Laplacian Regularized Least Research Articles

Inferring circRNA-drug sensitivity associations via dual hierarchical attention networks and multiple kernel fusion

Increasing evidence has shown that the expression of circular RNAs (circRNAs) can affect the drug sensitivity of cells and significantly influence drug efficacy. Therefore, research into the relationships between circRNAs and drugs can be of great significance in increasing the comprehension of circRNAs function, as well as contributing to the discovery of new drugs and the repurposing of existing drugs. However, it is time-consuming and costly to validate the function of circRNA with traditional medical research methods. Therefore, the development of efficient and accurate computational models that can assist in discovering the potential interactions between circRNAs and drugs is urgently needed. In this study, a novel method is proposed, called DHANMKF , that aims to predict potential circRNA-drug sensitivity interactions for further biomedical screening and validation. Firstly, multimodal networks were constructed by DHANMKF using multiple sources of information on circRNAs and drugs. Secondly, comprehensive intra-type and inter-type node representations were learned using bi-typed multi-relational heterogeneous graphs, which are attention-based encoders utilizing a hierarchical process. Thirdly, the multi-kernel fusion method was used to fuse intra-type embedding and inter-type embedding. Finally, the Dual Laplacian Regularized Least Squares method (DLapRLS) was used to predict the potential circRNA-drug sensitivity associations using the combined kernel in circRNA and drug spaces. Compared with the other methods, DHANMKF obtained the highest AUC value on two datasets. Code is available at https://github.com/cuntjx/DHANMKF.

Prioritizing potential circRNA biomarkers for bladder cancer and bladder urothelial cancer based on an ensemble model

Bladder cancer is the most common cancer of the urinary system. Bladder urothelial cancer accounts for 90% of bladder cancer. These two cancers have high morbidity and mortality rates worldwide. The identification of biomarkers for bladder cancer and bladder urothelial cancer helps in their diagnosis and treatment. circRNAs are considered oncogenes or tumor suppressors in cancers, and they play important roles in the occurrence and development of cancers. In this manuscript, we developed an Ensemble model, CDA-EnRWLRLS, to predict circRNA-Disease Associations (CDA) combining Random Walk with restart and Laplacian Regularized Least Squares, and further screen potential biomarkers for bladder cancer and bladder urothelial cancer. First, we compute disease similarity by combining the semantic similarity and association profile similarity of diseases and circRNA similarity by combining the functional similarity and association profile similarity of circRNAs. Second, we score each circRNA-disease pair by random walk with restart and Laplacian regularized least squares, respectively. Third, circRNA-disease association scores from these models are integrated to obtain the final CDAs by the soft voting approach. Finally, we use CDA-EnRWLRLS to screen potential circRNA biomarkers for bladder cancer and bladder urothelial cancer. CDA-EnRWLRLS is compared to three classical CDA prediction methods (CD-LNLP, DWNN-RLS, and KATZHCDA) and two individual models (CDA-RWR and CDA-LRLS), and obtains better AUC of 0.8654. We predict that circHIPK3 has the highest association with bladder cancer and may be its potential biomarker. In addition, circSMARCA5 has the highest association with bladder urothelial cancer and may be its possible biomarker.

Inferring human miRNA-disease associations via multiple kernel fusion on GCNII.

Increasing evidence shows that the occurrence of human complex diseases is closely related to the mutation and abnormal expression of microRNAs(miRNAs). MiRNAs have complex and fine regulatory mechanisms, which makes it a promising target for drug discovery and disease diagnosis. Therefore, predicting the potential miRNA-disease associations has practical significance. In this paper, we proposed an miRNA–disease association predicting method based on multiple kernel fusion on Graph Convolutional Network via Initial residual and Identity mapping (GCNII), called MKFGCNII. Firstly, we built a heterogeneous network of miRNAs and diseases to extract multi-layer features via GCNII. Secondly, multiple kernel fusion method was applied to weight fusion of embeddings at each layer. Finally, Dual Laplacian Regularized Least Squares was used to predict new miRNA–disease associations by the combined kernel in miRNA and disease spaces. Compared with the other methods, MKFGCNII obtained the highest AUC value of 0.9631. Code is available at https://github.com/cuntjx/bioInfo.

Finding Lung-Cancer-Related lncRNAs Based on Laplacian Regularized Least Squares With Unbalanced Bi-Random Walk.

Lung cancer is one of the leading causes of cancer-related deaths. Thus, it is important to find its biomarkers. Furthermore, there is an increasing number of studies reporting that long noncoding RNAs (lncRNAs) demonstrate dense linkages with multiple human complex diseases. Inferring new lncRNA-disease associations help to identify potential biomarkers for lung cancer and further understand its pathogenesis, design new drugs, and formulate individualized therapeutic options for lung cancer patients. This study developed a computational method (LDA-RLSURW) by integrating Laplacian regularized least squares and unbalanced bi-random walk to discover possible lncRNA biomarkers for lung cancer. First, the lncRNA and disease similarities were computed. Second, unbalanced bi-random walk was, respectively, applied to the lncRNA and disease networks to score associations between diseases and lncRNAs. Third, Laplacian regularized least squares were further used to compute the association probability between each lncRNA-disease pair based on the computed random walk scores. LDA-RLSURW was compared using 10 classical LDA prediction methods, and the best AUC value of 0.9027 on the lncRNADisease database was obtained. We found the top 30 lncRNAs associated with lung cancers and inferred that lncRNAs TUG1, PTENP1, and UCA1 may be biomarkers of lung neoplasms, non-small–cell lung cancer, and LUAD, respectively.

Inferring human microbe–drug associations via multiple kernel fusion on graph neural network

Complex and diverse microbial communities have certain impacts on human health, and specific drugs are needed to treat diseases caused by microbes. However, most of the discovery of associations between microbes and drugs is through biological experiments, which are time-consuming and expensive. Therefore, it is crucial to develop an effective and computational model to detect novel microbe–drug associations. In this study, we propose a model based on Multiple Kernel fusion on Graph Convolutional Network, called MKGCN, for inferring novel microbe–drug associations. Our model is built on the heterogeneous network of microbes and drugs to extract multi-layer features, through Graph Convolutional Network (GCN). Then, we respectively calculate the kernel matrix by embedding features on each layer, and fuse multiple kernel matrices based on the average weighting method. Finally, Dual Laplacian Regularized Least Squares is used to infer new microbe–drug associations by the combined kernel in microbe and drug spaces. Compared with the existing tools for detecting biological bipartite networks, our model has excellent prediction effect on three datasets via three types of cross-validation. Furthermore, we also conduct a case study of the SARS-Cov-2 virus and make a deduction about drugs that may be able to associate with COVID-19. We have proved the accuracy of the prediction results through the existing literature.

VDA-RWLRLS: An anti-SARS-CoV-2 drug prioritizing framework combining an unbalanced bi-random walk and Laplacian regularized least squares

BackgroundA new coronavirus disease named COVID-19, caused by severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2), is rapidly spreading worldwide. However, there is currently no effective drug to fight COVID-19. MethodsIn this study, we developed a Virus-Drug Association (VDA) identification framework (VDA-RWLRLS) combining unbalanced bi-Random Walk, Laplacian Regularized Least Squares, molecular docking, and molecular dynamics simulation to find clues for the treatment of COVID-19. First, virus similarity and drug similarity are computed based on genomic sequences, chemical structures, and Gaussian association profiles. Second, an unbalanced bi-random walk is implemented on the virus network and the drug network, respectively. Third, the results of the random walks are taken as the input of Laplacian regularized least squares to compute the association score for each virus-drug pair. Fourth, the final associations are characterized by integrating the predictions from the virus network and the drug network. Finally, molecular docking and molecular dynamics simulation are implemented to measure the potential of screened anti-COVID-19 drugs and further validate the predicted results. ResultsIn comparison with six state-of-the-art association prediction models (NGRHMDA, SMiR-NBI, LRLSHMDA, VDA-KATZ, VDA-RWR, and VDA-BiRW), VDA-RWLRLS demonstrates superior VDA prediction performance. It obtains the best AUCs of 0.885 8, 0.835 5, and 0.862 5 on the three VDA datasets. Molecular docking and dynamics simulations demonstrated that remdesivir and ribavirin may be potential anti-COVID-19 drugs. ConclusionsIntegrating unbalanced bi-random walks, Laplacian regularized least squares, molecular docking, and molecular dynamics simulation, this work initially screened a few anti-SARS-CoV-2 drugs and may contribute to preventing COVID-19 transmission.

Predicting Microbe-Drug Association based on Similarity and Semi-Supervised Learning

Increasing clinic evidences have showed that microbial communities play important roles in human health and disease. Predicting hidden microbe-drug associations can be helpful in understanding the microbe-drug association mechanisms in clinical treatment, drug discovery, combinations and repositioning. Some computational methods were proposed to predict the associations of microbes and drugs. However, the prediction performance of these methods needs to be improved. In this study, a new computational model (LRLSMDA) is proposed for identifying Microbe-Drug Associations based on the Laplacian Regularized Least Square algorithm. LRLSMDA integrates the chemical structure similarity of drugs and known microbe-drug associations. The microbe Gaussian Interaction Profile (GIP) kernel similarity is computed based on known microbe-drug associations. We compute the drug GIP kernel similarity and the drug chemical structure similarity based on known microbe-drug associations and drug chemical structures. The drug GIP kernel similarity and the drug chemical structure similarity are integrated into a more comprehensive drug similarity matrix by the linear weighted method. Finally, the Laplacian regularized least squares algorithm is applied to predict hidden microbe-drug associations. LRLSMDA has achieved the average Area Under the Curve (AUC) values of 0.8983±0.0019, 0.9043±0.0015 and 0.9095 in 5-fold Cross-Validation (5CV), 10-fold Cross-Validation (10CV) and Leave One Out Cross-Validation (LOOCV), respectively. These experimental results show that the prediction performance of LRLSMDA outperforms three compared models.

Identification of Drug–Target Interactions via Dual Laplacian Regularized Least Squares with Multiple Kernel Fusion

Detection of Drug–Target Interactions (DTIs) is the time-consuming and laborious experiment via biochemical approaches. Machine learning based methods have been widely used to mine meaningful information of drug research. In this study, we establish a novel computational method to predict DTIs via Dual Laplacian Regularized Least Squares model (DLapRLS) with Hilbert–Schmidt Independence Criterion-based Multiple Kernel Learning (HSIC-MKL). Multiple kernels are built from different information sources (drug and target spaces). Then, above corresponding kernels are integrated by HSIC-MKL. At last, DLapRLS model is trained by Alternating Least Squares Algorithm (ALSA) and employed to predict new DTIs. On four benchmark datasets, the results of our method are comparable and even better than existing models.

A Novel lncRNA-Disease Association Prediction Model Using Laplacian Regularized Least Squares and Space Projection-Federated Method

Recent studies indicated that numerous long noncoding RNAs (lncRNAs) are closely related to human diseases and can serve as potential biomarkers and drug targets for complex diseases. Therefore, identifying lncRNAs associated with diseases through computational methods is conducive to the exploration of disease pathogenesis. Most previous studies had shortcomings, such as low prediction accuracy, the need for negative samples, and weak generalization. Such studies established shallow prediction models and failed to fully capture the complex relationships among lncRNA-disease associations, lncRNA similarity, and disease similarity. LRLSSP, a new computational method based on Laplacian regularized least squares (LRLS) and space projection was used to predict candidate disease lncRNAs in this study. LRLSSP deeply integrates information on lncRNA similarity, disease similarity, and known lncRNA-disease associations. The estimated score of lncRNA-disease association was obtained through LRLS, and network projection was utilized to reliably predict disease-related lncRNAs. Leave-one-out cross validation(LOOCV) was implemented to evaluate the prediction performance of LRLSSP. Results showed that LRLSSP performed was better than other state-of-the-art methods in predicting lncRNA-disease associations. In addition, case studies conducted on melanoma,cervical cancer, ovarian cancer and breast cancer indicated that LRLSSP can discover potential and novel lncRNA-disease associations. Overall, the results demonstrated that LRLSSP may serve as a reliable and effective computational tool for disease-related lncRNAs prediction.

MDA-SKF: Similarity Kernel Fusion for Accurately Discovering miRNA-Disease Association.

Identifying accurate associations between miRNAs and diseases is beneficial for diagnosis and treatment of human diseases. It is especially important to develop an efficient method to detect the association between miRNA and disease. Traditional experimental method has high precision, but its process is complicated and time-consuming. Various computational methods have been developed to uncover potential associations based on an assumption that similar miRNAs are always related to similar diseases. In this paper, we propose an accurate method, MDA-SKF, to uncover potential miRNA-disease associations. We first extract three miRNA similarity kernels (miRNA functional similarity, miRNA sequence similarity, Hamming profile similarity for miRNA) and three disease similarity kernels (disease semantic similarity, disease functional similarity, Hamming profile similarity for disease) in two subspaces, respectively. Then, due to limitations that some initial information may be lost in the process and some noises may be exist in integrated similarity kernel, we propose a novel Similarity Kernel Fusion (SKF) method to integrate multiple similarity kernels. Finally, we utilize the Laplacian Regularized Least Squares (LapRLS) method on the integrated kernel to find potential associations. MDA-SKF is evaluated by three evaluation methods, including global leave-one-out cross validation (LOOCV) and local LOOCV and 5-fold cross validation (CV), and achieves AUCs of 0.9576, 0.8356, and 0.9557, respectively. Compared with existing seven methods, MDA-SKF has outstanding performance on global LOOCV and 5-fold. We also test case studies to further analyze the performance of MDA-SKF on 32 diseases. Furthermore, 3200 candidate associations are obtained and a majority of them can be confirmed. It demonstrates that MDA-SKF is an accurate and efficient computational tool for guiding traditional experiments.

FKL-Spa-LapRLS: an accurate method for identifying human microRNA-disease association

BackgroundIn the process of post-transcription, microRNAs (miRNAs) are closely related to various complex human diseases. Traditional verification methods for miRNA-disease associations take a lot of time and expense, so it is especially important to design computational methods for detecting potential associations. Considering the restrictions of previous computational methods for predicting potential miRNAs-disease associations, we develop the model of FKL-Spa-LapRLS (Fast Kernel Learning Sparse kernel Laplacian Regularized Least Squares) to break through the limitations.ResultFirst, we extract three miRNA similarity kernels and three disease similarity kernels. Then, we combine these kernels into a single kernel through the Fast Kernel Learning (FKL) model, and use sparse kernel (Spa) to eliminate noise in the integrated similarity kernel. Finally, we find the associations via Laplacian Regularized Least Squares (LapRLS). Based on three evaluation methods, global and local leave-one-out cross validation (LOOCV), and 5-fold cross validation, the AUCs of our method achieve 0.9563, 0.8398 and 0.9535, thus it can be seen that our method is reliable. Then, we use case studies of eight neoplasms to further analyze the performance of our method. We find that most of the predicted miRNA-disease associations are confirmed by previous traditional experiments, and some important miRNAs should be paid more attention, which uncover more associations of various neoplasms than other miRNAs.ConclusionsOur proposed model can reveal miRNA-disease associations and improve the accuracy of correlation prediction for various diseases. Our method can be also easily extended with more similarity kernels.

LRLSHMDA: Laplacian Regularized Least Squares for Human Microbe\u2013Disease Association prediction

An increasing number of evidences indicate microbes are implicated in human physiological mechanisms, including complicated disease pathology. Some microbes have been demonstrated to be associated with diverse important human diseases or disorders. Through investigating these disease-related microbes, we can obtain a better understanding of human disease mechanisms for advancing medical scientific progress in terms of disease diagnosis, treatment, prevention, prognosis and drug discovery. Based on the known microbe-disease association network, we developed a semi-supervised computational model of Laplacian Regularized Least Squares for Human Microbe–Disease Association (LRLSHMDA) by introducing Gaussian interaction profile kernel similarity calculation and Laplacian regularized least squares classifier. LRLSHMDA reached the reliable AUCs of 0.8909 and 0.7657 based on the global and local leave-one-out cross validations, respectively. In the framework of 5-fold cross validation, average AUC value of 0.8794 +/−0.0029 further demonstrated its promising prediction ability. In case studies, 9, 9 and 8 of top-10 predicted microbes have been manually certified to be associated with asthma, colorectal carcinoma and chronic obstructive pulmonary disease by published literature evidence. Our proposed model achieves better prediction performance relative to the previous model. We expect that LRLSHMDA could offer insights into identifying more promising human microbe-disease associations in the future.

FMLNCSIM: fuzzy measure-based lncRNA functional similarity calculation model.

Accumulating experimental studies have indicated the influence of lncRNAs on various critical biological processes as well as disease development and progression. Calculating lncRNA functional similarity is of high value in inferring lncRNA functions and identifying potential lncRNA-disease associations. However, little effort has been attempt to measure the functional similarity among lncRNAs on a large scale. In this study, we developed a Fuzzy Measure-based LNCRNA functional SIMilarity calculation model (FMLNCSIM) based on the assumption that functionally similar lncRNAs tend to be associated with similar diseases. The performance improvement of FMLNCSIM mainly comes from the combination of information content and the concept of fuzzy measure, which was applied to the directed acyclic graphs of disease MeSH descriptors. To evaluate the effectiveness of FMLNCSIM, we further combined it with the previously proposed model of Laplacian Regularized Least Squares for lncRNA-Disease Association (LRLSLDA). As a result, the integrated model, LRLSLDA-FMLNCSIM, achieve good performance in the frameworks of global LOOCV (AUCs of 0.8266 and 0.9338 based on LncRNADisease and MNDR database) and 5-fold cross validation (average AUCs of 0.7979 and 0.9237 based on LncRNADisease and MNDR database), which significantly improve the performance of previous classical models. It is anticipated that FMLNCSIM could be used for searching functionally similar lncRNAs and inferring lncRNA functions in the future researches.

ILNCSIM: improved lncRNA functional similarity calculation model.

Increasing observations have indicated that lncRNAs play a significant role in various critical biological processes and the development and progression of various human diseases. Constructing lncRNA functional similarity networks could benefit the development of computational models for inferring lncRNA functions and identifying lncRNA-disease associations. However, little effort has been devoted to quantifying lncRNA functional similarity. In this study, we developed an Improved LNCRNA functional SIMilarity calculation model (ILNCSIM) based on the assumption that lncRNAs with similar biological functions tend to be involved in similar diseases. The main improvement comes from the combination of the concept of information content and the hierarchical structure of disease directed acyclic graphs for disease similarity calculation. ILNCSIM was combined with the previously proposed model of Laplacian Regularized Least Squares for lncRNA-Disease Association to further evaluate its performance. As a result, new model obtained reliable performance in the leave-one-out cross validation (AUCs of 0.9316 and 0.9074 based on MNDR and Lnc2cancer databases, respectively), and 5-fold cross validation (AUCs of 0.9221 and 0.9033 for MNDR and Lnc2cancer databases), which significantly improved the prediction performance of previous models. It is anticipated that ILNCSIM could serve as an effective lncRNA function prediction model for future biomedical researches.

Kinase Identification with Supervised Laplacian Regularized Least Squares.

Phosphorylation is catalyzed by protein kinases and is irreplaceable in regulating biological processes. Identification of phosphorylation sites with their corresponding kinases contributes to the understanding of molecular mechanisms. Mass spectrometry analysis of phosphor-proteomes generates a large number of phosphorylated sites. However, experimental methods are costly and time-consuming, and most phosphorylation sites determined by experimental methods lack kinase information. Therefore, computational methods are urgently needed to address the kinase identification problem. To this end, we propose a new kernel-based machine learning method called Supervised Laplacian Regularized Least Squares (SLapRLS), which adopts a new method to construct kernels based on the similarity matrix and minimizes both structure risk and overall inconsistency between labels and similarities. The results predicted using both Phospho.ELM and an additional independent test dataset indicate that SLapRLS can more effectively identify kinases compared to other existing algorithms.

Learning from normalized local and global discriminative information for semi-supervised regression and dimensionality reduction

Semi-supervised dimensionality reduction is one of the important topics in pattern recognition and machine learning. During the past decade, Laplacian Regularized Least Square (LapRLS) and Semi-supervised Discriminant Analysis (SDA) are the two widely-used semi-supervised dimensionality reduction methods. In this paper, we show that SDA and LapRLS can be unified into a constrained manifold regularized least square framework. The manifold term, however, cannot fully utilize the underlying discriminative information. We thus introduce a new and effective semi-supervised dimensionality reduction method, called Learning from Local and Global Information (LLGDI), to solve the problem. The proposed LLGDI method adopts a set of local classification functions to preserve both local geometrical and discriminative information of dataset. It also adopts a global classification function to preserve the global discriminative information, and an uncorrelated constraint to calculate the projection matrix for simultaneously solving regression and dimensionality reduction problem. As a result, the LLGDI method is able to preserve local discriminative, manifold information as well as the global discriminative information. Theoretical analysis and extensive simulations presented in the paper show the effectiveness of the LLGDI algorithm. The results also demonstrate LLGDI can achieve superior performance compared with other existing methods.

Constructing lncRNA functional similarity network based on lncRNA-disease associations and disease semantic similarity.

Increasing evidence has indicated that plenty of lncRNAs play important roles in many critical biological processes. Developing powerful computational models to construct lncRNA functional similarity network based on heterogeneous biological datasets is one of the most important and popular topics in the fields of both lncRNAs and complex diseases. Functional similarity network consturction could benefit the model development for both lncRNA function inference and lncRNA-disease association identification. However, little effort has been attempted to analysis and calculate lncRNA functional similarity on a large scale. In this study, based on the assumption that functionally similar lncRNAs tend to be associated with similar diseases, we developed two novel lncRNA functional similarity calculation models (LNCSIM). LNCSIM was evaluated by introducing similarity scores into the model of Laplacian Regularized Least Squares for LncRNA–Disease Association (LRLSLDA) for lncRNA-disease association prediction. As a result, new predictive models improved the performance of LRLSLDA in the leave-one-out cross validation of various known lncRNA-disease associations datasets. Furthermore, some of the predictive results for colorectal cancer and lung cancer were verified by independent biological experimental studies. It is anticipated that LNCSIM could be a useful and important biological tool for human disease diagnosis, treatment, and prevention.

Novel human lncRNA–disease association inference based on lncRNA expression profiles

More and more evidences have indicated that long-non-coding RNAs (lncRNAs) play critical roles in many important biological processes. Therefore, mutations and dysregulations of these lncRNAs would contribute to the development of various complex diseases. Developing powerful computational models for potential disease-related lncRNAs identification would benefit biomarker identification and drug discovery for human disease diagnosis, treatment, prognosis and prevention. In this article, we proposed the assumption that similar diseases tend to be associated with functionally similar lncRNAs. Then, we further developed the method of Laplacian Regularized Least Squares for LncRNA-Disease Association (LRLSLDA) in the semisupervised learning framework. Although known disease-lncRNA associations in the database are rare, LRLSLDA still obtained an AUC of 0.7760 in the leave-one-out cross validation, significantly improving the performance of previous methods. We also illustrated the performance of LRLSLDA is not sensitive (even robust) to the parameters selection and it can obtain a reliable performance in all the test classes. Plenty of potential disease-lncRNA associations were publicly released and some of them have been confirmed by recent results in biological experiments. It is anticipated that LRLSLDA could be an effective and important biological tool for biomedical research. The code of LRLSLDA is freely available at http://asdcd.amss.ac.cn/Software/Details/2.

G-Optimal Feature Selection with Laplacian regularization

Feature selection is an important preprocessing step in many applications where the data points are of high dimension. It is designed to find the most informative feature subset to facilitate data visualization, clustering, classification, and ranking. In this paper, we consider the feature selection problem in unsupervised scenarios. Typical unsupervised feature selection algorithms include Q-α and Laplacian Score. Both of them select the most informative features by discovering the clustering or geometrical structure in the data. However, they fail to consider the performance of some specific learning task, e.g. regression, by using the selected features. Based on Laplacian Regularized Least Squares (LapRLS) which incorporates the manifold structure into the regression model, we propose a novel feature selection approach called Laplacian G-Optimal Feature Selection (LapGOFS). It minimizes the maximum variance of the predicted value of the regression model. By using techniques from manifold learning and optimal experimental design, our proposed approach can select the most informative features which can improve the learning performance the most. Extensive experimental results over various real data sets have demonstrated the effectiveness of the proposed algorithm.

G-Optimal Design with Laplacian Regularization

In many real world applications, labeled data are usually expensive to get, while there may be a large amount of unlabeled data. To reduce the labeling cost, active learning attempts to discover the most informative data points for labeling. Recently, Optimal Experimental Design (OED) techniques have attracted an increasing amount of attention. OED is concerned with the design of experiments that minimizes variances of a parameterized model. Typical design criteria include D-, A-, and E-optimality. However, all these criteria are based on an ordinary linear regression model which aims to minimize the empirical error whereas the geometrical structure of the data space is not well respected. In this paper, we propose a novel optimal experimental design approach for active learning, called Laplacian G-Optimal Design (LapGOD), which considers both discriminating and geometrical structures. By using Laplacian Regularized Least Squares which incorporates manifold regularization into linear regression, our proposed algorithm selects those data points that minimizes the maximum variance of the predicted values on the data manifold. We also extend our algorithm to nonlinear case by using kernel trick. The experimental results on various image databases have shown that our proposed LapGOD active learning algorithm can significantly enhance the classification accuracy if the selected data points are used as training data.