In this paper, the databases, viz. DrugBank [7], SuperTarget [18], BRENDA [19], and KEGG BRITE [6] provide four benchmark datasets including Enzyme, Ion Channel, GPCRs, and Nuclear Receptor for us to execute the established model. Enzyme data set stores 445 drugs, 664 proteins, and 2926 DTIs. Ion channel data set stores 210 drugs, 204 proteins, and 1467 DTIs. GPCRs data set stores 223 drugs, 95 proteins, and 635 DTIs. Nuclear Receptor data set stores 54 drugs, 26 proteins, and 90 DTIs. Table 1 clearly listed the experimental statistics of these benchmark datasets.

Drug and protein interactions were represented as a bipartite graph; drugs and proteins formed the nodes of the graph, and the verified interactions between them were denoted by edges within the graph. In the experiments, all drug-target pairs which are connected by edges are categorized to positive dataset, the other pairs are treated as negative samples. Considering the number of the nodes, the known interactions only take a little account of all relationships of drug-target pairs. Take GPCRs dataset for an example, there are 42,840 (210 $\times$ 204) types of relationships exist in the network. However, the interactions which have been certified by biotechnology are 1467 which accounts for 3.42%. Consequently, the down sampling algorithm is employed to extract the same number of negative samples as the positive data set to ensure sample balance. The 1467 positive samples are verified by clinical experiments, and the remaining samples were verified as negative samples. However, it is hardly to ignore the false verification caused by the error in the clinical experiment. Meanwhile, considering the number of negative samples only accounted for 3.55% of the remaining samples, the possibility that positive samples which exist in the remaining samples are assigned to negative data set can be ignored for the huge quantity gap.

Recently, the molecular fingerprints which contain chemical substructure information can effectively reflect drug structure [20]. It transforms the molecular structures into a series of binary fingerprint sequences by detecting specific fragments in the molecular structure [21]. Although the molecular is divided into several independent parts, it still ensures the integrality of the entire drug structural information [22]. Studies substantiate that the molecular fingerprints inhibit the information loss and accumulated error of screening procedures. Meanwhile, it also reduces the complexity of the calculation in the description process. Specifically, when the fraction matches a molecular substructure, the corresponding position of carrier will be assigned as 1. Mature fingerprint databases provide reliable tools for the generation of molecular fingerprints. We selected the fingerprint map which contains 881 substructures from Pubchem system (https://pubchem.ncbi.nlm.nih.gov/) [23]. Therefore, the describers of drug molecules are completely converted into a series of 881-dimentional Boolean vectors. Fig. 2 gives the transformation of Zanamivir into a fingerprint.

In recent years, various Physico-chemical methods are applied to numerically characterize protein which is composed of 20 types of letters [24]. Position-Specific Scoring Matrix (PSSM) is extensively utilized in protein binding site prediction, protein secondary structure prediction, and protein subcellular localization [25]. In this section, PSSM is employed to excavate the evolutionary information by calculating the probability of an amino acid emerges in a specific location of protein primary sequence. PSSM matrix is showed as follows.

(1)

where PSSM is a matrix, where L$\times$ 20 denotes the length of the target, and 20 represents the number of amino acids. ${\mathrm{\ell }}_{i,j}$ represents the evolutionary score that $ith$ residue mutate into $jth$ amino acid during the evolutionary process. After optimizing Position-Specific Iterated Basic Local Alignment Search Tool (PSI-BLAST), parameter e is set to 0.001 and the iteration frequency is set to 3. Fig. 3 gives the example of Lipoprotein Lipase converting into PSSM.

Fuzzy Local Ternary Pattern (FLTP) can be utilized to precisely describe the texture feature, and it has a wide application in preventing face spoofing and image tampering areas [26]. For the anti-rotation ability of FLTP, it is also robust to the noise in the image. This method dynamically calculates the threshold based on Weber’s law to extract multiple features. Meanwhile, it can be extended to circles and neighborhoods with different radius. In this paper, FLTP is employed to describe the characteristics of PSSMs. The algorithm converts the difference between neighborhood pixels and center pixels into the upper and lower binary codes. The upper binary code can be expressed as $FLT{P}_{-}{S}_{P,R}^{upper}$, the lower one can be expressed as $FLT{P}_{-}{S}_{P,R}^{lower}$. The complete describer is defined as follows:

(2)$$FLT{P}_{-}{S}_{P,R}=[FLT{P}_{-}{S}_{P,R}^{upper},FLT{P}_{-}{S}_{P,R}^{lower}$$

where $FLT{P}_{-}{S}_{P,R}^{upper}$ can be calculated as follows.

(3)$$FLT{P}_{-}{S}_{P,R}^{\text{upper}}(x_c,y_c)=\sum _{i=0}^{P-1}s\left(i_i-\left(i_c+\tau \right)\right)2^i$$

(4)

where $FLT{P}_{-}{S}_{P,R}^{lower}$ can be calculated as follows.

(5)$$FLT{P}_{-}{S}_{P,R}^{lower}(x_c,y_c)=\sum _{i=0}^{P-1}s\left(i_i-\left(i_c-\tau \right)\right)2^i$$

(6)

where $(x_c,y_c)$ represents the circular central pixel, and $i_i$ represents the gray value of neighborhood pixel. When calculating the upper binary code, if the gray value of neighborhood pixel is greater than $i_c+\tau$, the neighborhood pixel is marked as 1. When calculating the lower binary code, if the gray value of the neighborhood pixel is less than $i_c-\tau$, the neighborhood pixel is marked as 0. The gray value of the circular central pixel $i_i$ which was generated by the nonlinear interpolation algorithm and dynamic threshold $\tau$ are calculated as follows.

(7)$$i_i=I(x_{\mathrm{c}}+R\sin \frac{2\pi i}{P},y_c-R\cos \frac{2\pi i}{P})$$

(8)$$\frac{\left|i_i-i_c\right|}{i_c}=\tau$$

Finally, the FLTP feature vector can be obtained as follow.

(9)$$H(k)=\sum _{i=0}^I\sum _{j=0}^{J}f(FLT{P}_{-}{S}_{P,R}(i,j),k),k\in [0,255]$$

In this experiment, the radius of the circular domain R = 1, the number of pixels in circular domain P = 8. The upper and lower binary codes are transformed into 256 dimensional vectors respectively. Hence, the entire descriptor of PSSM is a matrix of 1 $\times$ 512.

Rodriguez et al. [27] proposed rotation forest (RF) based on integrated forest [27, 28]. This ensemble classifier succeeds in the classification of small-sized data set. Significantly, RF also has good effects on promoting sample difference [29]. Within the experiments, we utilized rotation forest to detect DTIs. Firstly, RF stochastically separates the sample set into L disjoint subsets. Subsequently, Principal Component Analysis (PCA) approaches to convert subsets to generate rotation forest. Finally, send them to different base classifiers for scorning each subtree. The matrix $C$ of $n\times N$ is regarded to be the train set containing $N$ features of $n$ samples, and $T={(t_1,t_2,\mathrm{\cdots },t_n)}^T$ gathers the labels of different samples. The method has $K$ base classifiers $R_i$. The sequential training steps of the base classifier are as follows.

(I) Follow obtaining the optimized parameter L, dataset P is separated to L disjoint subsets stochastically, each subset has $N/L$ features.

(II) Let $P_{i,j}$ represents $jth$ the subset of P, and $C_{i,j}$ denotes the feature set of $P_{i,j}$. Then calculate the new training features set $C_{i,j}^{\prime }$ by bootstrap sampling on 75% of $C_{i,j}$.

(III) Execute PCA on $C_{i,j}^{\prime }$ to get the principal component coefficients $a_{i,j}^{(1)},a_{i,j}^{(2)},\mathrm{\cdots }{a}_{i,j}^{\left(m_j\right)}$.

(IV) These coefficients make up the sparse rotation matrix $Q_i$ as:

In the process of classification, the possibility that sample x belongs to category $t_i$ is $d_{i,j}\left(x{Q}_i^a\right)$ yielded by base classifier $R_i$. Afterword, calculate the confidence degrees that x belongs to different classes as follows:

(11)$${\theta }_j(x)=\frac{1}{K}\sum _{i=1}^K{d}_{i,j}\left(x{Q}_i^a\right)$$

Finally, the sample x will be classified in accordance with the degree.

For improving the reliability of the experimental performance, the evaluative indices, viz. accuracy (Acc.), precision (Prec.), sensitivity (Sen.), specificity (Spec.), and Matthews correlation coefficient (MCC) are utilized to analyze the results of 5-fold CV.

(12)$$Acc.=\frac{TP+TN}{TP+TN+FP+FN}$$

(13)$$\mathrm{Pr}ec.=\frac{TP}{TP+FP}$$

(14)$$\mathit{\text{Sen.}}=\frac{TP}{TP+FN}$$

(15)$$\text{𝑆𝑝𝑒𝑐}.=\frac{TN}{TP+FP}$$

(16)$$\mathrm{MCC}=\frac{\mathrm{TP}\times \mathrm{TN}-\mathrm{FP}\times \mathrm{FN}}{\sqrt{(\mathrm{TP}+\mathrm{FP})\times (\mathrm{TP}+\mathrm{FN})\times (\mathrm{TN}+\mathrm{FN})\times (\mathrm{TN}+\mathrm{FP})}}$$

where true positive (TP) records the aggregate of interacting drug-target pairs which were assigned to positive set; true negative (TN) denotes the sum of non-interacting drug-target pairs which were assigned to negative set; false positive (FP) is the quantity of non-interacting drug-target pairs which were assigned in positive set; false negative (FN) denotes the count of interacting drug-target pairs which were assigned to negative set. In addition, the receiver operating characteristic (ROC) curves were pictured to visualize the prediction results [30], the area under the curves (AUC) was also attached to ROC for justifying the established model [31]. We also utilized PR curves and AUPR values to indicate the sample balance and model performance.

In RF classifier, the main parameters K and L denote the numbers of feature sub-sets and decision trees which affect the classification accuracy. To get the optimal parameters, this paper employs grid-search algorithm to study the influence of parameters on prediction results [32]. When L-value increased from 0 to 38, the experimental results show that the accuracy was increasing, then it decreased sharply. Meanwhile, the accuracy was growing with the increase of K-value. In consideration of the model efficiency, the optimal parameters K and L are set to 18 and 38, respectively. Fig. 4 depicts the prediction accuracy surface with factors of K-value and L-value.

To certify the feasibility of the established model and avoid over-fitting, we executed 5-fold CV on four benchmark data sets with the same parameters. Specifically, each data set is separated into 5 equal-sized and disjointed fractions. The independent fractions take turns to be treated as test sets, while the other fractions serve as train sets. Tables 2,3,4,5 display the experimental results of our method on four standard data sets.

The statistics of results has been shown in Table 6. The average criteria of accuracy, sensitivity, precision, specificity and Matthews correlation coefficient are 89.08%, 90.32%, 87.52%, 90.62%, and 78.17% on Enzyme data set. Their standard deviations are 0.68%, 0.59%, 1.21%, 0.43%, and 1.32%. We obtained the average criteria of 86.14%, 86.46%, 85.69%, 86.60%, and 72.28% on Ion Channel data set. Their standard deviations are 1.67%, 2.61%, 1.18%, 2.42%, and 3.37%. On GPCRs data set, our model generated the average criteria of 82.41%, 82.10%, 81.97%, 82.96%, and 64.85% with standard deviation of 2.20%, 3.48%, 3.12%, 1.60%, and 4.43%. In terms of Nuclear Receptor dataset, the average criteria are 78.40%, 76.33%, 77.78%, 76.43%, and 56.02%, respectively, with standard deviation of 5.07%, 7.02%, 14.65%, 5.99%, and 12.21%. As can be noted, the small size of Nuclear Receptor data set leads to a higher standard deviation. Figs. 5,6,7,8 record the performance of our model on four benchmark datasets, while the average AUC values of 0.9535, 0.9292, 0.8901, and 0.8534 are also attached to them. Figs. 9,10,11,12 plot the PR curve of our model on four golden standard datasets, while the average AUPR values of 0.9608, 0.9345, 0.8941, and 0.8636 are also attached to them.

For strictly validating the feature describing ability of fuzzy local ternary pattern (FLTP) method. We constructed the comparative experiment by replacing FLTP descriptors with Zernike Moments (ZMs) descriptors which have strong Rotational Invariance [33, 34]. ZMs method is widely utilized in the field of edge detection by extracting global feature information at different scales [35]. Table 7 shows the comparison of ZMs and FLTP with the same classifier. These experimental statistic shows that FLTP method has a significant performance improvement compared with Zernike Moments on benchmarks. The criteria values entirely get promoted on Enzyme, Ion Channel, and GPCRs dataset. Fig. 13 displays the mean ROC curves of FLTP model and ZMs model by an interpolation method. It is noteworthy that the AUC values of FLTP-embedded model are comprehensive greater than ZMs model, and the mean value gaps attain 2.55%, 0.89%, 1.17%, and 4.09%, respectively. The results indicate that our model provides an effective way to characterize PSSM for detecting potential DTIs.

Thus far, some machine learning-based classifiers are utilized to identify DTIs. To fairly verify the performance of the proposed model, we embed the state of art support vector machine (SVM) and light gradient boosting machine (LGBM) algorithm into our model with fuzzy local ternary pattern. Within RF classifier, we set parameters K = 18, L = 38 which was discussed above. The SVM utilized inner product kernel function instead of nonlinear mapping to high dimensional space, it also adopts small-sample learning method to greatly simplify the process of classification and regression. There are 400 experiments with different combinations of parameters c and g were carried out to get the highest accuracy, and we set c-value, g-value to 0.7 and 40, respectively. The kernel of SVM was select as radial basis function (RBF) based on LIBSVM tool. The LGBM method is the improved gradient boosting decision trees (GBDT) algorithm to reduce the time cost and power consumption in industrial applications. After parameter optimizations, the leaves-number, the learning rate, and the training rounds were set to 55, 0.05, and 37, respectively.

Fig. 14 records the comparison between RF, LGBM, and SVM on Enzyme, Ion Channel, GPCRs, and Nuclear Receptor data sets. The results indicate that model which embeds RF classifier has higher prediction accuracy. Compared with SVM classifier, the average accuracy promotions of RF are 10.49%, 10.57%, 8.40%, and 15.20%, the accuracy gaps between RF and LGBM are 3.93%, 3.24%, 3.21%, 6.77% on four benchmark dataset. Figs. 15,16 plot the ROC curves of the golden standard datasets based on the rates of 1-specificity against sensitivity. The model which has higher AUC values predict more accurate. As shown in Figs. 15,16, the AUC value gaps of four data sets attain to 0.1051, 0.1162, 0.0944, and 0.2232 between RF and SVM, the value gaps between RF and LGBM attain to 0.1013, 0.1013, 0.0910, and 0.1329, respectively. Therefore, it is considered that the proposed model is more efficient at predicting DTIs.

So far, numerous advanced models have been established to predict DTIs and assist drug design. In this section, we compared our model with partial state-of-art models for fully evaluating the model performance by adopting 5-fold CV. After experimenting the previous methods such as SIMCOMP [36], DCT [37], Bigram-PSSM [38], LOOP [39] on benchmark datasets. Table 8 gives the comparison of AUC value and AUPR values. It is clearly that the performance of the established model has risen significantly. Although the AUC value of our model is 0.006 lower than LOOP on Ion Channel dataset, the AUC values of Enzyme, GPCRs, and Nuclear Receptors have grown 0.003, 0.004, and 0.034, respectively, and the AUPR values of four benchmark datasets have grown 0.028, 0.014, 0.029, and 0.042, respectively. As a result, the experiments substantiate that the model which combining FLTP descriptors and rotation forest can remarkably enhance the performance of predicting DTIs.