Deep-Representation-Learning-Based Classification Strategy for Anticancer Peptides

Abstract

Cancer, with its complexity and numerous origins, continues to provide a huge challenge in medical research. Anticancer peptides are a potential treatment option, but identifying and synthesizing them on a large scale requires accurate prediction algorithms. This study presents an intuitive classification strategy, named ACP-LSE, based on representation learning, specifically, a deep latent-space encoding scheme. ACP-LSE can demonstrate notable advancements in classification outcomes, particularly in scenarios with limited sample sizes and abundant features. ACP-LSE differs from typical black-box approaches by focusing on representation learning. Utilizing an auto-encoder-inspired network, it embeds high-dimensional features, such as the composition of g-spaced amino acid pairs, into a compressed latent space. In contrast to conventional auto-encoders, ACP-LSE ensures that the learned feature set is both small and effective for classification, giving a transparent alternative. The suggested approach is tested on benchmark datasets and demonstrates higher performance compared to the current methods. The results indicate improved Matthew’s correlation coefficient and balanced accuracy, offering insights into crucial aspects for developing new ACPs. The implementation of the proposed ACP-LSE approach is accessible online, providing a valuable and reproducible resource for researchers in the field.

1. Introduction

Cancer continues to be a major health problem worldwide, taking millions of lives [1,2,3,4,5,6,7,8]. Cancer, rather than being a single ailment, is a broad spectrum of complicated disorders characterized by uncontrolled cell growth and the propensity to rapidly infect other parts of the body. The inherent complexity and heterogeneity pose serious challenges in developing effective anticancer therapies [9].

Conventional methods like radiotherapy and chemotherapy are usually beneficial but have high costs and considerable adverse effects on normal cells. Furthermore, the development of resistance by cancer cells to the existing chemotherapeutic drugs presents a challenging obstacle [10,11]. As a result, there is an ongoing need for the discovery of novel anticancer drugs. Traditional therapies destroy both cancer and normal cells, leading to exorbitant medical costs [12,13,14,15]. Peptide-based treatment is a promising option because of its high specificity, enhanced tumor penetration, and minimal toxicity under normal physiological conditions [16]. The discovery of anticancer peptides has transformed this landscape by enabling the selective targeting of cancer cells while protecting normal cells [17,18,19].

Anticancer peptides (ACPs) have therapeutic potential for numerous malignancies, as they selectively target cancer cells without affecting normal physiological processes [20,21]. ACPs, ranging in length from 5 to 50 amino acids, have cationic amphipathic structures that interact with the anionic lipid membrane of cancer cells, enabling selective targeting [22,23]. They exhibit broad-spectrum cytotoxicity against many cancer cells while sparing normal cells due to their electrostatic interaction with the plasma membrane of cancer cells [24]. Over the last decade, several peptide-based therapies have been evaluated in pre-clinical and clinical trials, highlighting the need to discover novel ACPs for cancer treatment [25]. ACPs, primarily derived from antimicrobial peptides (AMPs), represent a new direction in anticancer drug development [24,26]. The safety and efficacy of ACPs make them viable alternatives to traditional broad-spectrum drugs. The extensive research into ACP therapies in pre-clinical and clinical trials against numerous tumor types indicates a paradigm shift, though identifying clinically viable ACPs remains a challenge due to the time-consuming and expensive nature of the experimental methods. Computational methods are, therefore, essential for efficient ACP identification.

Bioinformatics encompass a myriad of computational methodologies [27,28,29,30,31,32], with a particular emphasis on machine-learning-based approaches for identifying anticancer peptides (ACPs). The pioneering tool, Anti-CP, used a support vector machine (SVM) with sequence-based features and binary profiles [33]. Chou’s pseudo-amino acid composition (PseAAC) and local alignment kernel were used in [34] for ACP prediction, while g-gap dipeptide components were optimized in [35]. The amino acid composition, average chemical shifts, and reduced amino acid composition were selected in [36]. Several other methodologies have been proposed, including feature representation learning models [37], 400-dimensional features with g-gap dipeptide features [38], and a generalized chaos game representation (CGR) method [39]. Notably, the investigation into deep learning architectures indicated the advantages of recurrent neural networks [40]. ACP prediction research has grown in popularity over the last decade, with more experimentally validated ACPs generated from protein sequences [41]. The surge in the accessible proteins from high-throughput sequencing efforts indicates a rapid growth in potential ACPs. Given the challenges inherent in experimental procedures, computational approaches, particularly machine learning, have gained popularity. However, the short length of ACPs makes it difficult to capture the specificity information.

In recent years, there has been a proliferation of machine-learning-based methods, notably, efficient feature representation algorithms. While there are several sequence-based feature descriptors available, combining several types of features to train classifiers raises concerns about the curse of dimensionality and information redundancy. Efficient approaches are required to optimize the information contained in feature descriptors. Furthermore, the integration of physicochemical information has been proposed, as ACPs considerably vary from non-ACPs in terms of these characteristics [22].

Inspired by the success of deep representation learning [42,43,44] in natural language processing, several sequence-based deep representation learning algorithms for proteins and peptides have emerged [45,46,47,48,49,50,51,52]. Unsupervised or semi-supervised learning methods, such as ProFET [53], UniRep [46], ProGen [54], and UDSMProt [55], use large datasets and show promise for protein-related predictions. For instance, in [56], authors reviewed different deep learning architectures including various embedding techniques used for the feature extraction and model designing for protein sequences prediction tasks. In [57], authors have shown that a deep transfer learning using ProteinBERT representations produces promising results where the labeled data are limited. Transfer learning enables these models to be employed as pre-training models for novel tasks such as ACP prediction. While prior techniques have shown promising results, taking into account the dimensional advantages of the model is critical. Methods like ACP-DA [58] use data augmentation to improve ACP prediction performance, addressing the curse of dimensionality by concatenating binary profile features and physicochemical properties. Similarly, iACP-DRLF [59] employs deep representation learning and LGBM feature selection, outperforming previous methods like ACPred-Fuse [60] and AntiCP 2.0 [61].

In a nutshell, advancements in ACP prediction methods have been substantial, but there is still a need to enhance prediction accuracy and consider the dimensionality advantages of the models. Computational methods, particularly those leveraging machine learning and deep representation learning, hold promise for rapid ACP identification.

While current machine learning approaches provide some advantages in predicting ACPs, there is still room for improvement. Deep learning models are highly effective, but their black-box nature can obscure the rationale behind classification decisions. In contrast, a very simple model may lack the precision required for accurate classification. To this end, [62] proposed ACP-KSRC, which uses a sparse-representation classification (SRC) technique [63,64], incorporating polynomial kernel-based principal component analysis (PCA) embedding to reduce feature space dimensions. Furthermore, it employs the synthetic minority oversampling technique (SMOTE) with K-Means [65] to balance sample space dimensions, facilitating the construction of the kernel SRC model.

The ACP-KSRC [62], leveraging a carefully curated feature set and robust signal processing tools, improves decision-making transparency, resulting in better explainability in classification. In line with the growing emphasis on explainable machine learning, a novel deep-latent-space encoding scheme, termed DeepLSE, is introduced. This approach demonstrates significant advancements in classification outcomes, particularly in scenarios with a small sample size and an abundance of features [66,67,68,69].

The DeepLSE method uses representation learning [42,43] and an auto-encoder (AE) to project high-dimensional data into a compressed latent space. In contrast to classic AEs, where compressed representations may not guarantee discriminating features, the proposed DeepLSE learns a meaningful feature set that is both compact and effective for classification.

Section 2 provides comprehensive details of the proposed approach, encompassing datasets, feature encoding techniques, and classification methods. Subsequently, Section 3 presents the results of the experimental analysis and offers a detailed discussion. The paper concludes in Section 4, summarizing the key findings and outlining potential directions for future research.

2. Proposed DeepLSE-Based ACP Classification Approach (ACP-LSE)

This section introduces ACP-LSE, a deep-representation-learning-based classification technique for anticancer peptide sequences. The proposed technique is evaluated with several protocols and popular datasets. Figure 1 depicts the entire classification process using a flow chart. The following subsections provide extensive explanations of each step.

2.1. Dataset

Several datasets, including those in [34,35,37], are publicly available for research purposes. This study employs two benchmark datasets to develop and evaluate the proposed ACP classification strategy. The first dataset, identified as ACP344, was taken from [34] and contained 344 peptide sequences. Of these sequences, 138 are classified as ACPs, with the remaining 206 being non-ACP samples. The second dataset, denoted ACP740, is drawn from the research by Chen et al. [35] and Wei et al. [37]. This collection contains 740 peptide sequences, including 376 ACP and 364 non-ACP samples. Additionally, [70] provides a refined version of the ACP740 dataset. Each dataset is subjected to the design and evaluation of distinct classifiers by the known protocols in the literature. Specifically, ACP344 is subjected to both 5-fold and 10-fold cross-validation protocols, whereas ACP740 is only evaluated using a 5-fold cross-validation protocol.

2.2. Feature Space: Composition of g-Spaced Amino-Acid Pairs

Protein or peptide sequences are typically recorded and stored in the FastA format, where alphabetic symbols represent individual amino acids (see Figure 2 for an illustration). These sequences, varying in length, are processed by varied sequence encoding techniques, such as AAC, di-peptide AAC (DAAC), etc., to extract meaningful numerical features. AAC is the core feature encoding approach, producing a feature vector including the frequency count of essential amino acids. As a result, the entire length of the AAC feature vector is equal to the total number of amino acids, which is denoted as 20. Similarly, DAAC indicates the frequency of peptide pairings, and the total length of the feature vector equals the number of potential combinations of 20 amino acid pairs (i.e., $20\times 20=400$). As shown in the Figure 2, the DAAC feature vector includes the frequencies of 0-spaced amino acid pairs (i.e., the DAAC of amino acid pairs separated by $G=0$ residues).

Both AAC and DAAC are popular sequence encoding approaches that have successfully designed classifiers for diverse protein and peptide sequences [71]. However, these techniques are limited in their representation since they do not account for the varied patterns of amino acid pairings. To improve pattern capture in DAAC, a modified version is presented in [71], where the DAAC feature vectors of most G-spaced amino acid pairs are concatenated. For instance, with $G=2$, ${\mathit{\psi }}_g$ must be computed for $g=0,1,2$, and the final Cg-SAAP feature vector, ${\mathsf{\Psi }}_G$, is a concatenated version of ${\mathit{\psi }}_0$, ${\mathit{\psi }}_1$, and ${\mathit{\psi }}_2$. Here, g denotes a gap value used for the calculation of the gth DAAC feature vector (${\mathit{\psi }}_g$), and G represents the largest possible gap for which the CGSAAP feature vector ${\mathsf{\Psi }}_G$ is calculated. Figure 2 provides an example of the ${\mathsf{\Psi }}_2$ calculation.

2.3. Network Architecture, Loss Function, and Training Configurations (Hyper-Parameters)

The proposed DeepLSE model consists of three modules: (1) encoder $\mathcal{E}$, (2) decoder $\mathcal{D}$, and (3) classifier $\mathcal{C}$. The encoder $\mathcal{E}$ block projects feature space information to latent space. Here, latent-space encoding refers to the representation learning of compressed data using the $LV$ number of latent variables.

Let $x\in {\mathbf{R}}^F$ be a feature vector of size F. The decoder ${\mathcal{D}}_{LV}$ and encoded $Ex=\mathcal{E}\left(x\right)$ are used to re-project features to the original feature space $Dx=\mathcal{D}\left(Ex\right)$. In an ideal scenario, the decoded feature $Dx$ should be the same as the original feature vector x, i.e., $x=\mathcal{D}\left(\mathcal{E}\right(x\left)\right)$. However, due to the compression constraint on latent space, some of the less significant information is suppressed. In the proposed DeepLSE, latent-space representation is further constrained by classifier $\mathcal{C}$ loss, which forces the network to learn compact feature representation that maintains both the most informative and the discriminating information for inter-class separability. In other words, the class-similar samples tend to cluster together, whereas the class-invariant samples are projected apart. Therefore, the redundant information within the representation of data in the latent space is removed, and only the representative features related to the class and reconstruction of the data are kept. This creates a fair balance between the classification and reconstruction tasks, in turn, learning the class-specific as well as sample-specific information inside the latent-space encoding of the raw data. The DeepLSE model is built using a combination of fully connected (FC) layers, batch-normalization and dropout layers to avoid over-fitting.

Table 1. Proposed DeepLSE model architecture.

Network	Layer	Units	Activation
Encoder	Input	-	-
	Enc-1 (FC)	50	ReLU
	Enc-1 (BatchNorm)	-	-
	Enc-1 (Dropout)	0.3	-
	Enc-2 (FC)	25	ReLU
	Enc-2 (BatchNorm)	-	-
	Enc-2 (Dropout)	0.3	-
	Enc-3 (FC)	10	ReLU
	Enc-3 (BatchNorm)	-	-
	Enc-3 (Dropout)	0.3	-
Latent Space	LS (FC)	LV	Sigmoid
Decoder	Dec-1 (FC)	10	ReLU
	Dec-1 (BatchNorm)	-	-
	Dec-1 (Dropout)	0.3	-
	Dec-2 (FC)	25	ReLU
	Dec-2 (BatchNorm)	-	-
	Dec-2 (Dropout)	0.3	-
	Dec-3 (FC)	50	ReLU
	Dec-3 (BatchNorm)	-	-
	Dec-3 (Dropout)	0.3	-
	Dec-out (FC)	-	Sigmoid
Classifier	C-1 (FC)	10	ReLU
	C-2 (FC)	10	ReLU
	C-out	2	Softmax

summarizes the architecture of the model.

The DeepLSE network uses binary cross-entropy (BCE) and mean-squared-error (MSE) as loss functions for the classifier and the auto-encoder networks, respectively. Both the loss functions have been fused using a loss mixing parameter $\lambda$ as

$$\begin{array}{c}\hfill {\mathcal{L}}_{\mathrm{DeepLSE}}=\lambda ·{\mathcal{L}}_{\mathrm{Class}}+(1-\lambda )·{\mathcal{L}}_{\mathrm{Recon}},\end{array}$$

with

$$\begin{array}{c}\hfill {\mathcal{L}}_{\mathrm{Class}}=-(ylog(p)+(1-y)log(1-p\left)\right),\end{array}$$

and

$$\begin{array}{c}\hfill {\mathcal{L}}_{\mathrm{Recon}}=\frac{1}{F}\sum _{i=1}^F{(x_i-{\widehat{x}}_i)}^2,\end{array}$$

where y is the binary indicator (0 or 1) for the actual class label, and p is the predicted probability of observation. x, and $\widehat{x}=\mathcal{D}\left(\mathcal{E}\left(x\right)\right)$ are the input and reconstructed feature vectors of size F, respectively.

The DeepLSE network is trained with various configurations of $\lambda$, Gap value G, and latent variable $LV$. The experimental results related to the selection of these hyper-parameters are presented in the Section 3.

2.4. Evaluation Protocol

The proposed algorithm has been evaluated on various performance assessment metrics, including the true positive rate (TPR) or sensitivity ($S_n$), true negative rate (TNR) or specificity ($S_p$), prediction accuracy ($\mathrm{Acc}$), Matthew’s correlation coefficient ($\mathrm{MCC}$), balanced accuracy ($\mathrm{Bal}.\mathrm{Acc}.$), Youden’s index ($\mathrm{YI}$), and $F1$ Score. Here,

$$\begin{array}{cc}\hfill & S_n:=\frac{\mathrm{trueP}}{\mathrm{trueP}+\mathrm{falseN}},\hfill \\ \hfill & S_p:=\frac{\mathrm{trueN}}{\mathrm{trueN}+\mathrm{falseP}},\hfill \\ \hfill & \mathrm{Acc}.:=\frac{\mathrm{trueP}+\mathrm{trueN}}{\mathrm{trueP}+\mathrm{trueN}+\mathrm{falseP}+\mathrm{falseN}},\hfill \\ \hfill & \mathrm{MCC}:=\frac{\mathrm{trueP}·\mathrm{trueN}-\mathrm{falseP}·\mathrm{falseN}}{\sqrt{\left(\mathsf{\Omega }\right)}},\hfill \\ \hfill & \mathrm{Bal}.\mathrm{Acc}.:=\frac{S_n+S_p}{2},\hfill \\ \hfill & \mathrm{YI}:=S_n+S_p-1,\hfill \\ \hfill & \mathrm{F}1\mathrm{Score}:=2·\frac{\mathrm{Pr}·S_n}{\mathrm{Pr}+S_n},\hfill \end{array}$$

where trueP, falseP, trueN, and falseN represent the true positive, false positive, true negative, and false negative, respectively. The measure of precision (Pr) and $\mathsf{\Omega }$ are given by $\mathrm{Pr}:=\mathrm{trueP}/(\mathrm{trueP}+\mathrm{falseP})$ and $\mathsf{\Omega }:=(\mathrm{trueP}+\mathrm{falseP})(\mathrm{trueN}+\mathrm{falseN})(\mathrm{trueP}+\mathrm{falseN})(\mathrm{trueN}+\mathrm{falseP})$.

3. Experimental Results

This section provides a detailed study of the DeepLSE approach, utilizing several numerical experiments. The proposed DeepLSE-based anticancer peptide classification method, ACP-LSE, is validated in terms of methodology, and supporting experiments offer a rationale for hyperparameter selection. The experiments are organized in the following order. Section 3.1 focuses on demonstrating how the proposed DeepLSE more effectively compresses feature dimensions compared to a conventional auto-encoder and the original feature space. In the same section, the impact of different values of G in Cg-SAAP embeddings on model performance is also analyzed. In Section 3.2, the influence of the feature and latent-space dimension is investigated for different values of $\lambda$. In Section 3.3, the effect of $\lambda$ on the latent space is also analyzed. Section 3.4 evaluates the robustness of ACP-LSE against random mutations. Section 3.5 examines the performance consistency of ACP-LSE for various training and testing sample split ratios. Finally, Section 3.6 discusses the findings from comparing the performance of ACP-LSE to existing state-of-the-art approaches.

3.1. Latent Space: Latent-Space Encoding of Cg-SAAP

Modern machine learning methods need vast amounts of training data to achieve better generalization and performance. However, a phenomenon known as the curse of dimensionality occurs when the quantity of measurements or samples is limited but the attributes proliferate ($F>S$). Here, F and S represent the number of features/attributes and samples, $S=N_s+P_s$, where $N_s$ and $P_s$ are the numbers of negative and positive samples in the dataset, respectively. In the context of this study, the dataset consists of a small number of samples (e.g., 344, 740, etc.), although the attributes may number in the thousands. For example, the description of the Cg-SAAP with $G=9$ has 4000 attributes. The curse of dimensionality not only makes our classification task theoretically ill-posed but it also poses a significant challenge in developing an effective latent-space representation for compressed representation, particularly when $F>>S$. To address this, the proposed ACP-LSE removes the least representative dimensions, reducing the original feature space of $F\times S=4000\times S$ to a deep latent-space representation of size $LV\times S$, where $LV<<S<<F$.

To assess the performance of the proposed ACP-LSE method, a comparison of the generalized multi-dimension distribution overlap (GMDM) [72,73] scores is presented in Figure 3. To that end, two models with identical encoder and decoder settings undergo training for 10-fold cross-validation on the ACP344 dataset. For both models, the number of latent-space variables (LV) was fixed to 5. The latent-space encoded features from these models are fed into the GMDM function to measure the degree of overlap between the feature spaces of two classes. Specifically, one model with $\lambda =0$ is a conventional auto-encoder without a classification constraint, while the other is the DeepLSE with $\lambda =0.5$, incorporating a constraint on the latent-space representation. As a baseline, the original feature space is also evaluated for GMDM scores, and the process is repeated for 10 different values of gaps (G) in Cg-SAAP.

It is evident from Figure 3 that the original feature space is highly cluttered, resulting in very low class separability. In contrast, both the auto-encoder and the proposed DeepLSE effectively compress the feature dimensions, leading to higher relative class separability scores. It is noteworthy that the GMDM suggests using a weighted contribution of the projected variables based on their eigen-spread values. However, since the goal of this experiment is to assess overlap in the original space without noise removal, no PCA embedding is employed during the GMDM calculation. Furthermore, to prevent data leakage, no training sample is used to calculate GMDM scores, and the average results of the 10-fold cross-validation are plotted.

The above experiment is focused on demonstrating, through GMDM, how the proposed DeepLSE more effectively compresses feature dimensions compared to a conventional auto-encoder and the original feature space. From the analysis, we can conclude that the higher values of G bring some useful information that is cluttered by other redundant features/information. Unlike conventional AE, where cluttered information is encoded in an ineffective way, unable to harness useful discriminating information, the proposed DeepLSE efficiently represents them in a compact discriminating feature space.

To further showcase the impact of different values of G on the model performance, size, and number of features, the additional results are presented in

Table 2. Effect of the Gap (G) parameter on the overall performance of the proposed method. Similar to the previous experiment, here, the number of latent-space variables is kept as LV = 5.

Gap (G)	Input Size	Total Parameters	MCC Score
			$\mathbf{\lambda }=\mathbf{0}.\mathbf{5}$
0	400	44,454	0.72
1	800	84,854	0.79
2	1200	125,254	0.82
3	1600	165,654	0.87
4	2000	206,054	0.87
5	2400	246,454	0.83
6	2800	286,854	0.87
7	3200	327,254	0.85
8	3600	367,654	0.86

, highlighting DeepLSE classification results for different values of Gap (G) in terms of the MCC score. Similar to the previous analysis, the results presented in Table 2 clearly show that higher values of G provide additional discriminating information and help improve classification performance at the cost of model complexity, which is evident in the number of input features generated by Cg-SAAP for different values of G. It is also noteworthy that the larger models often need more training data, therefore, we can see that after the gap value of $G=3,$ the model performance is capped to the MCC value of $0.87$.

3.2. Analyzing the Effect of Feature and Latent-Space Dimension for Different Values of $\lambda$

In the proposed DeepLSE-based ACP classification approach, several parameters can affect the classification performance. For instance, the GAP (G) between two amino-acid pairs in Cg-SAAP controls the length of the feature space. Similarly, the latent-space dimension ($LV$) controls the size of the output of the encoder module, and loss mixing weight ($\lambda$) controls the training priority for a specific loss. To analyze the sensitivity of DeepLSE for the aforementioned hyperparameters, for each $\lambda$, seventy experiments are performed, where each experiment is a 10-fold cross-validation on the ACP344 dataset.

In particular, for five different values of $\lambda =[0.01,0.25,0.5,0.75,0.99]$, seven combinations of $LV=[2,3,4,5,6,7,8]$ and ten GAP values $G=[0,1,2,3,4,5,6,7,8,9]$ are evaluated, resulting in 700 training and testing trials. The findings of this exhaustive analysis are summarized through surface plots in Figure 4. It is seen that irrespective of the choice of $LV$, GAP G, and $\lambda$, the overall test classification performance in terms of balanced accuracy is somewhat consistent in the range of 0.80∼0.98.

Table 3. Comparison of the best configurations of the 10-fold cross-validation experiment on ACP344 database for different values of $\lambda$.

$\mathit{\lambda }$	LV	GAP	Accuracy	Sensitivity	Specificity	F1-Score	MCC	Balanced Accuracy	Youden’s Index	AUC	AUPR	MSE (dB)
0.01	4	3	0.945 ±0.04	0.964 ± 0.05	0.932 ± 0.07	0.935 ± 0.04	0.895 ± 0.07	0.948 ± 0.03	0.897 ± 0.07	0.967 ± 0.02	0.957 ± 0.03	−24.33 ± 0.26
0.25	2	7	0.947 ± 0.03	0.927 ± 0.07	0.961 ± 0.04	0.933±0.04	0.893 ± 0.07	0.944 ± 0.04	0.888 ± 0.07	0.957 ± 0.04	0.959 ± 0.04	−8.26 ± 2.38
0.5	7	6	0.95 ± 0.03	0.905 ± 0.06	0.98 ± 0.03	0.935 ± 0.04	0.90 ± 0.06	0.943 ± 0.03	0.886 ± 0.07	0.963 ± 0.02	0.962 ± 0.02	−6.77 ± 1.79
0.75	4	4	0.95 ± 0.04	0.927 ± 0.07	0.966 ± 0.04	0.937 ± 0.05	0.899 ± 0.08	0.946 ± 0.04	0.893 ± 0.08	0.965 ± 0.03	0.96 ± 0.03	−6.33 ± 0.49
0.99	4	4	0.959 ± 0.02	0.92 ± 0.06	0.985 ± 0.02	0.946 ± 0.03	0.917 ± 0.06	0.953 ± 0.03	0.906 ± 0.06	0.972 ± 0.02	0.97 ± 0.02	−6.05 ± 0.01

summarizes the results in the form of a comparison of the best mean statistics of 10-fold cross-validation results for different $\lambda$ values. This demonstrates the adaptability of the proposed DeepLSE method for learning effective solutions for the given problem under variable conditions.

However, it can also be seen that the model is sensitive to the choice of these parameters, and the a carefully selected combination can help in designing a better classification model. In this regard, the best performance of the model was observed for $\lambda =0.99$ with $LV=4$ and a GAP value of $G=4$. Figure 5 illustrates the MCC values for different $\lambda$ with $LV=4$ and a GAP value of $G=4$. This is interesting because on one hand, higher values of $\lambda =0.99$ tend to favor classification over reconstruction (see Figure 4e: high MSE(dB) with good MCC), and lower values such as $\lambda =0.01$ prioritize reconstruction loss (see Figure 4a: lowest MSE(dB) with comparable MCC). A general assumption is that the classifier trained solely for the classification task must produce the best results, but it is observed from Figure 5 that the reconstruction constraint on latent space could help in learning additional useful information that can aid during the inference phase. A more prominent gain could be seen in larger feature spaces. For example, with GAP ($G=7$), a model with $\lambda =0.25$ achieved the best results; see Table 3. Similarly, a model with $\lambda =0.50$ achieved the best results for GAP ($G=6$). This further strengthens the proposed claim about using representational learning.

3.3. Analyzing the Effect of $\lambda$ on Latent-Space

By choosing a suitable value of the loss mixing hyperparameter $\lambda$ from $0<\lambda <1$, one can control the contribution of reconstruction and classification losses. To analyze the effect of $\lambda$ on the learned representation of features, deep latent-space encodings (output of the encoder block) are visualized for three values: $\lambda =0.01$, $\lambda =0.5$, and $\lambda =0.99$.

For this experiment, the ACP-LSE model is trained on the ACP344 dataset with the aforementioned values of $\lambda$, Gap $G=6$, and latent space of the size $LV=7$. Since the output of the latent space is relatively large for easy visualization, it is first reduced to a 2D projected version using PCA and TSNE [74].

Figure 6 shows scatter plots of the PCA and TSNE-based 2D projections of the encoded outputs. The findings show that with a large value of $\lambda =0.99$, the DeepLSE model focuses on classification accuracy and projects samples of the same class closer together. With the lower value of $\lambda =0.01$, the model reduces classification accuracy and focuses on reducing reconstruction loss. Ideally, it is better to have the best classification accuracy; however, a large value of $\lambda$ gives the classifier more freedom during the training phase and might lead the model to overfit the training data. Therefore, for better generalization, $\lambda$ should be balanced. This enables the encoder to learn variability in input features, while the latent-space representation constrains the classifier module to learn a decision boundary that maximizes inter-class separability.

3.4. Analyzing the Robustness of DeepLSE against Random Mutations

Figure 7 shows the original (unmutated) ACP344 dataset alongside two of its mutation variants. This experiment attempts to evaluate the robustness of the proposed ACP-LSE method against mutations in ACP sequences. Specifically, the TSNE [74] plots of Cg-SAAP (with $G=8$) features from the original ACP344 dataset are compared to mutants of 138 ACPs derived from the ACP344 dataset. The purpose of this experiment is to determine the susceptibility of latent-space encoding to random mutations.

The findings show that in the original feature space, the separability of ACPs and non-ACPs in empirical distributions reduces significantly with the mutation rate. When more amino acids in ACPs are mutated, the chance increases that these mutant ACP features will not have anticancer properties. However, the proposed ACP-LSE, which was trained purely on original (unmutated) data, retains class separability even when three amino acids are randomly mutated or replaced. This demonstrates the effectiveness of representation learning in extracting robust representations.

3.5. Analyzing Performance Consistency versus Ratio of Training and Testing Samples Splits

To assess the influence of dataset size on the performance and consistency of the proposed method, an experiment is designed where the performance of the proposed ACP-LSE is evaluated on various train and test dataset split ratios. For this experiment, the latent-space feature (LV) value was set to $LV=7$ and Gap was set to $G=1$, allowing us to perform comprehensive testing in comparatively less time. Figure 8 displays the Matthew’s correlation coefficient ($\mathrm{MCC}$) values for models trained and tested on the ACP344 dataset for various sample sizes.

For a fair comparison, both the DeepLSE and conventional DNN models are designed with identical numbers of neurons in their feature extraction (encoder) and classification modules. The DeepLSE was trained with a default weight mixing ratio of $\lambda =0.5$. For the standard DNN, the loss mixing ratio was set to $\lambda =1$ (because there is no decoder/reconstruction loss).

Both models were evaluated for nine different train–test split ratios ranging from $10\%$ training and $90\%$ testing samples to $90\%$ training and $10\%$ training samples. In each experiment, the training and testing samples were randomly shuffled, and weights were reinitialized to random values. To obtain statistically meaningful results, all experiments were repeated five times, and the mean results were compared.

The findings in Figure 8 show that the proposed method is more robust in classification performance compared to standard DNN and produces superior outcomes with consistency. The proposed method outperforms the standard DNN classifiers in both extreme cases: $10\%$ training, $90\%$ testing samples and $90\%$ training, $10\%$ testing samples. Similarly, for other distributions of training and testing sample splits, the classification performance of DeepLSE is either high or comparable to that of the standard DNN. This highlights the superiority of the proposed representation-learning approach, where the latent space is constrained by reconstruction loss, allowing for the learning of useful features using large models even when the number of training samples is extremely low.

3.6. Comparison with State-of-the-Art ACP Classification Approaches

This section compares the performance of the proposed anticancer peptide classification method, ACP-LSE, which is based on DeepLSE, to the current state-of-the-art ACP classification algorithms. The assessment uses two standard datasets: ACP344 [34] and ACP740 [70]. It is critical to emphasize that for a fair comparison, the training and testing samples across all methodologies are kept comparable, as outlined in the previous works. Specifically, the ACP344 dataset is assessed using 5-fold and 10-fold cross-validation protocols, whereas the ACP740 dataset is examined using a 5-fold cross-validation approach.

Table 4. Configuration of best-performing models. Here, n is the number of folds in cross-validation, and G is the maximum space between Cg-SAAP.

Dataset	n	G	LV	Training Epochs	Optimizer	Learning Rate	Early Stopping Patience	Pre-Processing
ACP-344	5	6	8	1000	RMSProp	1 × ${10}^{-4}$	100	-
ACP-344	10	6	7	1000	RMSProp	1 × ${10}^{-4}$	100	-
ACP-740	5	8	4	1000	RMSProp	1 × ${10}^{-4}$	100	l2-Norm

summarizes the hyperparameters used in this study, while any additional specifications about each experiment are presented in the respective subsections.

3.6.1. ACP344 Dataset

To guarantee a fair comparison, we analyze the proposed method on the ACP344 dataset using two well-known evaluation protocols reported in the literature.

Table 5. Performance comparison of the ACP-LSE with contemporary methods on 5-fold cross-validation on ACP344 dataset.

Methods	${\mathit{S}}_{\mathit{n}}$	${\mathit{S}}_{\mathit{p}}$	Acc.	Bal. Acc.	MCC	YI	F1-Score	Year
ZH method [34,75]	85.23%	92.73%	89.76%	88.00%	0.78	0.77	0.89	2014
IACP [75,76]	88.00%	89.10%	94.80%	93.05%	0.89	0.87	0.91	2015
Li method [35,75]	90.60%	96.70%	94.25%	93.05%	0.87	0.87	0.93	2016
EnACP [75]	92.20%	98.10%	95.41%	95.00%	0.91	0.90	0.94	2020
AntiCP (Model2) [77]	81.32%	90.02%	86.90%	85.07%	0.71	0.71	0.82	2021
ACP-KSRC [62]	96.07%	82.97%	90.02%	89.10%	0.81	0.79	0.92	2023
ACP-LSE	89.87%	97.07%	94.18%	93.47%	0.88	0.87	0.92	2024

and

Table 6. Performance comparison of the proposed ACP-LSE with contemporary methods on 10-fold cross-validation on ACP344 dataset.

Methods	${\mathit{S}}_{\mathit{n}}$	${\mathit{S}}_{\mathit{p}}$	Acc.	Bal. Acc.	MCC	YI	F1-Score	Year
SAP [38]	86.23%	95.63%	91.86%	90.93%	0.83	0.81	0.89	2018
ACP-DL [70]	75.82%	86.32%	82.16%	81.07%	0.62	0.62	0.77	2019
ACP-LDF (SVM) [78]	87.70%	96.10%	92.73%	91.90%	0.85	0.83	0.92	2020
ACP-LDF (LibD3C) [78]	85.50%	96.10%	92.15%	91.05%	0.84	0.82	0.92	2020
ACP-LDF (RF) [78]	86.20%	97.10%	92.70%	91.65%	0.85	0.83	0.92	2020
ACP-KSRC [62]	97.07%	86.97%	93.02%	91.89%	0.85	0.84	0.94	2023
ACP-LSE	90.55%	98.1%	95.1%	94.32%	0.90	0.89	0.94	2024

show the performance statistics of several algorithms on the ACP344 dataset using 5-fold and 10-fold cross-validation, respectively. Given the imbalanced nature of the dataset, conventional accuracy metrics are deemed inadequate to describe the overall performance. As a result, class-specific assessment criteria such as MCC and Youden’s index are employed to assess the comprehensive classification capability of classification models.

In 5-fold cross-validation, the proposed method achieves the third-best MCC score, demonstrating its effectiveness in differentiating the ACP features. The proposed ACP-LSE has an MCC value of $0.88$, which is only $3.4\%$ and $1.1\%$ lower than the values reported for EnACP [75] and IACP [75,76], respectively. It is also worth mentioning that the ACP344 dataset is severely unbalanced, with just a limited number of training samples (110 ACPs and 165 non-ACPs) available for learning in 5-fold cross-validation. Given that the auto-encoder model does not require classification labels, it might be interesting to investigate DeepLSE with pre-trained models to determine its potential impact on performance improvement. To investigate the influence of a larger training dataset, a 10-fold cross-validation protocol is used.

Significantly, the proposed method outperforms 10-fold cross-validation, demonstrating its effectiveness in classifying the features of ACP. Specifically, the proposed ACP-LSE achieved the highest MCC value of $0.90$, outperforming other methods. This value is $31.11\%$ higher than that of ACP-DL [70], $6.67\%$ higher than ACP-LDF [78] with the LibD3C, $5.55\%$ higher than ACP-SKRC [62], ACP-LDF [78] with RF and SVM classifiers, and $7.78\%$ higher than SAP with the SVM classifier [38]. This substantiates the argument that the proposed method has the potential to predict novel ACPs or ACP-like peptides. Other assessment metrics support this efficacy, emphasizing the substantial difference between ACPs and non-ACPs.

3.6.2. ACP740 Dataset

This section compares the proposed ACP-LSE on the ACP740 dataset to several state-of-the-art ACP classification methods, such as ACP-DL [70], ACP-DA [58], ACP-MHCNN [79], and ACP-KSRC [62].

Table 7. Performance comparison of ACP-LSE with contemporary methods on 5-fold cross-validation on ACP740 dataset.

Methods	${\mathit{S}}_{\mathit{n}}$	${\mathit{S}}_{\mathit{p}}$	Acc.	Bal. Acc.	MCC	YI	F1-Score	Year
ACP-DL [70]	82.61%	80.59%	83.48%	83.30%	0.63	0.62	0.71	2019
ACP-DA [58]	86.98%	83.26%	82.03%	85.12%	0.64	0.70	0.85	2021
ACP-MHCNN [79]	88.90%	83.10%	86.00%	86.00%	0.72	0.71	0.86	2021
ACP-KSRC [62]	86.23%	81.62%	83.91%	83.94%	0.67	0.67	0.84	2023
ACP-LSE	83.00%	89.29%	86.10%	86.13%	0.73	0.72	0.86	2024

summarizes the comparison results. The findings show that the proposed method outperforms the ACP-DL [70], ACP-DA [58], and ACP-KSRC [62] algorithms, as indicated by the class-specific evaluation parameter MCC. The improvements are significant, with margins of $0.10$, $0.09$, and $0.06$, respectively.

Notably, the ACP-LSE achieves the highest MCC value of $0.73$, outperforming ACP-DL, ACP-DA, and ACP-KSRC by $13.7\%$, $12.3\%$, and $8.2\%$, respectively. In addition, the performance of the proposed representation-based approach slightly outperforms the powerful ACP-MHCNN [79] method. This efficacy is consistent across various evaluation metrics, demonstrating the capability of the proposed ACP-LSE to distinguish between ACPs and non-ACPs. These findings indicate that the proposed method is promising for predicting ACPs or ACP-like peptides.

4. Conclusions

The diagnosis and treatment of cancer, a complex disease with diverse causes, are challenging in the field of medical research. Anticancer peptides (ACPs) are a promising approach in targeted therapy with the potential for precise and accurate treatment. However, for large-scale identification and synthesis, credible prediction approaches are required. In this paper, an intuitive yet powerful representation-learning-based method, ACP-LSE, is proposed, which shows significant improvements in classification performance, particularly in cases with small sample sizes and a large number of features.

For investigation, the results on two benchmark datasets (and three protocols) were analyzed, suggesting that the higher number of training samples either with 10-fold cross validation in ACP-344 or 5 fold cross validation in ACP-740; show a superior classification performance. Various experimental analyses show that the proposed method achieves improved classification performance and aids in learning compact latent-space representation. The suggested approach is tested for different quantitative and qualitative metrics and demonstrates a higher performance compared to the current methods. A key limitation of the proposed ACP-LSE method is that unlike contrastive learning, where a successfully trained model could learn maximum allowable class separability (i.e., infinite), in the proposed method, maximum class separability is bounded to unity. Additionally, unlike DNN where there is no decoder, the training steps in the proposed method involve learning a high number of training parameters due to the decoder network. Finally, for effective model designing using DeepLSE, the tuning of additional hyperparameters, e.g., $\lambda$, $LV$, etc., require computationally complex ablation studies, which take time. In the future research, I would like to investigate techniques to deal with the aforementioned limitations.