is scarce demonstrating efficiency in handling low- resource datasets. 6. Our method addresses limitations observed in prior work related to Anti-Cancer Peptide classification, showcasing its applicability to a broader range of clas- sification tasks. 2 Related Work Anti-cancer peptides (ACPs) can be reconstructed or modi- fied to increase their anti-cancer activity while lowering cy- totoxicity as demonstrated in [41]. Usually, this entails ACP side chain modification and main chain reconstruction [16]. However, this work delves into recent advancements in their reconstruction and modification, which is not applicable in our case. In another work, ACP MS is proposed in [44], which makes use of the monoMonoKGap technique to ex- tract properties from anticancer peptide sequences and cre- ate digital features. Sequential features or patterns or motifs and Physicochemical properties which encompass various molecular properties are used in [24]. The g-gap dipeptide components were optimized to create the sequence-based predictor known as iACP, which is presented by the au- thors of [12]. A lot of research has been conducted on the use of Neural Networks (NNs) in predicting anticancer pep- tides, for example, DeepACP a sequence-based deep learn- ing tool [43], a Long Short-Term Neural Network model [42] with integrated binary profile features and a k-mer sparse matrix of the reduced amino-acid alphabet, convolutional neural network-recurrent neural network (CNN-RNN) [43]. Although these NN-based methods exhibit accurate perfor- mance, they are computationally expensive. Natural Language Processing methods have made a significant mark in Anti Cancer Peptide (ACPs) classifica- .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint tion including pre-trained language models such as Protein- BERT [25]. In another work [27] Protein-based transform- ers such as ESM, ProtBert, BioBERT, and SciBERT, have shown promising results in identifying ACPs. In a recent research [2] a FastText-based word embedding method in- volving a skip-gram model has been used to represent each peptide for forming the embedding on which a deep neu- ral network (DNN) model is employed to accurately classify the ACPs. CancerGram [9] uses n-grams and random forests for predicting ACPs. UniRep [30], a Language model-based embedding is also used as a feature representation for anti- cancer peptides leading to improved ACP prediction. These Language model-based methods have shown improved clas- sification results but have high memory requirements. 3 Proposed Approach Our proposed approach consists of generating embedding for the ACP sequences based on k-mer compression and incremental NCD computation. Given a set of Sequences (S) we process each pair of these sequences represented as s1 and s2 in every iteration ultimately covering all possible pairs. The overall flow diagram of the proposed method is shown in Figure 1. Moreover, the pseudocode of our method is given in Algorithm 1. We first compute thek-mers of each sequence as shown in step (b) of Figure 1 and the line numbers 10 and 15 of Algorithm 1 for s1 and s2 respectively. This is followed by encoding these k-mers using the function Encode in line numbers 11 and 16 which is presented in Algorithm 1 and also shown in step (d) of Figure 1, it takes in a sequence in our case k-mer and uses NLP based method involving tokenization of k-mers followed by Count Vectorization of the tokens as shown in line number 2 and 3 of Algorithm 2 to form numerical representation of thek-mers which is then flattened in line number 4 of Algorithm 2 and converted into a string forming the encoded version of k-mers. It can also be noticed in line numbers 11 and 16 of Algorithm 1 and incremental stage of step(d) in Figure 1 that the encoded forms of k-mers keep adding up in each iteration leading to incremental encoding. These incrementally encoded k-mers are further compressed using Gzip as shown in Algorithm 3 and step (e) of Figure 1. This is followed by calculating the lengths of these compressed incrementally encoded k- mers in line numbers 13 and 18 for s1 and s2 respectively. To finally calculate the NCD values we need lengths of compressed concatenated sequences. In our algorithm, we adopt a unique method for concatenating by first segmenting the s1 and s2 into portions with increased length after every iteration and then concatenate in line number 19 of Algorithm 1, a detailed view of this technique is shown in step (c) of Figure 1 where the black lines show the formation of first concatenated fragments for each successive amino acid followed by red and blue lines that clearly show the increasing length of the fragments. These concatenated sequence fragments, also referred to as sub-sequences are further encoded as shown in step (d) of Figure 1 but this time without incremental stage as can be seen in line number 20 of Algorithm 1. Followed by compression and length computation stages in step(e) and step(f) of Figure 1. We then calculate NCD values using Equation 3.1. (3.1) N CD(s1, s2) = L(.) − min{Lks1 , Lks2 } max{Lks1 , Lks2 } where Lks1 and Lks2 represent the lengths of the com- pressed incrementally encoded k-mers of sequences s1 and s2 respectively, and L(.) denotes the length of the com- pressed form of the concatenated fragments of sequence s1 and s2. Finally, the NCD values are aggregated using the mean function to obtain a scalar value. These Scalar NCD values are appended in Distance Matrix (D) in line number 26 of Algorithm 1. This process is repeated for all pairs of se- quences, resulting in the incremental encoding distance ma- trix, which contains the pairwise similarity values between sequences. Algorithm 1 Incremental Encoding Distance Matrix Input:Set of Sequences (S) Output: Distance Matrix (D) 1: function INCENCOD DIST MAT(S) 2: D ← [] 3: k val ← 3 ▷ Length of k-mer 4: for s1 ← S do 5: initialize(Eks1 , Cks1 , Lks1 ) 6: D local 1, D local 2 ← [] 7: for s2 ← S do 8: initialize(Eks2 , Cks2 , Lks2 ) 9: for i ← range (len(s1) - k val + 1) do 10: kmers1 ← s1[i:i+k val] 11: Eks1 += ENCODE(kmers1 ) 12: Cks1 ← COMPRESS(Eks1 ) 13: Lks1 ← len(Cks1 ) 14: for j ← range (len(s2) - k val + 1) do 15: kmers2 ← s2[j:j+k val] 16: Eks2 += ENCODE(kmers2 ) 17: Cks2 ← COMPRESS(Eks2 ) 18: Lks2 ← len(Cks2 ) 19: concatSeq ← s1[:i+1] + s2[:j+1] 20: E(.) ← ENCODE(concatSeq) 21: C(.) ← COMPRESS(E(.)) 22: L(.) ← len(C(.)) 23: NCD ← L(.) −min(Lks1 ,Lks2 ) max(Lks1 ,Lks2 ) 24: D local 1.append(NCD) 25: end for 26: scalar value ← mean(D local 1) 27: D local 2.append(scalar value) 28: end for 29: end for 30: D.append(D local 2) 31: end for 32: return D 33: end function REMARK 1. NCD Lower Bound: NCD values are bounded by 0 when two sequences are identical. In this case, the compressed concatenation of the sequences will be .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint Figure 1: Flow diagram for the proposed approach. The figure is best seen in color. Algorithm 2 Encoding Input: Sequence (seq) Output: Encoded Sequence (E) 1: function ENCODE (seq) 2: tokens ← Tokenize(seq) 3: Vector ← CountVectorizer(tokens) 4: E ← GetString(Vector) ▷ Flatten and convert to string 5: return E 6: end function Algorithm 3 Gzip compression Input: Encoded Sequence (E) Output: Compressed Sequence (C) 1: function COMPRESS (E) 2: C ← Gzip(E) ▷ Encoded to utf-8 then compressed using Gzip 3: return C 4: end function the same as the compressed length of each sequence, i.e. N CD(s1, s2) = 0 if s1 = s2. REMARK 2. NCD Upper Bound: The NCD value is upper- bounded by 1 in the case where two sequences are com- pletely dissimilar, as the compressed concatenated sequence will not provide any significant compression advantage, i.e. N CD(s1, s2) ≤ 1. REMARK 3. Compression Efficiency Guarantees: The pro- posed algorithm’s performance depends on the efficiency of the compression algorithm (i.e. Gzip). Some key properties to note are the following: 1. Optimality in Compression: The Gzip compression algorithm ensures that common substrings or patterns within a sequence or concatenation are compressed efficiently, leading to shorter compressed lengths. 2. Monotonicity of Compression: The compression length for the concatenation of two sequences s1 + s2 will never exceed the sum of their individual compressed lengths, i.e. L(s1 + s2) ≤ L(s1) + L(s2). This ensures that the NCD is always well-defined. REMARK 4. Incremental Encoding Stability: The incre- mental encoding approach adds k-mers to the existing se- quence encoding. To ensure the stability of the algorithm, we can say the following: 1. Monotonic Growth in Encoding: The length of the encoded sequence grows monotonically as k-mers are added, which means the size of the encoded sequence after each iteration will never decrease. This guaran- tees that the compression length also grows or remains constant. 2. Asymptotic Compression Convergence: As the k-mer sequences are incrementally encoded and compressed, the compression lengths for large enough sequences should converge to a stable value, reflecting the overall sequence similarity. 3.1 Distance Matrix Symmetry The Distance matrix (D) obtained is of size n × n, where n represents the number of sequences in set S. Note that D is non-symmetric, so we convert it into a symmetric matrix by taking the average of upper and lower triangle values and replacing the original values of the matrix with the average values. 3.2 Kernel Matrix Computation Then we generate a Kernel matrix from the symmetric distance matrix using a .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint Gaussian Kernel. First, we calculate Euclidean Distance (W ) between two pairs of distances using the equation: (3.2) Wblm,blt = ||blm − blt|| where blm and blt represent any two values of the symmetric Distance matrix. The Gaussian Kernel (G) is defined as a measure of similarity between blm and blt : (3.3) G(blm, blt) = exp( −Wblm,blt 2 σ2 ) where σ2 represents the bandwidth of the kernel. The kernel value is computed for each pair of distances in the symmetric distance matrix to get n × n dimensional kernel matrix using the following theory: ( G = 1, if blm and blt are identical G − →0, b lm and blt move further apart After computing the kernel matrix, we apply ker- nel Principal Component Analysis (PCA) to get a lower- dimensional embedding of the data. It preserves the es- sential information while retaining the relationships among the anti-cancer peptide sequences, including non-linear rela- tions. This representation proves valuable for various tasks, including classification. 4 Experimental Setup This section outlines the experimental setup, including de- tails on the dataset, visualization techniques, baseline mod- els, and metrics used for evaluation. All experiments were conducted on a computing system equipped with an In- tel(R) Xeon(R) CPU E7-4850 v4 running at a clock speed of 2.10GHz and operating on a 64-bit Ubuntu OS (version 16.04.7 LTS Xenial Xerus), with a total memory capacity of 3023 GB. The algorithms were implemented using Python. The dataset was partitioned into training and testing sets us- ing a 70 − 30% split ratio. To account for variability, experi- ments were conducted with5 different random initializations for the train-test splits, and the results reported include both average values and standard deviations. For hyperparameter tuning, a 5-fold cross-validation strategy was employed. 4.1 Dataset Statistics The dataset on Membranolytic anti- cancer peptides (ACPs) [21] provides details regarding pep- tide sequences and their corresponding anticancer effective- ness against breast and lung cancer cell lines. The target labels are classified into four groups: “very active,” “moder- ately active,” “experimental inactive,” and “virtual inactive.” In total, the dataset comprises 949 and 901 peptide sequences for breast and lung cancer, respectively. Table 1 shows the distribution. A CPs Category Count Min. Max. Average Inacti ve-Virtual 750 8 30 16.64 Moderate Active 98 10 38 18.44 Inactive-Experimental 83 5 38 15.02 Very Active 18 13 28 19.33 T otal 949 - - - Breast cancer data A CPs Category Count Min. Max. Average Inacti ve-Virtual 750 8 30 16.64 Moderate Active 75 11 38 17.76 Inactive-Experimental 52 5 38 14.5 Very Active 24 13 28 20.70 T otal 901 - - - Lung cancer data Table 1: Dataset statistics for the Breast cancer and Lung cancer data. Columns represent the min., max., and average lengths of the peptide sequence. 4.2 Data Visualization A widely used visualization tech- nique, namely t-stochastic distributed neighborhood embed- ding (t-SNE) [15, 38], is employed to visualize the feature vectors from different embedding methods. The t-SNE plots are presented in Figure 2 and Figure 3 (in the appendix) for Breast Cancer and Lung Cancer, respectively. These plots showcase the distribution and grouping patterns of the em- beddings and facilitate the qualitative assessment of how well the embeddings capture the inherent structure and re- lationships within the data. We can observe in Figure 2 that the proposed k-mers compression-based method can group similar classes reasonably well. 4.3 Baseline Models Detail We selected the baseline and state-of-the-art (SOTA) methods that represent different cat- egories of sequence classification. These categories in- clude feature engineering, kernel methods, neural networks, and pre-trained large language models. The feature engi- neering approache include One-Hot encoding (OHE) [28], Spike2Vec [4], Minimizers [20], Spaced k-mer [35], and PWM2Vec [5]. The kernel method includes String kernel [6] and Sinkhorn-Knopp Algorithm [3]. The neural network

include WDGRL [34] and AutoEncoder [40]. Fi- nally, the pre-trained large language models (LLMs) include SeqVec [23], Protein Bert [8], and TAPE [33]. Each method is summarized in Table 2. 4.4 Evaluation Metrics And Classifiers For classifica- tion tasks, we employ several classifiers including Support Vector Machine (SVM), Naive Bayes (NB), Multi-Layer Perceptron (MLP), K-Nearest Neighbors (KNN) withK = 5 (selected through the standard validation set approach [17]), Random Forest (RF), and Logistic Regression (LR). To as- .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint (a) OHE (b) Spike2Vec (c) Minimizer (d) Spaced k-mer (e) PWM2Vec (f) String kernel (g) WDGRL (h) AutoEncoder (i) SeqVec (j) Ours Figure 2: t-SNE plots for (Breast Cancer Data) for different structure embeddings. The figure is best seen in color.

Description Source OHE This

is introduced for generating fixed-length nu- merical feature vectors. It creates a binary vector (0-1) by assigning positions to characters in the sequence. [28] Spik e2Vec This approach utilizes the concept of k-mers to generate numerical embeddings. k-mers are contiguous substrings of length k derived from a spike sequence. [4] Minimizer The minimizer-based feature vector approach involves computing a ”minimizer” of length m (where m < k ) for a given k-mer. This ”m-mer” is the lexicographically smallest in both forward and reverse order of the k-mer. [20] Spaced K-mers Spaced k-mers, also known as g-mers, represent non- contiguous substrings of length k, resulting in smaller and less sparse feature vectors. [35] PWM2V ec This method takes a biological sequence as input and generates fixed-length numerical embeddings. [5] String Kernel This approach designs an n × n kernel matrix that can be used with kernel classifiers or kernel PCA to obtain feature vectors based on principal components. [6] WDGRL WDGRL aims to optimize the network by minimizing the Wasserstein distance (WD) between the source and target networks. The input is one-hot encoded (OHE) vectors, and it produces the corresponding embeddings [34] AutoEncoder The autoencoder technique leverages an encoder-decoder architecture to derive feature embeddings. [40] SeqV ec A large language model (LLM) that takes biological se- quences as input and fine-tunes the weights based on a pre- trained model to obtain the final embeddings. [23] ProteinBER T This is a pre-trained LLM protein sequence model that utilizes the Transformer/Bert architecture to classify the given biological sequences. [8] T APE TAPE is a semi-supervised LLM, protein representation learning method that works by training a protein large lan- guage model and then generating numerical embeddings. [33] SKA The Sinkhorn-Knopp Algorithm (SKA) uses the idea of generating a kernel matrix using the Sinkhorn-Knopp ap- proach, which can then be used with kernel PCA to gener- ate low-dimensional embeddings. [3] Table 2: Description of different baseline models. sess the effectiveness, we utilize a range of evaluation met- rics, including average accuracy, precision, recall, weighted metrics, and the area under the Receiver Operating Charac- teristic (ROC) curve (AUC). 5 Results And Discussion We discuss the results of the proposed method and its com- parisons with the baselines and SOTA in this section. 5.1 Classification Results The classification results aver- aged over 5 runs for both datasets are reported in Table 3 and 4. Breast Cancer classification results show our pro- posed Gzip-based representation outperformed all baselines according to accuracy, precision, recall, weighted F1 score, and ROC-AUC. Even after fine-tuning the Large language models (LLM) such as SeqVec, Protein Bert, and TAPE, the proposed parameter-free method significantly outperforms the LLMs for all evaluation metrics. TAPE has better ROC- AUC but it is very marginal and for other metrics our pro- posed method still outperforms. For classification training runtime, WDGRL with Naive Bayes performs the best due to the smaller embedding size. We observe similar results for Lung Cancer classification, where our Gzip-based method outperforms all baselines in the majority of the metrics ex- cept for ROC-AUC and F1 Macro score. 5.2 Class-Wise Analysis Using Heatmaps We employ heat maps to delve deeper into the effectiveness of our pro- posed approach in distinguishing between various classes. These maps are created by initially calculating the pairwise cosine similarity between embeddings of different classes and then averaging the similarity values to derive a singu- lar value for each class pair. Heatmaps are shown in Figure 4 and Figure 5 (in the appendix) for Breast Cancer and Lung .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint Embedding

ML Algo. Acc. ↑ Prec. ↑ Recall ↑ F1 (W eig.) ↑ F1 (Macro) ↑ ROC AUC ↑ Training Time (sec.) ↓OHE SVM 0.882 0.883 0.882 0.880 0.568 0.764 0.247 NB 0.844 0.842 0.844 0.834 0.451 0.686 0.028 MLP 0.849 0.868 0.849 0.857 0.521 0.742 7.933 KNN 0.609 0.853 0.609 0.676 0.395 0.678 0.069 RF 0.880 0.864 0.880 0.867 0.554 0.726 0.720 LR 0.888 0.880 0.888 0.881 0.575 0.755 0.052 Spik e2Vec SVM 0.878 0.870 0.878 0.868 0.534 0.727 8.342 NB 0.855 0.844 0.855 0.842 0.470 0.695 0.181 MLP 0.756 0.834 0.756 0.788 0.441 0.700 27.214 KNN 0.241 0.298 0.241 0.212 0.200 0.550 0.133 RF 0.893 0.885 0.893 0.883 0.606 0.752 1.812 LR 0.890 0.876 0.890 0.878 0.557 0.733 0.092 Minimizer SVM 0.773 0.808 0.773 0.784 0.424 0.668 3.788 NB 0.733 0.806 0.733 0.762 0.355 0.653 0.315 MLP 0.766 0.822 0.766 0.788 0.441 0.689 28.805 KNN 0.577 0.807 0.577 0.635 0.332 0.616 0.149 RF 0.731 0.817 0.731 0.761 0.410 0.660 2.832 LR 0.843 0.836 0.843 0.833 0.483 0.690 0.109 Spaced k-mer SVM 0.865 0.842 0.865 0.845 0.465 0.674 127.502 NB 0.469 0.865 0.469 0.599 0.359 0.607 4.302 MLP 0.420 0.851 0.420 0.497 0.341 0.624 204.755 KNN 0.276 0.460 0.276 0.253 0.216 0.559 1.036 RF 0.348 0.864 0.348 0.363 0.304 0.598 38.087 LR 0.869 0.848 0.869 0.851 0.480 0.682 1.445 PWM2V ec SVM 0.804 0.834 0.804 0.811 0.434 0.687 132.720 NB 0.826 0.846 0.826 0.823 0.408 0.670 0.887 MLP 0.764 0.841 0.764 0.791 0.462 0.720 36.824 KNN 0.199 0.808 0.199 0.221 0.190 0.541 0.618 RF 0.754 0.857 0.754 0.788 0.460 0.717 6.479 LR 0.839 0.819 0.839 0.824 0.434 0.670 16.056 String K ernel SVM 0.808 0.865 0.808 0.829 0.503 0.730 0.316 NB 0.874 0.880 0.874 0.873 0.545 0.746 0.011 MLP 0.634 0.789 0.634 0.684 0.358 0.648 5.259 KNN 0.881 0.860 0.881 0.862 0.494 0.705 0.030 RF 0.879 0.862 0.879 0.861 0.498 0.697 1.133 LR 0.790 0.843 0.790 0.812 0.464 0.707 0.398 WDGRL SVM 0.804 0.646 0.804 0.716 0.223 0.500 0.026 NB 0.779 0.718 0.779 0.735 0.305 0.535 0.002 MLP 0.778 0.714 0.778 0.735 0.301 0.536 3.588 KNN 0.794 0.715 0.794 0.730 0.270 0.518 0.016 RF 0.667 0.689 0.667 0.672 0.301 0.532 0.021 LR 0.818 0.825 0.818 0.749 0.301 0.531 0.006 Auto- Encoder SVM 0.816 0.813 0.816 0.813 0.443 0.678 0.109 NB 0.735 0.754 0.735 0.738 0.360 0.630 0.009 MLP 0.806 0.808 0.806 0.806 0.451 0.675 15.740 KNN 0.832 0.802 0.832 0.804 0.431 0.645 0.067 RF 0.846 0.805 0.846 0.817 0.439 0.648 2.210 LR 0.834 0.820 0.834 0.826 0.464 0.684 0.693 SeqV ec SVM 0.886 0.881 0.886 0.882 0.531 0.735 80.105 NB 0.625 0.757 0.625 0.665 0.244 0.607 4.691 MLP 0.848 0.872 0.848 0.856 0.516 0.743 160.886 KNN 0.674 0.819 0.674 0.725 0.389 0.651 22.253 RF 0.887 0.874 0.887 0.876 0.551 0.725 11.360 LR 0.769 0.872 0.769 0.813 0.465 0.725 1816.404 Protein Bert 0.893 0.893 0.893 0.893 0.602 0.779 64.849 T APE SVM 0.890 0.892 0.890 0.890 0.579 0.774 0.042 NB 0.859 0.888 0.859 0.870 0.584 0.795 0.022 MLP 0.886 0.893 0.886 0.889 0.592 0.781 0.926 KNN 0.886 0.875 0.886 0.879 0.551 0.745 0.021 RF 0.885 0.863 0.885 0.871 0.523 0.724 3.141 LR 0.893 0.894 0.893 0.894 0.592 0.778 0.530 SKA SVM 0.840 0.808 0.840 0.799 0.425 0.613 0.347 NB 0.884 0.881 0.884 0.873 0.547 0.752 0.011 MLP 0.542 0.681 0.542 0.588 0.280 0.545 11.433 KNN 0.236 0.226 0.236 0.213 0.199 0.546 0.080 RF 0.875 0.848 0.875 0.858 0.483 0.708 1.412 LR 0.793 0.629 0.793 0.702 0.221 0.500 0.084 Ours SVM 0.783 0.614 0.783 0.688 0.220 0.500 0.247 NB 0.587 0.880 0.587 0.694 0.453 0.679 0.018 MLP 0.752 0.662 0.752 0.696 0.263 0.518 2.201 KNN 0.783 0.614 0.783 0.688 0.220 0.500 0.271 RF 0.915 0.910 0.915 0.910 0.579 0.784 0.728 LR 0.783 0.614 0.783 0.688 0.220 0.500 0.055 Table 3: Average classification results for Breast Cancer dataset. The best values for each metric are underlined. Overall best values are shown in bold Cancer data, respectively. These figures show the inter-class and intra-class similarity. The light color diagonals in all fig- Embedding

ML Algo. Acc. ↑ Prec. ↑ Recall ↑ F1 (W eig.) ↑ F1 (Macro) ↑ ROC AUC ↑ Training Time (sec.) ↓ OHE SVM 0.917 0.922 0.917 0.917 0.639 0.808 0.142 NB 0.904 0.899 0.904 0.896 0.585 0.742 0.022 MLP 0.864 0.894 0.864 0.876 0.573 0.784 15.337 KNN 0.804 0.907 0.804 0.835 0.537 0.781 0.117 RF 0.921 0.916 0.921 0.913 0.667 0.778 0.457 LR 0.895 0.909 0.895 0.900 0.629 0.805 0.637 Spik e2Vec SVM 0.893 0.888 0.893 0.884 0.546 0.734 218.389 NB 0.894 0.884 0.894 0.881 0.571 0.731 0.498 MLP 0.834 0.889 0.834 0.854 0.554 0.773 70.784 KNN 0.877 0.919 0.877 0.883 0.590 0.790 0.590 RF 0.918 0.914 0.918 0.912 0.657 0.789 3.141 LR 0.897 0.905 0.897 0.899 0.587 0.786 19.848 Minimizer SVM 0.832 0.851 0.832 0.837 0.508 0.711 65.717 NB 0.821 0.860 0.821 0.832 0.532 0.765 0.632 MLP 0.835 0.870 0.835 0.847 0.565 0.767 110.362 KNN 0.858 0.835 0.858 0.840 0.455 0.681 0.837 RF 0.872 0.871 0.872 0.865 0.546 0.723 8.444 LR 0.861 0.862 0.861 0.858 0.562 0.735 6.078 Spaced k-mer SVM 0.886 0.874 0.886 0.871 0.540 0.706 210.539 NB 0.506 0.862 0.506 0.604 0.441 0.706 43.705 MLP 0.846 0.882 0.846 0.856 0.556 0.752 2567.545 KNN 0.883 0.871 0.883 0.862 0.530 0.699 21.594 RF 0.796 0.887 0.796 0.804 0.550 0.727 317.588 LR 0.900 0.895 0.900 0.890 0.590 0.756 56.141 PWM2V ec SVM 0.853 0.864 0.853 0.852 0.544 0.738 105.862 NB 0.886 0.891 0.886 0.880 0.539 0.743 1.328 MLP 0.790 0.845 0.790 0.811 0.487 0.725 119.903 KNN 0.452 0.842 0.452 0.511 0.335 0.614 0.931 RF 0.878 0.885 0.878 0.878 0.578 0.761 14.993 LR 0.877 0.871 0.877 0.870 0.584 0.736 26.217 String K ernel SVM 0.867 0.884 0.867 0.871 0.519 0.731 0.203 NB 0.889 0.903 0.889 0.889 0.561 0.761 0.009 MLP 0.647 0.823 0.647 0.709 0.378 0.658 5.243 KNN 0.909 0.906 0.909 0.899 0.592 0.752 0.035 RF 0.878 0.834 0.878 0.851 0.424 0.638 0.900 LR 0.874 0.886 0.874 0.878 0.566 0.757 0.290WDGRL SVM 0.843 0.729 0.843 0.775 0.259 0.514 0.062 NB 0.125 0.738 0.125 0.126 0.115 0.525 0.005 MLP 0.831 0.799 0.831 0.813 0.363 0.598 7.815 KNN 0.862 0.820 0.862 0.822 0.360 0.583 0.050 RF 0.858 0.812 0.858 0.823 0.366 0.587 0.968 LR 0.849 0.769 0.849 0.789 0.301 0.536 0.021 Auto- Encoder SVM 0.911 0.918 0.911 0.912 0.619 0.800 0.078 NB 0.870 0.887 0.870 0.871 0.560 0.780 0.012 MLP 0.910 0.920 0.910 0.911 0.603 0.799 5.965 KNN 0.910 0.908 0.910 0.906 0.602 0.771 0.090 RF 0.917 0.912 0.917 0.913 0.627 0.780 1.303 LR 0.917 0.921 0.917 0.918 0.629 0.806 0.933 SeqV ec SVM 0.927 0.925 0.927 0.923 0.689 0.822 159.204 NB 0.361 0.800 0.361 0.366 0.183 0.587 5.130 MLP 0.897 0.896 0.897 0.894 0.621 0.792 264.274 KNN 0.886 0.882 0.886 0.878 0.604 0.761 33.326 RF 0.912 0.906 0.912 0.902 0.660 0.774 11.063 LR 0.789 0.900 0.789 0.828 0.566 0.829 1635.13 Protein Bert 0.923 0.936 0.923 0.923 0.639 0.803 63.599 T APE SVM 0.900 0.903 0.900 0.900 0.602 0.782 0.045 NB 0.893 0.911 0.893 0.898 0.639 0.823 0.032 MLP 0.902 0.908 0.902 0.903 0.636 0.800 1.274 KNN 0.906 0.915 0.906 0.906 0.637 0.797 0.091 RF 0.897 0.886 0.897 0.884 0.574 0.731 3.199 LR 0.913 0.920 0.913 0.912 0.655 0.802 0.521 SKA SVM 0.852 0.889 0.852 0.864 0.510 0.727 0.155 NB 0.886 0.901 0.886 0.888 0.580 0.771 0.019 MLP 0.680 0.826 0.680 0.735 0.378 0.662 1.475 KNN 0.907 0.896 0.907 0.894 0.536 0.732 0.012 RF 0.890 0.858 0.890 0.865 0.471 0.665 2.973 LR 0.842 0.709 0.842 0.770 0.229 0.500 0.064 Ours SVM 0.830 0.688 0.830 0.752 0.227 0.500 0.042 NB 0.573 0.863 0.573 0.659 0.392 0.722 0.007 MLP 0.788 0.710 0.788 0.744 0.248 0.508 5.629 KNN 0.830 0.688 0.830 0.752 0.227 0.500 0.038 RF 0.931 0.938 0.931 0.932 0.661 0.827 0.636 LR 0.830 0.688 0.830 0.752 0.227 0.500 0.048 Table 4: Average classification results for Lung Cancer dataset. The best values for each metric are underlined. Overall best values are shown in bold ures show a high positive intra-class similarity, depicting a strong resemblance of the ACP sequences belonging to the .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint same category. The portions other than the diagonals in the heatmap represent inter-class similarity. The heatmaps for the proposed k-mer compression-based method are given in Figure 4j and Figure 5j. It can be observed that the similar- ity between different classes is very low, showing that our proposed embedding differentiates between classes. While the heatmaps for baselines, especially WDGRL and SeqVec, shown in Figure (4g-4i) and Figure (5g-5i) mostly have pos- itive high similarity between all the classes showing zero to very weak differentiation between different classes of ACPs in the embedding feature space as they are very close to each other. 5.3 Class-Wise Analysis Using Bar Plots We use bar plots to analyze the values in different embeddings and com- pute their kernel values to observe which ones have better class-wise separations. An example of a pair of embeddings (using the Spike2Vec approach) belonging to the same class and a pair of embeddings belonging to a different class is shown in Figure 6 for randomly selected pairs for the breast cancer dataset (in the appendix). In Figure 6 (a) and (b), we can observe the Spike2Vec-based k-mers spectrum for the “mod. active” label. As they belong to the same class, we expect the pairwise Gaussian kernel value to be as big as possible. The Gaussian kernel value for Figure 6 (a) and (b) is 0.98412732 using k-mers spectrum embedding, while for our proposed k-mer Compression-based embed- ding, the Gaussian kernel value is 0.99999999, hence show- ing that the proposed method captures the similarity among same class better. Similarly, Figure 6 (c) and (d) represent k-mers spectrum embeddings for different classes (selected randomly), and we can expect the Gaussian kernel value to be smaller, which we observed in the case of the proposedk- mers compression-based approach compared to Spike2Vec- based k-mers spectrum. For the Lung cancer ACP dataset, we can observe sim- ilar behavior in Figure 7 (in the appendix). The Gaussian kernel value for Figure 7 (a) and (b), which represents the label “very active”, is 0.9884221 for Spike2Vec, while for k-mer Compression, it is 0.9999999 (larger value is better). Similarly, the Gaussian kernel value for Figure 7 (c) and (d) is 0.9999060 for Spike2Vec, which represents the label “inactive-exp” and “very active”, while for the k-mer Com- pression, the Gaussian kernel value is0.99989160 (a smaller kernel value is better). This behavior also shows that the em- beddings generated using the proposed k-mers compression- based approach better show the inter-class-based separations and intra-class-based closeness. 5.4 Statistical Significance We conducted a student t-test, the p-values were derived from the average and standard deviations obtained from five independent random runs. It is noteworthy that all computed p-values were below 0.05, indicating the statistical significance of the results. This observation can be attributed to the generally low standard deviation (SD) values across the data. The SD results for breast cancer and lung cancer datasets are in Table 5 and Table 6 (in the appendix), respectively. We can observe that the SD values of our method and most of the baselines are very small, which shows that the results are stable. From the overall average and SD results, we can see that our method outperforms the SOTA for predictive per- formance on the real-world Anti-Cancer Peptides (ACPs) sequence datasets. The results demonstrate the effective- ness of our Gzip-based representation method over various baselines across multiple evaluation metrics. This superi- ority is particularly notable in terms of accuracy, precision, recall, weighted F1 score, and ROC-AUC. Such consistent outperformance indicates the robustness and reliability of our approach across different classification tasks. Despite fine-tuning large language models (LLMs) like SeqVec and Protein Bert, our parameter-free method outperforms them across all evaluation metrics. This observation is particularly intriguing given the complexity and expressiveness of LLMs, suggesting that domain-specific representations, such as the Gzip-based method proposed, can provide more tailored and effective solutions for sequence analysis. Also, it can help bi- ologists better understand Cancer Biology and come up with improved cancer prediction and treatment methods. While the proposed method excels in classification ac- curacy, computational efficiency is crucial for large-scale ap- plications. Despite competitive performance, methods like SeqVec and Spacedk-mers may require more computational resources, posing practical limitations. Class-wise similar- ity plots reveal strong intra-class similarities and low inter- class similarities, indicating effective differentiation and val- idating the discriminative power of the proposed embedding method. These promising results open up avenues for its ap- plication in various bioinformatics and medical domains be- yond cancer classification. Such as facilitating the develop- ment of diagnostic tools, drug discovery pipelines, and per- sonalized medicine approaches. 6 Conclusion We propose a lightweight and efficient compression-based

involving k-mer strategy and NLP-based encoding for classifying Anti-Cancer Peptide sequences. Our method achieves SOTA performance without the need for parameter tuning or pre-trained models. The compression-based model successfully overcame the limitations of neural network- based methods, offering improved accessibility and com- putational efficiency, especially in low-resource scenarios. In future research, we will explore the applications of our model in other biological domains and investigate ways to optimize the method for specific biological datasets. .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint

[1] S. A HMED , R. M UHAMMOD , ET AL ., Acp-mhcnn: An accurate multi-headed deep-convolutional neural network to predict anticancer peptides, Scientific reports, 11 (2021), p. 23676. [2] S. A KBAR , M. H AYAT, ET AL ., cacp-deepgram: classifica- tion of anticancer peptides via deep neural network and skip- gram-based word embedding model, Artificial intelligence in medicine, 131 (2022), p. 102349. [3] S. A LI, T. E. A LI, T. MURAD , H. M ANSOOR , AND M. PAT- TERSON , Molecular sequence classification using efficient kernel based embedding, Information Sciences, 679 (2024), p. 121100. [4] S. A LI, B. B ELLO , P. C HOURASIA , R. T. P UNATHIL , P.- Y. C HEN , I. U. K HAN , AND M. P ATTERSON , Virus2vec: Viral sequence classification using machine learning, arXiv preprint arXiv:2304.12328, (2023). [5] S. A LI ET AL ., PWM2Vec: An efficient embedding approach for viral host specification from coronavirus spike sequences, Biology, 11 (2022), p. 418. [6] S. A LI, B. S AHOO , M. A. K HAN , A. Z ELIKOVSKY , I. U. KHAN , AND M. P ATTERSON , Efficient approximate kernel based spike sequence classification, IEEE/ACM Transactions on Computational Biology and Bioinformatics, (2022). [7] D. A ZEVEDO , A. M. R ODRIGUES , H. C ANH ˜AO, A. M. CARVALHO , AND A. S OUTO , Zgli: A pipeline for clustering by compression with application to patient stratification in spondyloarthritis, Sensors, 23 (2023). [8] N. B RANDES , D. O FER , Y. P ELEG , N. R APPOPORT , AND M. L INIAL , Proteinbert: A universal deep-learning model of protein sequence and func., Bioinformatics, 38 (2022). [9] M. B URDUKIEWICZ ET AL ., Cancergram: An effective clas- sifier for differentiating anticancer from antimicrobial pep- tides, Pharmaceutics, 12 (2020), p. 1045. [10] P. C HAROENKWAN , W. C HIANGJONG , ET AL ., Improved prediction and characterization of anticancer activities of peptides using a novel flexible scoring card method, Scientific reports, 11 (2021), p. 3017. [11] L. C HEN , Z. HU, ET AL ., Deep2pep: A deep learning method in multi-label classification of bioactive peptide, Computa- tional Biology and Chemistry, (2024), p. 108021. [12] W. C HEN , H. D ING , P. F ENG , H. L IN, AND K.-C. C HOU, iacp: a sequence-based tool for identifying anticancer pep- tides, Oncotarget, 7 (2016), p. 16895. [13] Z. C HEN , P. ZHAO, F. LI, ET AL ., ifeature: a python package and web server for features extraction and selection from protein and peptide sequences, Bioinformatics, 34 (2018), pp. 2499–2502. [14] W. C HIANGJONG , S. C HUTIPONGTANATE , AND S. H ON- GENG , Anticancer peptide: Physicochemical property, func- tional aspect and trend in clinical application, International journal of oncology, 57 (2020), pp. 678–696. [15] P. C HOURASIA ET AL ., Enhancing t-sne performance for bi- ological sequencing data through kernel selection, in ISBRA, Springer, 2023, pp. 442–452. [16] J. E. C RONAN , The chain-flipping mechanism of acp (acyl carrier protein)-dependent enzymes appears universal, Bio- chemical Journal, 460 (2014), pp. 157–163. [17] P. D EVIJVER AND J. K ITTLER , Pattern recognition: A statistical approach, in London, GB: Prentice-Hall, 1982, pp. 1–448. [18] Z. D U, X. D ING , Y. X U, AND Y. L I, Unidl4biopep: a universal deep learning architecture for binary classification in peptide bioactivity, Briefings in Bioinformatics, 24 (2023), p. bbad135. [19] E. F AZAL , M. S. I BRAHIM , ET AL ., Anticancer peptides classification using kernel sparse representation classifier, IEEE Access, 11 (2023), pp. 17626–17637. [20] S. G IROTTO , C. P IZZI , ET AL ., Metaprob: accurate metage- nomic reads binning based on probabilistic sequence signa- tures, Bioinformatics, 32 (2016), pp. i567–i575. [21] G RISONI ET AL ., ’de novo design of anticancer peptides by ensemble artificial neural networks’, ’Journal of Molecular Modeling’, ’25’ (’2019’), p. ’112’. [22] Z. H AJISHARIFI , M. P IRYAIEE , ET AL ., Predicting anti- cancer peptides with chou’s pseudo amino acid composition and investigating their mutagenicity via ames test, Journal of theoretical biology, 341 (2014), pp. 34–40. [23] M. H EINZINGER ET AL ., Modeling aspects of the language of life through transfer-learning protein sequences, BMC bioinformatics, 20 (2019), pp. 1–17. [24] K.-Y. H UANG , Y.-J. T SENG , ET AL ., Identification of sub- types of anticancer peptides based on sequential features and physicochemical properties, Scientific reports, 11 (2021), p. 13594. [25] L. J IANG , N. S UN, Y. Z HANG , X. Y U, AND X. L IU, Bioactive peptide recognition based on nlp pre-train algo- rithm, IEEE/ACM Transactions on Computational Biology and Bioinformatics, (2023). [26] Z. J IANG ET AL ., Low-resource” text classification: A parameter-free classification method with compressors, in Findings of the Association for Computational Linguistics: ACL 2023, 2023, pp. 6810–6828. [27] Z. H. K ILIMCI AND M. Y ALCIN , Acp-esm: A novel framework for classification of anticancer peptides us- ing protein-oriented transformer approach, arXiv preprint arXiv:2401.02124, (2024). [28] K. K UZMIN , A. E. A DENIYI , ET AL ., Machine learning

accurately predict host specificity of coronaviruses based on spike sequences alone, Biochemical and Biophysi- cal Research Communications, 533 (2020), pp. 553–558. [29] C. L ESLIE , E. E SKIN , ET AL ., Mismatch string kernels for svm protein classification, Advances in neural information processing systems, (2003), pp. 1441–1448. [30] Z. L V, F. C UI, ET AL ., Anticancer peptides prediction with deep representation learning features, Briefings in bioinfor- matics, 22 (2021), p. bbab008. [31] S. M ANTACI , A. R ESTIVO , AND M. S CIORTINO , Distance measures for biological sequences: Some recent approaches, Journal of Approximate Reasoning, 47 (2008), pp. 109–124. [32] R. N USSINOV , H. J ANG , ET AL ., Precision medicine and driver mutations: computational methods, functional as- says and conformational principles for interpreting cancer .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint drivers, PLoS computational biology, 15 (2019), p. e1006658. [33] R. R AO, N. B HATTACHARYA , N. T HOMAS , Y. D UAN, P. C HEN , J. C ANNY, P. A BBEEL , AND Y. S ONG, Evaluat- ing protein transfer learning with tape, Advances in neural information processing systems, 32 (2019). [34] J. S HEN , Y. Q U, ET AL ., Wasserstein distance guided rep- resentation learning for domain adaptation, in AAAI confer- ence on artificial intelligence, 2018. [35] R. S INGH , A. S EKHON , ET AL ., Gakco: a fast gapped k-mer string kernel using counting, in Joint ECML and KDD, 2017, pp. 356–373. [36] H. S UNG , J. F ERLAY, ET AL ., Global cancer statistics 2020: Globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA: a cancer journal for clinicians, 71 (2021), pp. 209–249. [37] H. T AO, S. S HAN , H. F U, C. Z HU, AND B. L IU, An aug- mented sample selection framework for prediction of anti- cancer peptides, Molecules, 28 (2023), p. 6680. [38] L. V AN DER MAATEN AND G. H INTON , Visualizing data using t-sne., Journal of machine learning research, 9 (2008). [39] J.-P. V ERT, H. S AIGO , AND T. A KUTSU , Local alignment kernels for biological sequences, Kernel methods in compu- tational biology, (2004), pp. 131–154. [40] J. X IE, R. G IRSHICK , AND A. FARHADI , Unsupervised deep embedding for clustering analysis , in International confer- ence on machine learning, 2016, pp. 478–487. [41] M. X IE, D. L IU, AND Y. YANG, Anti-cancer peptides: Clas- sification, mechanism of action, reconstruction and modifica- tion, Open biology, 10 (2020), p. 200004. [42] H.-C. Y I, Z.-H. Y OU, ET AL ., Acp-dl: a deep learning long short-term memory model to predict anticancer pep- tides using high-efficiency feature representation, Molecular Therapy-Nucleic Acids, 17 (2019), pp. 1–9. [43] L. Y U, R. J ING , ET AL ., Deepacp: a novel computational approach for accurate identification of anticancer peptides by deep learning algorithm, Molecular Therapy-Nucleic Acids, 22 (2020), pp. 862–870. [44] C. Z HOU , D. P ENG , ET AL ., Acp ms: prediction of an- ticancer peptides based on feature extraction, Briefings in Bioinformatics, 23 (2022), p. bbac462. .CC-BY 4.0 International licenseavailable under a (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 The copyright holder for this preprintthis version posted October 8, 2024. ; https://doi.org/10.1101/2024.10.05.616787doi: bioRxiv preprint