# Prediction of Cell-Penetrating Peptides Using a Novel HSIC-Based Multiview TSK Fuzzy System
## 1 Introduction  
Traditional therapeutic drugs are greatly limited due to the complexity of the human immune system and the selective penetration of the cell membrane. As such, many diseases require treatment at the molecular level. We expect to deliver drugs directly to target cells while minimizing the impact on cells and avoiding permanent damage. Cell-penetrating peptides (CPPs) can be used to complete this task. CPPs are a class of short peptides with a length between 5-50 amino acid residues [1] that can carry DNA, protein, and other biomolecules into cells and will not cause irreparable damage to cells when the concentration of CPPs is low. CPPs are widely utilized due to their powerful loading capacity and transduction efficiency. Therefore, the correct identification of CPPs is of great significance. Unfortunately, the traditional experimental approach is time-consuming and costly to predict CPPs, and the prediction accuracy is not satisfactory. In recent years, machine learning-based methods have been widely applied [2, 3] to predict CPPs. These methods have two main steps, namely, (1) selecting a suitable feature extraction method to transform the original sequence into vector form. In this process, to reduce information loss, a variety of descriptors are often adopted to convert the sequence into multiview data. The second step is to (2) build a learning model and utilize the features obtained in the above step as input to train the model. Such machinelearning-based predictors have evolved rapidly in the past few years. CellPDD, proposed by [PERSON] et al. [4], adopts several feature representation methods, such as the amino acid composition, dipeptide composition, and binary spectroscopy. [PERSON] et al. [5] improved the prediction performance by utilizing the amino acid frequency and physicochemical property features. [PERSON] et al. constructed a high-quality dataset, CPP924, and presented two effective predictors: SkipCPP-Pred [6] and CPPred-RF [7]. An adaptive skip dipeptide composition descriptor and random forest algorithm were employed. The TargetCPP proposed by [PERSON] et al. [8] adopted split amino acid composition and composite protein sequence representation, covering multiview information, and the gradient boost decision tree algorithm was employed to improve the prediction performance. [PERSON] et al. [9] built a predictor named StackCPPred based on the residue pairwise energy matrix and employed support vector machine recursive feature elimination and correlation bias reduction to improve the identification ability. In addition to these predictors for CPPs, some methods have been used to predict other therapeutic peptides. PEPred, proposed by [PERSON] et al. [10], and PPTTPP, proposed by [PERSON] et al. [11], can be used to predict eight therapeutic peptides: AAP, ABP, ACP, AIP, AVP, CPP, QSP, and SBP. ITP-Pred, proposed by [PERSON] et al. [12], can predict both CPP and QSP. These prediction methods improve the ability to discriminate CPPs and lay the foundation for the wide application of CPPs. A fuzzy system is a rule-based system that implements knowledge representation via fuzzy logic and inference. The core of a fuzzy system is a knowledge base composed of IF-THEN rules. In this paper, the Takagi-Sugeno-Kang (TSK) fuzzy system [13; 14] was adopted due to its excellent interpretability and data-driven learning ability [15; 16; 17]. In multiview learning, each view can benefit from knowledge from other views, which is the complementarity principle. In addition, some studies [18] have noted that the independence of different views can serve as a beneficial complement to multiview learning. In this paper, the Hilbert-Schmidt independence criterion (HSIC) [19] is employed to measure the independence of different views and realize the idea of the complementarity principle. Although there are many methods available to predict CPPs, some critical questions remain unanswered.