In the experiment, the fivefold cross-validation technique is used to evaluate the predictive performance of the CPIELA model. Cross-validation is a widely used approach to estimate the generalization performance of the prediction model. The k-fold cross-validation method usually randomly separates the instances into k equal-sized disjoint groups. Then, the k-1 groups are used as a training dataset, and the remaining group is retained as the testing samples. This process is repeated k times. The predictive results of the proposed method are evaluated using five criteria, including precision (Prec.), accuracy (Acc.), sensitivity (Sen.), specificity (Spec.), and Matthews correlation coefficient (MCC). The calculation formulas are listed as follows: A c c u . = T N + T P F P + F N + T P + T N , (1) S e n . = T P F N + T P , (2) P r e c . = T P F P + T P , (3) S p e c . = T N F P + T N , (4) M C C = T P × T N − F P × F N ( T P + F P ) ( T N + F P ) ( T P + F N ) ( T N + F N ) , (5) where TP, FP, TN, and FN represent the number of true-positive, false-positive, true-negative, and false-negative samples, respectively. Furthermore, the Receiver Operating Characteristic (ROC) curve is employed to describe and compare the performance of a prediction model (Broadhurst and Kell, 2006). The y-axis and x-axis of the ROC curve are the sensitivity (the true positive rate, TPR) and 1 − specificity (the false positive rate, FPR), respectively. The area under the ROC curve (AUC) is a frequently used measure of performance for classification. An AUC of 0.5 means a random classifier, while the ideal value of AUC would be 1.0. For the convenience of presentation, the specific steps of the CPIELA method for identifying plant PPIs are shown in Figure 1.

To verify the high predictive performance of the CPIELA model, we performed it on three plant PPIs datasets: Arabidopsis thaliana, Oryza sativa, and Zea mays. To guarantee the stability of the predictive results, the fivefold cross-validation technique is used to estimate the generalization capacity of the proposed learning model. Because the predictive performance of a rotation forest (ROF) ensemble is highly associated with the number L of decision trees (DT) and the number K of feature subset, a grid search method is conducted for tuning multiple parameters of the RF model. Considering the tradeoff between the computational complexity and accuracy rate, we set the number of decision trees to 3 and the number of feature subsets to 10 for all experiments.

The experimental results on the Arabidopsis thaliana dataset are outlined in Table 1. It can be seen from Table 1 that the average accuracy of the proposed method is as high as 98.63%. In order to further quantify the prediction performance of the proposed method, some other evaluation measures are calculated. From Table 1, we can observe that the overall sensitivity, precision, specificity, MCC, and AUC are 97.56%, 99.69%, 99.70%, 97.30%, and 0.9954, respectively. The standard deviations of them are 0.43%, 0.10%, 0.09%, 0.42%, and 0.0009, respectively.

For the Zea mays dataset, it can be observed from Table 2 that the proposed CPIELA achieved good performance of accuracy 98.09%, precision 99.03%, sensitivity 97.13%, specificity 99.05%, MCC 96.25%, and AUC 0.9912, respectively. We also tested the CPIELA method on the Oryza sativa dataset. Table 3 lists the predictive results of fivefold cross-validation. We achieved the high accuracy of 94.02%, the precision value of 94.39%, the sensitivity value of 93.63%, the specificity value of 94.43%, the MCC value of 88.79%, and the AUC value of 0.9581 on the Oryza sativa dataset. Furthermore, from Table 3, we can also see that the standard deviations of accuracy, precision, sensitivity, specificity, MCC, and AUC are 1.45%, 2.20%, 1.08%, 2.19%, 2.61%, and 0.014, respectively.

Figures 2A–C plot the ROC curves generated by the CPIELA method on the Arabidopsis thaliana, Zea mays, and Oryza sativa datasets. It can be seen from the above experimental results that the CPIELA method is effective for predicting plant PPIs. The better prediction performance mainly comes from the discriminative LOOP descriptors and the powerful ROF classifier. More specifically, the PSSM not only encodes the sequence into the matrix but also obtains sufficient evolutionary information on plant proteins, which can significantly improve the prediction accuracy. As a popular ensemble classifier, the ROF model has a considerably high predictive capability for identifying potential PPIs, making us more convinced that the proposed CPIELA can be a useful tool for predicting plant PPIs.

In this section, we conduct an experiment to compare the prediction performance of the state-of-the-art SVM classifier (Chih-Chung and Chih-Jen, 2011), the standard random forest (RF), and the rotation forest (ROF). The experimental results of the above-mentioned classifiers combined with the LOOP descriptor are listed in Table 4. It can be seen from Table 4 that the average accuracies of SVM, RF, and ROF classifier on the Arabidopsis thaliana dataset are 89.37%, 97.21%, and 98.63%, respectively. To demonstrate the predictive ability of the proposed CPIELA more comprehensively, we also computed the values of sensitivity, precision, MCC, and AUC. As observed from Table 4, the proposed CPIELA model achieved the highest performance on the Arabidopsis thaliana dataset with the sensitivity value of 97.56%, precision value of 99.69%, MCC value of 97.30%, and AUC value of 0.9954. In addition, we could observe in detail from Table 4 that the corresponding standard deviation of accuracy, precision, sensitivity, MCC, and AUC is 0.22%, 0.10%, 0.43%, 0.42%, and 0.0009, respectively.

The precision, sensitivity, MCC, and AUC of the SVM classifier are 94.16%, 83.95%, 80.89%, and 0.9495, respectively. The precision, sensitivity, MCC, and AUC of the RF model are 98.22%, 96.15%, 94.58%, and 0.9720, respectively. It is evident that the SVM model achieved poor accuracy compared to the RF and ROF classifiers. It is specifically notable in the case of MCC. The proposed CPIELA method is the model with the best predictive results in terms of MCC for Arabidopsis thaliana PPIs datasets.

We also pay attention to the other two plant PPIs datasets. Table 4 shows the experimental results obtain on the Zea mays dataset, from which we can observe that the average accuracies of SVM, RF, and ROF classifiers are 84.46%, 94.65%, and 98.09%, respectively. Here, it could also be observed that the average accuracies obtained by the SVM, RF, and ROF models on the Oryza sativa dataset are 88.95%, 90.90%, and 94.02%, respectively.

Figures 3A–C show the ROC curve generated by different classifiers with the LOOP descriptor on the Arabidopsis thaliana, Zea mays, and Oryza sativa PPIs datasets, respectively.

In order to further evaluate the predictive performance of CPIELA, we also compared it with several other protein descriptors. In the experiment, local phase quantization (LPQ), first proposed by Ojansivu et al. (2008), Heikkilä et al. (2014), is employed to evaluate the performance of predicting plant PPIs on Arabidopsis thaliana, Zea mays, and Oryza sativa datasets, respectively. The fivefold cross-validation results of the LOOP and LPQ descriptor combined with ROF classifier on three plant PPIs datasets are summarized in Table 5. It can be observed that the LPQ descriptor achieved 73.17% average accuracy, 72.55% average sensitivity, 73.46% average precision, 73.79% average specificity, 60.74% average MCC, and 0.7873 average AUC on the Arabidopsis thaliana dataset. Meanwhile, the LOOP descriptor achieved 98.63% average accuracy, 97.56% average sensitivity, 99.69% average precision, 99.70% average specificity, 97.30% average MCC, and 0.9954 average AUC on the Arabidopsis thaliana dataset.

As we can see in Figure 3D, for Arabidopsis thaliana, the area under the ROC curve corresponding to LOOP is significantly larger than that of the LPQ descriptor. In terms of the indicator AUC, the AUC value of LOOP reaches 0.9957, which is 26.42% higher than that of the LPQ method. The experimental results also demonstrate that the LOOP descriptor exhibited significantly better performance than the LPQ descriptor on the other two plant PPIs datasets. Furthermore, the higher prediction accuracies and lower standard deviations indicate that the LOOP descriptor can effectively extract the features from protein sequence and significantly improve the predictive performance in plant PPIs prediction.

In the previous works, some researchers have put forward several computational approaches to solve the problem of plant PPIs prediction (Pan et al., 2021a; Pan et al., 2021b). Therefore, we compare the predictive performance of CPIELA against the recently proposed approaches. Experimental results of predictive performance comparison on Oryza sativa dataset between CPIELA and several related models are demonstrated in Table 6. It can be clearly observed from this table that the range of AUC generated by other approaches is from 0.7931 to 0.9440, the range of MCC obtained is from 37.39% to 78.26%, the range of accuracy generated by other models is from 66.63% to 82.60%, and the corresponding values obtained by CPIELA are 0.9581, 88.79%, and 94.02%. It shows that the predictive performance (AUC, MCC, accuracy) of CPIELA is better than that of existing models. We can see from Table 6 that the CPIELA model also gives better performance than the above-mentioned models for sensitivity, precision, and specificity metrics. Overall, the proposed CPIELA model shows better predictive performance than the previous prediction model on the Oryza sativa dataset.

With the rapid advances of high-throughput biological technologies, many resources currently provide plant PPIs for different species. To construct a plant PPIs prediction model and compare it with existing prediction approaches, three plant PPIs datasets (Zea mays, Oryza sativa, and Arabidopsis thaliana) are employed in this work. For the interactome of Zea mays, 14,230 experimentally verified PPIs are downloaded from the Protein-Protein Interaction Database for Maize (PPIM) (Zhu et al., 2017) and agriGO (Tian et al., 2017). Because there is no available confirmed non-interacting plant PPIs, constructing negative PPIs dataset remains a challenging task in PPIs prediction. In order to build the negative dataset, 14,230 maize protein pairs located in different subcellular localization are randomly chose in this study. Consequently, the whole Zea mays dataset consists of 28,460 protein pairs.

A total of 4,800 non-redundant Oryza sativa protein interaction pairs among 1,834 rice proteins are downloaded from the PRIN database (http://bis.zju.edu.cn/prin) (Gu et al., 2011). The Arabidopsis thaliana PPIs dataset is collected from the public databases of BioGrid (Rose et al., 2018), TAIR (Yon et al., 2003), and IntAct (Kerrien et al., 2011). Meanwhile, the protein pairs containing a protein with fewer than fifty amino acids or having ≤40% sequence identity are removed. Finally, the 28,110 protein pairs from 7,437 Arabidopsis thaliana proteins comprise the positive dataset. The 28,110 protein pairs occurring in two different subcellular localizations are generated as a negative PPIs dataset. In this way, the whole Arabidopsis thaliana dataset is constructed by more than 56,220 protein pairs. The summary of plant PPIs used in this study is shown in Table 7.

The position-specific scoring matrix (PSSM) was first proposed by Gribskov et al. to detect distantly related proteins and is now widely applied for the representation and prediction of PPIs (Gribskov et al., 1987; You et al., 2014; Wong et al., 2015; You et al., 2016b). A PSSM for a given protein is a 20×M matrix P = { P i j : i = 1,2 , … , 20   a n d   j = 1,2 , … , M } , where M is the length of the target protein sequence. The PSSM matrix p can be represented as follows: P = [ P 1,1 P 1,2       ⋯ P 1 , M P 2,1 P 2,2       ⋯ P 2 , M ⋮             ⋮               ⋮         ⋮     P 20,1 P 20,2       ⋯ P 20 , M ] , (6) where each element denotes the log-likelihood of the particular amino acid substitution at that position in the template. For example, it assigns a value P i , j for the ith residue in the jth position of the query protein sequence with a small score representing a weekly conserved position and a large score indicating a highly conserved position.

In the experiment, we employed the position-specific iterated BLAST (PSI-BLAST) tool and SwissProt database to build the PSSM for each protein amino acid sequence (Altschul et al., 1997; Altschul and Koonin, 1998; Amos and Rolf, 1999). The PSI-BLAST approach is highly sensitive in discovering similar proteins in distantly related species and new members of the protein family. To obtain high homologous sequences, we set the number of iterations to three, the e-value to 0.001, and the default value to the other parameters. The PSI-BLAST tool was downloaded from http://blast.ncbi.nlm.nih.gov/Blast.cgi.

Tapabrata et al. presented the local optimal-oriented pattern (LOOP) as a novel binary local pattern descriptor that encodes rotation invariance into the main formulation of the local binary descriptor (Chakraborti et al., 2018). The LOOP descriptor is an improvement designed on local binary pattern (LBP) (Ojala et al., 1994) and local directional pattern (LDP) (Jabid et al., 2010).

Given an image I , let i c be the intensity at pixel ( x c , y c ) . Suppose i n   ( n = 0 ,   1 , … ,   7 ) represents the intensity of a pixel in the 3 × 3 neighborhood of ( x c , y c ) keeping out the pixel i c . Figure 4 shows the Kirsch edge detectors centered at ( x c , y c ) in eight directions. Let m n   ( n = 0 ,   1 , … ,   7 ) be the eight responses of the Kirsch masks, corresponding to pixels with intensity i n   ( n = 0 ,   1 , … ,   7 ) . Suppose m k is the kth highest Kirsch activation. An exponential ω n for each of these pixels is assigned based on the rank of the magnitude of m n amongst the eight Kirsch mask outputs. Finally, the value of LOOP for the pixel ( x c , y c ) is calculated as follows: LOOP ( x c , y c ) = ∑ n = 0 7 s ( i n − i c ) .2 ω n , (7) where s ( x ) = { 1                     i f   x ≥ 0 0             o t h e r w i s e . (8) where i c denotes the intensity of the center pixel ( x , y ) . In our study, the input PSSM is a 20×M matrix. Thus, each protein sequence is represented by a 256-dimensional feature vector after employing the LOOP descriptor.

Rotation forest (ROF) is a popular ensemble classifier firstly proposed by Rodriguez et al. (2006). Compared with other classifiers, the ROF model is successfully used in dealing with many computational biology problems (He et al., 2021b). The basic idea of the rotation forest model is to simultaneously improve both individual accuracy and member diversity within an ensemble classifier. The success of the ROF method is attributed to the base classifier and rotation matrix created by the transformation algorithms, including principal component analysis (PCA) (Jolliffe, 2002), local fisher discriminant analysis (LFDA) (Masashi et al., 2010), maximum noise fraction (MNF) (Gordon, 2000), and independent component analysis (ICA) (Prasad, 2001). The framework of the ROF model is described as follows.

Let X be the training samples in the form of an N × n matrix, where N represents the number of samples and n denotes the number of features, respectively. Let a vector Y = [ y 1 , … , y N ] T be the corresponding class label, where y j ∈ { ω 1 , … , ω c } . Let F be the feature set, and F is randomly split into K equal subset. Suppose L is the number of base decision trees in the ensemble model, which could be represented as Γ 1 , Γ 2 , … , Γ L , respectively. It should be noticed that the number of base classifiers (L) and the number of feature subsets (K) are the two important tuning parameters for the ROF classifier. The training dataset for a single classifier Γ i is preprocessed as follows:

1) Randomly divide F into K disjointed feature sets, each subset containing M = n / K features.

The columns of R i should be rearranged to R i a according to the original feature set. Then, the transformed training dataset for classifier Γ i will become X R i a . In this way, all classifiers are trained in parallel.

In the prediction phase, provided a testing sample x , let d i , k ( x R i a ) be the probability generated by the classifier Γ i to the hypothesis that x belongs to class ω k . Then, the confidence of each class is calculated by means of the average combination as follows: μ k ( x ) = 1 L ∑ i = 1 L d i , k ( x R i a ) ,       k = 1 , … , c . (10)

Finally, the testing sample x is assigned to the class with the largest confidence.