LDA-VGHB: identifying potential lncRNA–disease associations with singular value decomposition, variational graph auto-encoder and heterogeneous Newton boosting machine

Abstract

Long noncoding RNAs (lncRNAs) participate in various biological processes and have close linkages with diseases. In vivo and in vitro experiments have validated many associations between lncRNAs and diseases. However, biological experiments are time-consuming and expensive. Here, we introduce LDA-VGHB, an lncRNA–disease association (LDA) identification framework, by incorporating feature extraction based on singular value decomposition and variational graph autoencoder and LDA classification based on heterogeneous Newton boosting machine. LDA-VGHB was compared with four classical LDA prediction methods (i.e. SDLDA, LDNFSGB, IPCARF and LDASR) and four popular boosting models (XGBoost, AdaBoost, CatBoost and LightGBM) under 5-fold cross-validations on lncRNAs, diseases, lncRNA–disease pairs and independent lncRNAs and independent diseases, respectively. It greatly outperformed the other methods with its prominent performance under four different cross-validations on the lncRNADisease and MNDR databases. We further investigated potential lncRNAs for lung cancer, breast cancer, colorectal cancer and kidney neoplasms and inferred the top 20 lncRNAs associated with them among all their unobserved lncRNAs. The results showed that most of the predicted top 20 lncRNAs have been verified by biomedical experiments provided by the Lnc2Cancer 3.0, lncRNADisease v2.0 and RNADisease databases as well as publications. We found that HAR1A, KCNQ1DN, ZFAT-AS1 and HAR1B could associate with lung cancer, breast cancer, colorectal cancer and kidney neoplasms, respectively. The results need further biological experimental validation. We foresee that LDA-VGHB was capable of identifying possible lncRNAs for complex diseases. LDA-VGHB is publicly available at https://github.com/plhhnu/LDA-VGHB.

INTRODUCTION

Long noncoding RNAs (lncRNAs) with more than 200 nucleotides are a key class of genes involved in various biological functions [1]. lncRNAs participate in multiple biological processes including gene transcription and expression, chromatin remodeling, transcriptional and post-transcriptional regulation [2]. Diseases (i.e. immune responses and cancers) may produce when lncRNAs fail to regulate the biological processes. That is, lncRNAs have close linkages with tumorigenesis, progression and drug resistance [3, 4]. Thus, they are a class of potential diagnostic and prognostic biomarkers of complex disease [5–10]. For example, lncRNA MALAT1 can sponge miR-106b-5p to induce the progression of colorectal cancers [11]. The oncogenic affect of lncRNA H19 can be inhibited through the under-regulation of renal carcinoma cells [12]. The lack of FARSA-AS1 can hinder tumor growth and metastasis [13]. The overexpressions of MNX1-AS1 and MALAT1 demonstrate high sensitivity and specificity in multiple tumor tissues [14–16]. MEG3 rs3087918 has been used to reduce the risk of breast cancer [17]. CRNDE promoted the proliferation and metastasis of hepatocellular carcinoma [18]. WWC2-AS1 was highly expressed in radiation-induced intestinal fibrosis [19]. In summary, there are complex associations between lncRNAs and diseases.

With the rapid advance of RNA sequencing technologies, many platforms provide massive RNA-relevant data resources, which significantly improved various association prediction for human cancers [20–24]. However, experimental techniques are high-cost, time-consuming and laborious [25–28]. Notably, LncRNADisease2.0 [29], Lnc2Cancer [30], NRED [31] and MNDR v2.0 [32] provide numerous lncRNA–disease association (LDA) information. Based on these databases, substantial computational methods have been developed. These methods include network-based methods and machine-learning-based methods [25, 33].

Network-based LDA prediction methods first construct a heterogeneous network, and then infer potential LDAs through random walk, label propagation or matrix decomposition. Chen et al. conducted a series of works for LDA prediction based on various biological information [34–37], for example, lncRNA expression profile-based method [34], lncRNA similarity and disease similarity-based method [35], KATZ [36] and micro RNA information-based method [37]. Xie et al. [38–41] presented several LDA prediction methods, HAUBRW [38], LDA-LNSUBRW [39], RWSF-BLP [40] and SSMF-BLNP [41]. HAUBRW [38] incorporated heat spread, probability diffusion and unbalanced bi-random walk. LDA-LNSUBRW [39] combined linear neighborhood similarity and unbalanced bi-random walk. RWSF-BLP [40] used random walk-based multi-similarity fusion with bidirectional label propagation. SSMF-BLNP [41] integrated selective similarity matrix fusion and bidirectional linear neighborhood label propagation. In addition, several network-based methods have been developed to identify potential LDAs. These methods include multi-layer network model (MHRWR) [42], Laplace normalized random walk with restart (LRWRHLDA) [43], weighted graph regularized collaborative matrix factorization (WGRCMF) [44], collaborative matrix factorization with the maximized correntropy (LDCMFC) [45], dual sparse collaborative matrix factorization (WGRCMF) [44] and graph regularized nonnegative matrix factorization (LDGRNMF) [46]. Based on existing studies, Chen et al. [25, 26] summarized LDA identification algorithms and lncRNA function prediction models. Heterogeneous network-based methods can fuse diverse multi-relational data and encode various inter- and intra-relations between lncRNAs and diseases, and thus have obtained an increasing attention in LDA prediction [47–49]. However, network-based methods rely heavily on heterogeneous LDA network and fail to find potential associations for an orphan lncRNA or disease.

Machine learning techniques especially deep learning have obtained wide applications in bioinformatics due to their better classification performance [50–55]. For LDA prediction, the type of methods first extract the features of lncRNAs and diseases, and design machine learning models to find possible LDAs [56–58]. These models include random forest regression [59], bidirectional generative adversarial network (BiGAN) [60], graph convolutional matrix completion (GCRFLDA) [2], graph autoencoder and random forest (GAERF) [61], graph attention network (GANLDA) [62], graph convolution network with conditional random field [63], combination of deep learning and positive-unlabeled learning [64] and heterogeneous graph attention network with meta-paths [65]. Machine learning-based methods efficiently improve LDA prediction; however, they are susceptible to noisy and irrelevant data. In addition, they need to extract the optimal features from biological information and topological structures of lncRNAs and diseases.

To improve the LDA prediction accuracy and identify potential associations for an orphan lncRNA or disease, in this manuscript, we developed LDA-VGHB, a novel method for identifying possible LDA by incorporating LDA feature extraction based on singular value decomposition (SVD) and variational graph auto-encoder (VGAE) and LDA classification based on heterogeneous Newton boosting machine. The LDA-VGHB performance has been validated under 5-fold cross-validations (CVs) on lncRNAs, diseases, lncRNA–disease pairs and independent lncRNAs and independent diseases. LDA-VGHB was able to accurately predict potential linkages between lncRNAs and diseases on the lncRNADisease and MNDR databases.

MATERIAL AND METHODS

Data preparation

Two human LDA datasets were collected [64]. The two datasets are from the lncRNADisease database [66] and the MNDR database [32], respectively. After excluding diseases with irregular names or without MESH information or lncRNAs without sequence information in each dataset, we obtained the two preprocessed LDA datasets. The detailed information about the datasets is shown in Table 1.

Consequently, an LDA network with |$n$| lncRNAs and |$m$| diseases is represented as |$\boldsymbol{Y} \in{\Re ^{n \times m}}$|⁠, where each element |$y_{i j}$| is defined by Eq. (1):

Based on the two datasets, we proposed a novel computational framework LDA-VGHB for predicting possible LDAs. As shown in Figure 1, first, lncRNA features and disease features are extracted by integrating lncRNA and disease similarity computation, linear feature extraction based on SVD and nonlinear feature extraction based on VGAE. Subsequently, unknown lncRNA–disease pairs are classified through a heterogeneous Newton boosting machine.

Similarity computation

To measure disease similarity, we first calculate their semantic similarity matrix |$\boldsymbol{S}_d^{sem}$| based on their MeSH descriptors using the IDSSIM model [67]. Since several diseases are lack of directed acyclic graph in the MeSH database, we are unable to compute their semantic similarity. Thus, we utilize Gaussian association profile (GAP) kernel similarity [68] as a complement to disease semantic similarity and further measure their similarity. For two diseases |$d_i$| and |$d_j$|⁠, let |${\boldsymbol{Y}}_{.i}$| and |${\boldsymbol{Y}}_{.j}$| be their GAPs, their GAP kernel similarity is defined by Eq. (2):

where |${\boldsymbol{Y}}_{.i}$| and |${\boldsymbol{Y}}_{.j}$| denote the |$i$|-th and |$j$|-th columns of |$\boldsymbol{Y}$|⁠, respectively.

Semantic similarity and GAP kernel similarity measure disease similarity from biological significance and topological structures, respectively. Subsequently, disease similarity matrix |$\boldsymbol{S}_d$| is constructed by combining the two types of similarities by (3):

where |$\alpha $| is a weight parameter.

Similarly, lncRNA functional similarity |$\boldsymbol{S}_l^{fun}$| is computed based on disease semantic similarities according to the IDSSIM model [67]. lncRNA GAP kernel similarity matrix |$\boldsymbol{G}_l$| is computed by Eq. (4):

where |${\boldsymbol{Y}}_{i.}$| and |${\boldsymbol{Y}}_{j.}$| denote the |$i$|-th and |$j$|-th rows of |$\boldsymbol{Y}$|⁠, respectively.

Consequently, lncRNA similarity matrix |$\boldsymbol{S}_l$| is constructed by Eq. (5):

Feature Extraction

Linear feature extraction

The SVD technique is a generalization of the eigen decomposition [69] and has been widely applied to feature extraction. By eigen decomposition, SVD decomposes a rectangular matrix into two orthogonal matrices and one diagonal matrix. In this study, we use SVD to extract linear features for diseases and lncRNAs. First, the LDA matrix |$\boldsymbol{Y} \in{\Re ^{n \times m}}$| is factorized into three matrices by Eq. (6):

where |$\boldsymbol{U}\in{R}^{{n\times n}}$| and |$\boldsymbol{V}\in{R}^{{m\times m}}$| are two real matrices, |$\boldsymbol{V}^{T}$| denotes the transpose of |$\boldsymbol{V}$| and |$\Sigma{\in }\boldsymbol{Y}^{{n\times m}}$| is a diagonal matrix where the |$i$|-th element |$\sigma _{i}$| denotes the |$i$|-th singular value of |$\boldsymbol{Y}$| and |$\sigma _{1}\geq \sigma _{2}\geq \cdots \geq \sigma _{n}\geq 0$|⁠.

Next, the |$k$| largest singular values are used to construct an approximation representation by Eq. (7);

Consequently, |$\boldsymbol{U}_{i}$| and |$\boldsymbol{V}_{j}^{T}$| are applied to characterize linear features of |$l_i$| and |$d_j$|⁠, respectively.

Nonlinear feature extraction

Variational graph autoencoder [70] efficiently combines graph convolutional network (GCN) and autoencoder. It fully utilizes latent variables of variable autoencoder and interpretable latent representation ability of GCN. Thus, it is widely applied to graph-structured data by incorporating graph structure and data distribution [2]. In this section, we use VGAE to extract nonlinear features for diseases and lncRNAs.

GCN [71] implements convolutional operations based on graph structures with non-Euclidean data. It can better extract node features by incorporating neighboring nodes’ characteristics and graph structures. It mainly comprises two categories based on different localized convolutional filter ways: spatial-based methods and spectral-based methods. In comparison with spatial-based methods, spectral-based methods obtain better performance via the spectrum of graph Laplacian [71, 72]. Thus, we use spectral-based methods [73] to extract features for lncRNAs and diseases from their similarity networks.

Let similarity matrix |${\boldsymbol{S}}_l$| denote the adjacency matrix of |$n$| lncRNAs. The initial scalar features of each lncRNA are represented through one corresponding row of the LDA matrix |$\boldsymbol{Y}$|⁠. Consequently, we obtain the initial scalar feature matrix |$\boldsymbol{{X}}_{l}^{(0)}$| of |$n$| lncRNAs. Taken the lncRNA similarity matrix |${\boldsymbol{S}}_l$| and initial scalar feature matrix |$\boldsymbol{{X}}_{l}^{(0)}$| as inputs, at the |${t}$|-th layer, GCN transforms the graph signal |$\boldsymbol{X}_{l}^{(t)}$| into a new signal |$\boldsymbol{X}_{l}^{(t+1)}$| for all lncRNAs by Eq. (8):

Here, |$ReLU(\cdot )=max(0,\cdot )$| is a nonlinear activation function, |$\tilde{\boldsymbol{S}}_l=\boldsymbol{S}_l+\boldsymbol{I}_N$| is an adjacency matrix corresponding to |$\boldsymbol{S}_l$| with all diagonal element value of 1, i.e. an undirected graph corresponding to |$\boldsymbol{S}_l$| with added self-loop and |$\boldsymbol{I}_N$| is an identity matrix. |$\left [\tilde{\boldsymbol{A}}_{l}\right ]_{i i}=\sum _{j}{[{\tilde{\boldsymbol{S}}_l}]_{ij}}$|⁠, and |$\beta _{l}^{(t)}$| denotes the parameters in the |$t$|-th layer of GCN. |$\boldsymbol{{X}}_{l}^{(t)}\in \Re ^{n\times d}$| denotes the matrix of activations at the |$t$|-th layer with |$\boldsymbol{{X}}_{l}^{(0)}=\boldsymbol{Y}$|⁠.

In encoder, VGAE takes |$\boldsymbol{S}_l$| and |$\boldsymbol{X}_l$| as input and outputs a latent variable by two-layer GCN. The first layer is used to generate a low-dimensional feature matrix |$\tilde{\boldsymbol{X}}_l$| by Eq. (9):

where |$\boldsymbol{Q}=\tilde{\boldsymbol{A}}_{l}^{-\frac{1}{2}} \tilde{\boldsymbol{S}}_l \tilde{\boldsymbol{A}}_{l}^{-\frac{1}{2}}$|⁠, and |$\boldsymbol{W}_{0}$| denotes the parameters in the first GCN layer.

The second layer is used to generate the data distribution by Eq. (10):

where |$\mu $| and |$\sigma $| denote the mean and variance of the node vector representation, and |$\boldsymbol{W}_{\mu }$| and |$\boldsymbol{W}_{\sigma }$| denote the corresponding parameters.

Consequently, suppose that |$\varepsilon $| follows the standard normal distribution |$N$|(0, 1), the latent variable |$\boldsymbol{Z}_l$| is obtained by Eq. (11):

In decoder, VGAE reconstructs adjacency matrix |$\boldsymbol{\hat{S}}_{l}$| by the sigmoid function based on latent variable |$\boldsymbol{Z}_l$| by Eq. (12):

During the learning, we define the following loss function by Eq. (13):

where the first term denotes the binary cross-entropy between |${\boldsymbol{S}}_{l}$| and |$\hat{\boldsymbol{S}}_{l}$|⁠, the second term denotes the Kullback–Leibler divergence between posterior probability distribution |$q(\boldsymbol{Z}_l|{\boldsymbol{X}}_l, {\boldsymbol{S}}_l)$| and standard Gaussian distribution |$p(\boldsymbol{Z}_l)$| and |$p(\boldsymbol{S}_l|\boldsymbol{Z}_l)]$| denotes the probability between two nodes computed by the embedded vectors in the graph. Finally, the obtained lncRNA latent variable matrix |$\boldsymbol{Z}_l$| is used to represent their nonlinear features.

Similarly, we characterize the initial scalar features of each disease as one corresponding column of the LDA matrix |$Y$| and obtain the initial scalar feature matrix |$\boldsymbol{X}_d^{(0)}$| of |$m$| diseases. Taken the disease similarity |${\boldsymbol{S}}_d$| and initial scalar feature matrix |$\boldsymbol{{X}}_{d}^{(0)}$| as inputs, the disease nonlinear feature matrix |$\boldsymbol{Z}_d$| is computed through VGAE.

Feature Integration

The linear and nonlinear features of each lncRNA are concatenated as a |$a$|-dimensional vector, and the linear and nonlinear features of each disease are concatenated as a |$b$|-dimensional vector. Finally, an lncRNA–disease pair is represented as a |$k(k=a+b)$|-dimensional vector.

LDA prediction

For a given LDA dataset |$D = (\hat{\boldsymbol{X}}, {\hat{\boldsymbol{Y}}})$| with |$p\,\, (p=n \times m)$| samples (i.e. lncRNA–disease pairs), let |$\hat{\boldsymbol{x}}_i\in \hat{\boldsymbol{X}}$| denote the |$i$|-th training sample with |$k$|-dimensional features, and |$\hat{\boldsymbol{y}}_i\in \hat{\boldsymbol{Y}}$| denote its label. |$\hat{\boldsymbol{y}}_i=1$| if the |$i$|-th lncRNA–disease pair is associated, otherwise |$\hat{\boldsymbol{y}}_i=0$|⁠. Inspired by heterogeneous Newton boosting machine [20, 74], we developed a heterogeneous Newton boosting machine-based LDA prediction model. Subsequently, we build an objective function by Eq. (14):

where |${\hat{\boldsymbol{y}}}_i$| and |$f(\hat{\boldsymbol{x}}_i)$| indicate the true label and the predicted label of |$\boldsymbol{x}_i$|⁠, respectively. And loss function |$l({\hat{\boldsymbol{y}}}_i,f(\hat{ \boldsymbol{x}}_i))$| is twice differentiable related to |$f(\hat{ \boldsymbol{x}}_i)$|⁠, |$l^{^{\prime}}({\hat{\boldsymbol{y}}}_i,f(\hat{ \boldsymbol{x}}_i))$| and |$l^{^{\prime\prime}}({\hat{\boldsymbol{y}}}_i,f(\hat{ \boldsymbol{x}}_i))$| represent its first and second derivatives, respectively.

At each boosting iteration, let |$\mathcal{H}^{(c)}$| represent the |$c$|-th subclass from |$C$| distinct subclasses defined by Eq. (15):

where |$\overline{\mathcal{H}}^{(c)}$| indicates a finite class with respect to |$b(\hat{ \boldsymbol{x}}_i)$|⁠: |$\mathbb{R}^{d} \to \mathbb{R}$| satisfying |${\sum \nolimits _{i = 1}^n {b({\hat{ \boldsymbol{x}}_i})} ^2} = 1$|⁠.

For the domain |$\mathcal{F}$| defined by Eq. (16):

one subclass is randomly selected to construct multiple binary decision trees. Let |$d_{min}$| and |$d_{max}$| denote the minimum and maximum depths among these decision trees, we randomly and uniformly set the maximum depth of each tree to a value between |$d_{min}$| and |$d_{max}$|⁠. Consequently, we obtain |$C=R_d+1$| (⁠|${R_d} = d_{max} - d_{min} + 1$|⁠) unique choices for the subclass. And the probability mass function |$\Phi $| is represented by Eq. (17):

At the |$k$|-th iteration, assume that |$O_{k}$| (⁠|$O_k=1,2,...,C$|⁠) denote one index with respect to the sampled subclass, the base assumption is built by Eq. (18):

where |$g_i=l^{^{\prime}}({\hat{\boldsymbol{y}}}_i,f_{k-1}(\hat{ \boldsymbol{x}}_i))$| and |$h_i=l^{^{\prime\prime}}({\hat{\boldsymbol{y}}}_i,f_{k-1}(\hat{ \boldsymbol{x}}_i)) $|⁠.

Lastly, for the |$i$|-th lncRNA–disease pair |$\hat{ \boldsymbol{x}}_i$|⁠, its interaction probability |$f_k(\hat{ \boldsymbol{x}}_i)$| is computed by iterating updating model (19) with a learning rate |$\beta> 0$|⁠:

RESULTS

Evaluation metrics and experimental setup

Precision, recall, accuracy, F1-score, area under the ROC curve (AUC) and area under the precision-recall curve (AUPR) [52] were used to evaluate the performance of LDA-VGHB with the other four classical LDA prediction models (i.e. SDLDA, LDNFSGB, IPCARF and LDASR) and the other four boosting algorithms (i.e. XGBoost, AdaBoost, CatBoost and LightGBM). Four different 5-fold CVs [75] were repeatedly conducted for 20 times:

5-fold CV on lncRNAs (⁠|$CV_l$|⁠): random rows in an LDA matrix |$\boldsymbol{Y}$| were masked for testing, i.e. 80% of lncRNAs were randomly selected as train set and the remaining was used as test set in each round.

5-fold CV on diseases (⁠|$CV_d$|⁠): random columns in an LDA matrix |$\boldsymbol{Y}$| were masked for testing, i.e. 80% of diseases were randomly selected for train set and the remaining was used as test set in each round.

5-fold CV on lncRNA–disease pairs (⁠|$CV_{ld}$|⁠): random lncRNA–disease pairs in an LDA matrix |$\boldsymbol{Y}$| were masked for testing, i.e. 80% of lncRNA–disease pairs were randomly selected as train set and the remaining was used as test set in each round.

5-fold CV on independent lncRNAs and independent diseases (⁠|$CV_{ind}$|⁠): First, 20% of lncRNAs and 20% of diseases were randomly selected to construct a ‘node test set’. Next, the remaining lncRNAs and diseases were taken as a ‘node train set’. Third, all edges linking a node in the ‘node train set’ with a node in the ‘node test set’ were removed. Finally, one learner was trained only on the ‘node train set’ to find potential LDAs within the ‘node test set’.

The above four CVs refer to association identification for (1) new lncRNAs without any associated disease, (2) new diseases without any associated lncRNA, (3) new lncRNA–disease pairs and (4) new independent lncRNAs and independent diseases, respectively. The average result on the 20 times is used as the final performance.

Baseline methods

LDA prediction models: SDLDA [76] extracts linear and nonlinear features for lncRNAs and diseases by combining SVD and deep learning and then uses a full connection layer with the sigmoid function to classify unknown lncRNA–disease pairs. LDNFSGB [77] first extracts the global and local features for lncRNAs and diseases, and uses autoencoder to reduce the feature dimensions, and finally implements LDA prediction through the gradient boosting algorithm. IPCARF [78] presents an incremental principal component analysis method to select LDA features and uses a random forest to predict potential LDAs. LDASR [79] employs autoencoder to obtain the optimal lncRNA and disease features and uses rotating forest to predict new LDAs. SDLDA [76], LDNFSGB [77], IPCARF [78] and LDASR [79] are state-of-the-art LDA prediction methods.

Boosting algorithms: XGBoost [20, 80] is an Extreme Gradient Boosting model. AdaBoost [81] manifests good generalization ability and low computational complexity. CatBoost [82] is known as categorical boosting algorithm. LightGBM [23, 83] integrates one-side sampling as well as exclusive feature bundling over gradient boosting decision trees. XGBoost [80], AdaBoost [81], CatBoost [82] and LightGBM [83] are powerful boosting models and achieve good predictions in diverse practical tasks.

Performance comparison

To evaluate the LDA-VGHB performance, we compared it with the other four classical LDA prediction methods (i.e. SDLDA [76], LDNFSGB [77], IPCARF [78] and LDASR [79]) and four popular boosting models (i.e. XGBoost [80], AdaBoost [81], CatBoost [82] and LightGBM [83]). We randomly selected negative LDAs with the same number as one of known positive LDAs from unlabeled lncRNA–disease pairs. Tables 2–5 show the performance of LDA-VGHB, SDLDA, LDNFSGB, LDASR and IPCAF on the lncRNADisease and MNDR databases under four different 5-fold CVs. Figure 2 depicts their receiver operating characteristic (ROC) and precision-recall (PR) curves under the four 5-fold CVs. In addition, Tables S1–S4 in Supplementary Materials give the results under the four different 10-fold CVs.

To assess the performance of LDA-VGHB and the other four LDA prediction methods in predicting potential diseases for a new lncRNA, we considered 5-fold CV on lncRNAs. Under 5-fold CV on lncRNAs (⁠|$CV_l$|⁠), all five LDA prediction methods randomly selected 80% of lncRNAs as train set and used the remaining as test set. As shown in Table 2 and Figure 2, LDA-VGHB obtained the best performance, followed by SDLDA, LDNFSGB, LDASR and IPCAF on the lncRNADisease and MNDR databases. Particularly, LDA-VGHB computed the best AUCs of 0.8814 and 0.9541, outperforming 8.97% and 1.83% than SDLDA on the two datasets, respectively. It also obtained the best AUPRs of 0.8949 and 0.9617, 5.45% and 0.87% better than SDLDA, respectively. In general, LDA-VGHB efficiently found potential associated diseases for a new lncRNA.

To evaluate the performance of LDA-VGHB and the other four LDA prediction methods in predicting potential lncRNAs for a new disease, we considered 5-fold CV on diseases. Under 5-fold CV on diseases (⁠|$CV_d$|⁠), all five LDA prediction methods randomly selected 80% of diseases as train set and used the remaining as test set. As shown in Table 3 and Figure 2, LDA-VGHB significantly outperformed SDLDA, LDNFSGB, LDASR and IPCAF on the two LDA datasets. For example, LDA-VGHB computed the highest AUCs of 0.9406 and 0.9741, was better 6.57% and 1.87% than SDLDA on the two datasets, respectively. It also computed the best AUPRs of 0.9429 and 0.9728, outperforming 5.25% and 1.72% compared with SDLDA, respectively. We found that LDA-VGHB could accurately predict possible lncRNAs for a new disease.

To assess the performance of LDA-VGHB with the other four LDA prediction methods in predicting potential LDAs for lncRNA–disease pairs, we considered 5-fold CV on lncRNA–disease pairs. Under 5-fold CV on lncRNA–disease pairs (⁠|$CV_{ld}$|⁠), all five methods randomly selected 80% of lncRNA–disease pairs as train set and used the remaining as test set. As shown in Table 4 and Figure 2, LDA-VGHB obviously improved LDA identification compared with SDLDA, LDNFSGB, LDASR and IPCAF under majority of conditions. It calculated the AUC values of 0.9271 and 0.9722, 5.36% and 1.67% better than the second-best method on the two datasets, respectively. It also calculated the AUPR values of 0.9364 and 0.9761, 4.40% and 1.25% better than the second-best method, respectively. Consequently, LDA-VGHB more accurately predicted possible LDAs based on known LDAs.

Lastly, to evaluate the performance of LDA-VGHB with the other four LDA prediction methods in predicting potential LDAs for independent lncRNAs and independent diseases, we considered 5-fold CV on independent lncRNAs and independent diseases. Under 5-fold CV on independent lncRNAs and independent diseases |$CV_{ind}$|⁠, first, all five LDA prediction methods randomly selected 20% of lncRNAs and 20% of diseases to construct a ‘node test set’. Next, the five LDA prediction methods took the remaining lncRNAs and diseases as a ‘node train set’, and removed all edges linking a node in the ‘node train set’ with a node in the ‘node test set’. Finally, the five methods were trained only on the ‘node train set’ and were assessed the performance within the ‘node test set’. As shown in Table 5 and Figure 2, LDA-VGHB computed the best recall, accuracy, F1-score, AUC and AUPR on the two LDA datasets. It computed the highest AUCs of 0.8924 and 0.9576, outperforming 13.17% and 3.44% than SDLDA, respectively. It also computed the best AUPRs of 0.9056 and 0.9621, better 8.51% and 1.97% than SDLDA, respectively. The results manifest that LDA-VGHB computed the optimal LDA prediction performance under independent datasets.

Furthermore, boosting is one of the most popular ensemble learning tools and significantly improves classification performance [84, 85]. To evaluate the LDA classification performance of various boosting models, we compared LDA-VGHB with the other four popular boosting algorithms, i.e. XGBoost [86], AdaBoost [81], CatBoost [82] and LightGBM [87] under four different CVs. The four boosting algorithms used the same similarity computation and feature extraction procedures as LDA-VGHB. Their difference is to use different boosting models for classifying unknown lncRNA–disease pairs. The experiments were repeatedly conducted for 20 times. Tables 6–9 show their LDA prediction performance under 5-fold CVs on lncRNAs, diseases, lncRNA–disease pairs, independent lncRNAs and independent diseases, respectively. The results demonstrate that LDA-VGHB computed the best LDA identification accuracy on the two LDA databases under the four CVs under majority of conditions, thereby elucidating the powerful LDA classification performance of heterogeneous Newton boosting machine.

The other performance comparison

In the proposed LDA-VGHB model, linear and nonlinear features were extracted to represent each lncRNA–disease pair based on SVD and VGAE, respectively. We analyzed their affects on the LDA identification performance. Figure 3 demonstrates the LDA-VGHB performance on two LDA datasets under four different 5-fold CVs when using linear features, nonlinear features or their combination. In most cases, the combination of linear features and nonlinear features improved the LDA prediction performance.

The parameter |$\alpha $| was used to measure the importance on the LDA identification performance. Thus, we analyzed the affect of the parameter |$\alpha $| at the range of [0,1] with the stepsize of 0 on the LDA prediction performance. As shown in Figure 4, when |$\alpha $| was set to 0.5, LDA-VGHB computed the best AUC and AUPR on the lncRNADisease and MNDR datasets under the four different CVs. Consequently, we set |$\alpha $| to 0.5. Tables S5-S8 in Supplementary Materials show the LDA-VGHB performance based on different |$\alpha $| under the four different 5-fold CVs.

The obtained feature dimensions of lncRNAs and diseases are unknown. However, we failed to implement dimension reduction because they were not high-dimensional. Consequently, we analyzed affects of different dimensions (i.e. 5, 10, 16, 32, 50, and 64) on the LDA identification performance. By comprehensively considering six evaluation index values, as shown in Table 10, we selected different dimensions on different datasets.

Case Study

Lung cancer, breast cancer, colorectal cancer and kidney cancer are four of the most frequent cancers worldwide. They demonstrate high morbidity and mortality. In the above section, we have verified the LDA-VGHB performance. Subsequently, we selected LDA-VGHB to identify potential lncRNAs for the four cancers. Figure 5 illustrates the top 20 lncRNAs associated with the four cancers on the lncRNADisease and MNDR databases. Tables 11–14 list the rankings of the top 20 lncRNAs according to the association scores between them and a query cancer, respectively.

In the lncRNADisease and MNDR databases, 10 and 7 lncRNAs have been verified by existing databases (Lnc2Cancer 3.0 [88], lncRNADisease v2.0 [29], RNADisease [89]) among the predicted top 20 lncRNAs associated with lung cancer, respectively. We predicted that HAR1A may associate with lung cancer with the rankings of 16 and 1 on the two databases, respectively. lncRNA HAR1A may be a tumor suppressor in many cancer including oral cancer, hepatocellular carcinoma, brease cancer and glioma [90–92]. Its knockdown boosted ALPK1 expression and downregulated BRD7, and further induce the progression of oral cancer [93]. Its expression has been examined in glioma, and was obviously lower in hepatocellular cancer than chronic hepatitis B [90, 91]. Its decreased expression could involve in poor prognosis of hepatocellular cancer [90]. Thus, we predicted that HAR1A could associate with lung cancer and need further experimental validation.

In the lncRNADisease and MNDR databases, 11 and 8 lncRNAs have been verified by existing three databases (Lnc2Cancer 3.0, lncRNADisease v2.0, RNADisease) among the predicted top 20 lncRNAs associated with breast cancer, respectively. We inferred that KCNQ1DN may associate with breast cancer with the rankings of 14 and 6, respectively. KCNQ1DN is an lncRNA with 1109 nucleotides. It is downregulated in the renalcell carcinoma tissues and could inhibit growth and progression of renalcell carcinoma cells [94]. Xin et al. [95] detected its expression in Wihns’ tumors and found that it may link with Wilms’ tumorigenesis along with IGF2.

In the lncRNADisease and MNDR databases, eight and four lncRNAs have been verified by three publicly available databases (Lnc2Cancer 3.0, lncRNADisease v2.0, RNADisease) among the predicted top 20 lncRNAs associated with colorectal cancer, respectively. In the two databases, we found that ZFAT-AS1 could associate with colorectal cancer. lncRNA ZFAT-AS1 is an antisense transcript of gene ZFAT, which encodes a protein that functions as a transcriptional regulator with respect to apoptosis and cell survival [96]. ZFAT-AS1 is prominently downregulated in glioma. Its over-expression could inhibit proliferation, migration and invasion, and accelerate apoptosis in glioma [97–99]. Its expression is downregulated in breast cancer [100], upregulated in hepatocellular, gastric, bladder and ovarian cancers and dysregulated in multiple malignant tumors [101]. In general, ZFAT-AS1 acts as a tumor-suppressive gene in many cancers including colorectal cancer and need further in vivo or in vitro experimental validation.

In the lncRNADisease and MNDR databases, two and 9nine lncRNAs have been reported by three publicly available databases (Lnc2Cancer 3.0, lncRNADisease v2.0, RNADisease) among the predicted top 20 lncRNAs associated with kidney neoplasms, respectively. In the two databases, we inferred that HAR1B could associate with kidney neoplasms. HAR1B helps the formation of stable RNA structures in human body [102]. Its expression is obviously lower in the hepatocellular carcinoma patients [90]. It can serve as a potential biomarker in bone and soft-tissue sarcomas [103]. Deregulated HAR1B has a greatly higher expression profile in aggressive colorectal cancers [104]. The association between kidney neoplasms and HAR1B needs further experimental confirmation.

CONCLUSION

In this study, we developed a computational model LDA-VGHB to investigate underlying LDAs. LDA-VGHB first extracted features of each lncRNA–disease pair by incorporating similarity computation, linear feature extraction based on SVD and nonlinear feature extraction based on VGAE. Subsequently, it used a heterogeneous Newton boosting machine to classify unobserved lncRNA–disease pairs. LDA-VGHB was compared with the other four classical LDA prediction methods (i.e. SDLDA [76], LDNFSGB [77], IPCARF [78] and LDASR [79]) and four popular boosting models (i.e. XGBoost [80], AdaBoost [81], CatBoost [82] and LightGBM [83]) under four 5-fold CVs on lncRNAs, diseases, lncRNA–disease pairs and independent lncRNAs and independent diseases, respectively. It significantly outperformed the eight methods with its best performance on the lncRNADisease and MNDR databases under the four different CVs. We further conducted case studies for lung cancer, breast cancer, colorectal cancer and kidney neoplasms and predicted the top 20 lncRNAs associated with them among all their unobserved lncRNAs. The results showed that most of the predicted top 20 lncRNAs have been verified by biomedical experiments provided by the Lnc2Cancer 3.0, lncRNADisease v2.0 and RNADisease databases. We inferred that HAR1A, KCNQ1DN, ZFAT-AS1 and HAR1B could associate with lung cancer, breast cancer, colorectal cancer and kidney neoplasms, respectively. The results need further biological experiment validation.

ACKNOWLEDGEMENTS

We would like to thank three anonymous reviewers and all authors of the cited references.

FUNDING

L.H.P. was supported by National Natural Science Foundation of China under Grant No. 61803151 and Natural Science Foundation of Hunan Province of China under Grant 2023JJ50201. M.C. was supported by National Natural Science Foundation of China under Grant No. 62172158. G.S.H. was supported by Natural Science Foundation of Hunan Province of China Grant 2021JJ30684 and Hunan Provincial Key Research Program (Grant No. 2022WK2009).

AUTHOR CONTRIBUTION STATEMENT

L.H.P. and L.L.H.: conceptualization; L.H.P., Q.L.S., G.T., M.C. and G.S.H.: funding acquisition; L.H.P., L.L.H., Q.L.S., G.T., M.C. and G.S.H.: project administration; L.L.H.: writing-original draft; L.H.P., L.L.H. and G.S.H.: writing-review and editing; L.H.P., L.L.H., Q.L.S., G.T., M.C. and G.S.H.: investigation; L.H.P. and L.L.H.: methodology; L.L.H.: software; L.L.H., Q.L.S., G.T., M.C., G.S.H.: validation. All authors contributed to the article and approved the submitted version.

DATA AVAILABILITY STATEMENT

Datasets and codes can be downloaded at https://github.com/plhhnu/LDA-VGHB.

Author Biographies

Lihong Peng is working in Hunan University of Technology as an associate professor. She received a PhD in College of Information Science and Engineering, Hunan University, China. Her research interests include Machine Learning, Data Mining and Bioinformatics.

Liangliang Huang is a postgraduate student in the School of Computer Science, Hunan University of Technology, China. His research interests include Machine Learning and Bioinformatics.

Qiongli Su is working in the Department of Pharmacy, the Affiliated Zhuzhou Hospital Xiangya Medical College CSU. Her research interests include Cardiovascular, tumor and thrombotic diseases.

Geng Tian is the chief executive officer in Geneis (Beijing) Co. Ltd, China. His research interests include Tumor Precise Medicine and Bioinformatics.

Min Chen is working in Hunan Institute of Technology as a professor. He received a PhD in the College of Information Science and Engineering, Hunan University, China. Her research interests include Machine Learning, Data Mining and Bioinformatics.

Guosheng Han is working in Xiangtan University as an associate professor. He received a PhD in School of Mathematics and Computational Science, Xiangtan University, China. His research interests include Machine Learning, Data Mining and Bioinformatics.

References

Author notes