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The ensemble method random forests has become a popular classification tool in bioinformatics and related fields. The out-of-bag error is an error estimation technique often used to evaluate the accuracy of a random forest and to select appropriate values for tuning parameters, such as the number of candidate predictors that are randomly drawn for a split, referred to as mtry. However, for binary classification problems with metric predictors it has been shown that the out-of-bag error can overestimate the true prediction error depending on the choices of random forests parameters. Based on simulated and real data this paper aims to identify settings for which this overestimation is likely. It is, moreover, questionable whether the out-of-bag error can be used in classification tasks for selecting tuning parameters like mtry, because the overestimation is seen to depend on the parameter mtry. The simulation-based and real-data based studies with metric predictor variables performed in this paper show that the overestimation is largest in balanced settings and in settings with few observations, a large number of predictor variables, small correlations between predictors and weak effects. There was hardly any impact of the overestimation on tuning parameter selection. However, although the prediction performance of random forests was not substantially affected when using the out-of-bag error for tuning parameter selection in the present studies, one cannot be sure that this applies to all future data. For settings with metric predictor variables it is therefore strongly recommended to use stratified subsampling with sampling fractions that are proportional to the class sizes for both tuning parameter selection and error estimation in random forests. This yielded less biased estimates of the true prediction error. In unbalanced settings, in which there is a strong interest in predicting observations from the smaller classes well, sampling the same number of observations from each class is a promising alternative. [ABSTRACT FROM AUTHOR]

The process of Nuclei detection in high-grade breast cancer images is quite challenging in the case of image processing techniques due to certain heterogeneous characteristics of cancer nuclei such as enlarged and irregularly shaped nuclei, highly coarse chromatin marginalized to the nuclei periphery and visible nucleoli. Recent reviews state that existing techniques show appreciable segmentation accuracy on breast histopathology images whose nuclei are dispersed and regular in texture and shape; however, typical cancer nuclei are often clustered and have irregular texture and shape properties. This paper proposes a novel segmentation algorithm for detecting individual nuclei from Hematoxylin and Eosin (H&E) stained breast histopathology images. This detection framework estimates a nuclei saliency map using tensor voting followed by boundary extraction of the nuclei on the saliency map using a Loopy Back Propagation (LBP) algorithm on a Markov Random Field (MRF). The method was tested on both whole-slide images and frames of breast cancer histopathology images. Experimental results demonstrate high segmentation performance with efficient precision, recall and dice-coefficient rates, upon testing high-grade breast cancer images containing several thousand nuclei. In addition to the optimal performance on the highly complex images presented in this paper, this method also gave appreciable results in comparison with two recently published methods—Wienert et al. (2012) and Veta et al. (2013), which were tested using their own datasets. [ABSTRACT FROM AUTHOR]

Motivation: Disease progression originates from the concept that an individual disease may go through different changes as it evolves, and such changes can cause new diseases. It is important to find a progression between diseases since knowing the prior-posterior relationship beforehand can prevent further complications or evolutions to other diseases. Furthermore, the series of progressions can be represented in the form of a chain, which enables us to readily infer successive influences from one disease to another after many passages through other diseases. Methods: In this paper, we propose a systematic approach for finding a disease progression chain from a source disease to a target one via exploring a disease network. The network is constructed based on various sets of biomedical data. To find the most influential progression chains, the k-shortest path search algorithm is employed. The most representative algorithms such as A*, Dijkstra, and Yen’s are incorporated into the proposed method. Results: A disease network consisting of 3,302 diseases was constructed based on four sources of biomedical data: disease-protein relations, biological pathways, clinical history, and biomedical literature information. The last three sets of data contain prior-posterior information, and they endow directionality on the edges of the network. The results were interesting and informative: for example, when colitis and respiratory insufficiency were set as a source disease and a target one, respectively, five progression chains were found within several seconds (when k = 5). Each chain was provided with a progression score, which indicates the strength of plausibility relative to others. Similarly, the proposed method can be expanded to any pair of source-target diseases in the network. This can be utilized as a preliminary tool for inferring complications or progressions between diseases. [ABSTRACT FROM AUTHOR]

High dimensional biomedical data contain tens of thousands of features, accurate and effective identification of the core features in these data can be used to assist diagnose related diseases. However, there are often a large number of irrelevant or redundant features in biomedical data, which seriously affect subsequent classification accuracy and machine learning efficiency. To solve this problem, a novel filter feature selection algorithm based on redundant removal (FSBRR) is proposed to classify high dimensional biomedical data in this paper. First of all, two redundant criteria are determined by vertical relevance (the relationship between feature and class attribute) and horizontal relevance (the relationship between feature and feature). Secondly, to quantify redundant criteria, an approximate redundancy feature framework based on mutual information (MI) is defined to remove redundant and irrelevant features. To evaluate the effectiveness of our proposed algorithm, controlled trials based on typical feature selection algorithm are conducted using three different classifiers, and the experimental results indicate that the FSBRR algorithm can effectively reduce the feature dimension and improve the classification accuracy. In addition, an experiment of small sample dataset is designed and conducted in the section of discussion and analysis to clarify the specific implementation process of FSBRR algorithm more clearly. [ABSTRACT FROM AUTHOR]

For studying cancer and genetic diseases, the issue of identifying high correlation genes from high-dimensional data is an important problem. It is a great challenge to select relevant biomarkers from gene expression data that contains some important correlation structures, and some of the genes can be divided into different groups with a common biological function, chromosomal location or regulation. In this paper, we propose a penalized accelerated failure time model CHR-DE using a non-convex regularization (local search) with differential evolution (global search) in a wrapper-embedded memetic framework. The complex harmonic regularization (CHR) can approximate to the combination and ℓq (1 ≤ q < 2) for selecting biomarkers in group. And differential evolution (DE) is utilized to globally optimize the CHR’s hyperparameters, which make CHR-DE achieve strong capability of selecting groups of genes in high-dimensional biological data. We also developed an efficient path seeking algorithm to optimize this penalized model. The proposed method is evaluated on synthetic and three gene expression datasets: breast cancer, hepatocellular carcinoma and colorectal cancer. The experimental results demonstrate that CHR-DE is a more effective tool for feature selection and learning prediction. [ABSTRACT FROM AUTHOR]

Several modern genomic technologies, such as DNA-Methylation arrays, measure spatially registered probes that number in the hundreds of thousands across multiple chromosomes. The measured probes are by themselves less interesting scientifically; instead scientists seek to discover biologically interpretable genomic regions comprised of contiguous groups of probes which may act as biomarkers of disease or serve as a dimension-reducing pre-processing step for downstream analyses. In this paper, we introduce an unsupervised feature learning technique which maps technological units (probes) to biological units (genomic regions) that are common across all subjects. We use ideas from fusion penalties and convex clustering to introduce a method for Spatial Convex Clustering, or SpaCC. Our method is specifically tailored to detecting multi-subject regions of methylation, but we also test our approach on the well-studied problem of detecting segments of copy number variation. We formulate our method as a convex optimization problem, develop a massively parallelizable algorithm to find its solution, and introduce automated approaches for handling missing values and determining tuning parameters. Through simulation studies based on real methylation and copy number variation data, we show that SpaCC exhibits significant performance gains relative to existing methods. Finally, we illustrate SpaCC’s advantages as a pre-processing technique that reduces large-scale genomics data into a smaller number of genomic regions through several cancer epigenetics case studies on subtype discovery, network estimation, and epigenetic-wide association. [ABSTRACT FROM AUTHOR]

Feature selection and classification are the main topics in microarray data analysis. Although many feature selection methods have been proposed and developed in this field, SVM-RFE (Support Vector Machine based on Recursive Feature Elimination) is proved as one of the best feature selection methods, which ranks the features (genes) by training support vector machine classification model and selects key genes combining with recursive feature elimination strategy. The principal drawback of SVM-RFE is the huge time consumption. To overcome this limitation, we introduce a more efficient implementation of linear support vector machines and improve the recursive feature elimination strategy and then combine them together to select informative genes. Besides, we propose a simple resampling method to preprocess the datasets, which makes the information distribution of different kinds of samples balanced and the classification results more credible. Moreover, the applicability of four common classifiers is also studied in this paper. Extensive experiments are conducted on six most frequently used microarray datasets in this field, and the results show that the proposed methods have not only reduced the time consumption greatly but also obtained comparable classification performance. [ABSTRACT FROM AUTHOR]

Microarray technology is important to simultaneously express multiple genes over a number of time points. Multiple classifier models, such as sparse representation (SR)-based method, have been developed to classify microarray gene expression data. These methods allocate the gene data points to different clusters. In this paper, we propose a novel collaborative representation (CR)-based classification with regularized least square to classify gene data. First, the CR codes a testing sample as a sparse linear combination of all training samples and then classifies the testing sample by evaluating which class leads to the minimum representation error. This CR-based classification approach is remarkably less complex than traditional classification methods but leads to very competitive classification results. In addition, compressive sensing approach is adopted to project the high-dimensional gene expression dataset to a lower-dimensional space which nearly contains the whole information. This compression without loss is beneficial to reduce the computational load. Experiments to detect subtypes of diseases, such as leukemia and autism spectrum disorders, are performed by analyzing the gene expression. The results show that the proposed CR-based algorithm exhibits significantly higher stability and accuracy than the traditional classifiers, such as support vector machine algorithm. [ABSTRACT FROM AUTHOR]

Integrative clustering is used to identify groups of samples by jointly analysing multiple datasets describing the same set of biological samples, such as gene expression, copy number, methylation etc. Most existing algorithms for integrative clustering assume that there is a shared consistent set of clusters across all datasets, and most of the data samples follow this structure. However in practice, the structure across heterogeneous datasets can be more varied, with clusters being joined in some datasets and separated in others. In this paper, we present a probabilistic clustering method to identify groups across datasets that do not share the same cluster structure. The proposed algorithm, Clusternomics, identifies groups of samples that share their global behaviour across heterogeneous datasets. The algorithm models clusters on the level of individual datasets, while also extracting global structure that arises from the local cluster assignments. Clusters on both the local and the global level are modelled using a hierarchical Dirichlet mixture model to identify structure on both levels. We evaluated the model both on simulated and on real-world datasets. The simulated data exemplifies datasets with varying degrees of common structure. In such a setting Clusternomics outperforms existing algorithms for integrative and consensus clustering. In a real-world application, we used the algorithm for cancer subtyping, identifying subtypes of cancer from heterogeneous datasets. We applied the algorithm to TCGA breast cancer dataset, integrating gene expression, miRNA expression, DNA methylation and proteomics. The algorithm extracted clinically meaningful clusters with significantly different survival probabilities. We also evaluated the algorithm on lung and kidney cancer TCGA datasets with high dimensionality, again showing clinically significant results and scalability of the algorithm. [ABSTRACT FROM AUTHOR]

With the recent technological developments a vast amount of high-throughput data has been profiled to understand the mechanism of complex diseases. The current bioinformatics challenge is to interpret the data and underlying biology, where efficient algorithms for analyzing heterogeneous high-throughput data using biological networks are becoming increasingly valuable. In this paper, we propose a software package based on the Prize-collecting Steiner Forest graph optimization approach. The PCSF package performs fast and user-friendly network analysis of high-throughput data by mapping the data onto a biological networks such as protein-protein interaction, gene-gene interaction or any other correlation or coexpression based networks. Using the interaction networks as a template, it determines high-confidence subnetworks relevant to the data, which potentially leads to predictions of functional units. It also interactively visualizes the resulting subnetwork with functional enrichment analysis. [ABSTRACT FROM AUTHOR]

Lung 4D computed tomography (4D-CT) plays an important role in high-precision radiotherapy because it characterizes respiratory motion, which is crucial for accurate target definition. However, the manual segmentation of a lung tumor is a heavy workload for doctors because of the large number of lung 4D-CT data slices. Meanwhile, tumor segmentation is still a notoriously challenging problem in computer-aided diagnosis. In this paper, we propose a new method based on an improved graph cut algorithm with context information constraint to find a convenient and robust approach of lung 4D-CT tumor segmentation. We combine all phases of the lung 4D-CT into a global graph, and construct a global energy function accordingly. The sub-graph is first constructed for each phase. A context cost term is enforced to achieve segmentation results in every phase by adding a context constraint between neighboring phases. A global energy function is finally constructed by combining all cost terms. The optimization is achieved by solving a max-flow/min-cut problem, which leads to simultaneous and robust segmentation of the tumor in all the lung 4D-CT phases. The effectiveness of our approach is validated through experiments on 10 different lung 4D-CT cases. The comparison with the graph cut without context constraint, the level set method and the graph cut with star shape prior demonstrates that the proposed method obtains more accurate and robust segmentation results. [ABSTRACT FROM AUTHOR]

Blood oxygenation mapping by the means of optical oximetry is of significant importance in clinical trials. This paper uses hyperspectral imaging technology to obtain in vivo images for blood oxygenation detection. The experiment involves dorsal skin fold window chamber preparation which was built on adult (8–10 weeks of age) female BALB/c nu/nu mice and in vivo image acquisition which was performed by hyperspectral imaging system. To get the accurate spatial and spectral information of targets, an automatic registration scheme is proposed. An adaptive feature detection method which combines the local threshold method and the level-set filter is presented to extract target vessels. A reliable feature matching algorithm with the correlative information inherent in hyperspectral images is used to kick out the outliers. Then, the registration images are used for blood oxygenation mapping. Registration evaluation results show that most of the false matches are removed and the smooth and concentrated spectra are obtained. This intensity invariant feature detection with outliers-removing feature matching proves to be effective in hyperspectral vessel image registration. Therefore, in vivo hyperspectral imaging system by the assistance of the proposed registration scheme provides a technique for blood oxygenation research. [ABSTRACT FROM AUTHOR]

Fuzzy co-clustering extends co-clustering by assigning membership functions to both the objects and the features, and is helpful to improve clustering accurarcy of biomedical data. In this paper, we introduce a new fuzzy co-clustering algorithm based on information bottleneck named ibFCC. The ibFCC formulates an objective function which includes a distance function that employs information bottleneck theory to measure the distance between feature data point and the feature cluster centroid. Many experiments were conducted on five biomedical datasets, and the ibFCC was compared with such prominent fuzzy (co-)clustering algorithms as FCM, FCCM, RFCC and FCCI. Experimental results showed that ibFCC could yield high quality clusters and was better than all these methods in terms of accuracy. [ABSTRACT FROM AUTHOR]

Gene expression data analysis has paramount implications for gene treatments, cancer diagnosis and other domains. Clustering is an important and promising tool to analyze gene expression data. Gene expression data is often characterized by a large amount of genes but with limited samples, thus various projective clustering techniques and ensemble techniques have been suggested to combat with these challenges. However, it is rather challenging to synergy these two kinds of techniques together to avoid the curse of dimensionality problem and to boost the performance of gene expression data clustering. In this paper, we employ a projective clustering ensemble (PCE) to integrate the advantages of projective clustering and ensemble clustering, and to avoid the dilemma of combining multiple projective clusterings. Our experimental results on publicly available cancer gene expression data show PCE can improve the quality of clustering gene expression data by at least 4.5% (on average) than other related techniques, including dimensionality reduction based single clustering and ensemble approaches. The empirical study demonstrates that, to further boost the performance of clustering cancer gene expression data, it is necessary and promising to synergy projective clustering with ensemble clustering. PCE can serve as an effective alternative technique for clustering gene expression data. [ABSTRACT FROM AUTHOR]

Spatial scan statistics with circular or elliptic scanning windows are commonly used for cluster detection in various applications, such as the identification of geographical disease clusters from epidemiological data. It has been pointed out that the method may have difficulty in correctly identifying non-compact, arbitrarily shaped clusters. In this paper, we evaluated the Gini coefficient for detecting irregularly shaped clusters through a simulation study. The Gini coefficient, the use of which in spatial scan statistics was recently proposed, is a criterion measure for optimizing the maximum reported cluster size. Our simulation study results showed that using the Gini coefficient works better than the original spatial scan statistic for identifying irregularly shaped clusters, by reporting an optimized and refined collection of clusters rather than a single larger cluster. We have provided a real data example that seems to support the simulation results. We think that using the Gini coefficient in spatial scan statistics can be helpful for the detection of irregularly shaped clusters. [ABSTRACT FROM AUTHOR]

Stain colour estimation is a prominent factor of the analysis pipeline in most of histology image processing algorithms. Providing a reliable and efficient stain colour deconvolution approach is fundamental for robust algorithm. In this paper, we propose a novel method for stain colour deconvolution of histology images. This approach statistically analyses the multi-resolutional representation of the image to separate the independent observations out of the correlated ones. We then estimate the stain mixing matrix using filtered uncorrelated data. We conducted an extensive set of experiments to compare the proposed method to the recent state of the art methods and demonstrate the robustness of this approach using three different datasets of scanned slides, prepared in different labs using different scanners. [ABSTRACT FROM AUTHOR]

Breast cancer is an all too common disease in women, making how to effectively predict it an active research problem. A number of statistical and machine learning techniques have been employed to develop various breast cancer prediction models. Among them, support vector machines (SVM) have been shown to outperform many related techniques. To construct the SVM classifier, it is first necessary to decide the kernel function, and different kernel functions can result in different prediction performance. However, there have been very few studies focused on examining the prediction performances of SVM based on different kernel functions. Moreover, it is unknown whether SVM classifier ensembles which have been proposed to improve the performance of single classifiers can outperform single SVM classifiers in terms of breast cancer prediction. Therefore, the aim of this paper is to fully assess the prediction performance of SVM and SVM ensembles over small and large scale breast cancer datasets. The classification accuracy, ROC, F-measure, and computational times of training SVM and SVM ensembles are compared. The experimental results show that linear kernel based SVM ensembles based on the bagging method and RBF kernel based SVM ensembles with the boosting method can be the better choices for a small scale dataset, where feature selection should be performed in the data pre-processing stage. For a large scale dataset, RBF kernel based SVM ensembles based on boosting perform better than the other classifiers. [ABSTRACT FROM AUTHOR]

In this paper, a total variation (TV) minimization strategy is proposed to overcome the problem of sparse spatial resolution and large amounts of noise in low dose positron emission tomography (PET) imaging reconstruction. Two types of objective function were established based on two statistical models of measured PET data, least-square (LS) TV for the Gaussian distribution and Poisson-TV for the Poisson distribution. To efficiently obtain high quality reconstructed images, the alternating direction method (ADM) is used to solve these objective functions. As compared with the iterative shrinkage/thresholding (IST) based algorithms, the proposed ADM can make full use of the TV constraint and its convergence rate is faster. The performance of the proposed approach is validated through comparisons with the expectation-maximization (EM) method using synthetic and experimental biological data. In the comparisons, the results of both LS-TV and Poisson-TV are taken into consideration to find which models are more suitable for PET imaging, in particular low-dose PET. To evaluate the results quantitatively, we computed bias, variance, and the contrast recovery coefficient (CRC) and drew profiles of the reconstructed images produced by the different methods. The results show that both Poisson-TV and LS-TV can provide a high visual quality at a low dose level. The bias and variance of the proposed LS-TV and Poisson-TV methods are 20% to 74% less at all counting levels than those of the EM method. Poisson-TV gives the best performance in terms of high-accuracy reconstruction with the lowest bias and variance as compared to the ground truth (14.3% less bias and 21.9% less variance). In contrast, LS-TV gives the best performance in terms of the high contrast of the reconstruction with the highest CRC. [ABSTRACT FROM AUTHOR]

One of fundamental challenges in cancer studies is that varying molecular characteristics of different tumor types may lead to resistance to certain drugs. As a result, the same drug can lead to significantly different results in different types of cancer thus emphasizing the need for individualized medicine. Individual prediction of drug response has great potential to aid in improving the clinical outcome and reduce the financial costs associated with prescribing chemotherapy drugs to which the patient’s tumor might be resistant. In this paper we develop a network based classifier (NBC) method for predicting sensitivity of cell lines to anticancer drugs from transcriptome data. In the literature, this strategy has been used for predicting cancer types. Here, we extend it to estimate sensitivity of cells from different tumor types to various anticancer drugs. Furthermore, we incorporate domain specific knowledge such as the use of apoptotic gene list and clinical dose information in our method to impart biological significance to the prediction. Our experimental results suggest that our network based classifier (NBC) method outperforms existing classifiers in estimating sensitivity of cell lines for different drugs. [ABSTRACT FROM AUTHOR]

Recent research has demonstrated that characteristic gene selection based on gene expression data remains faced with considerable challenges. This is primarily because gene expression data are typically high dimensional, negative, non-sparse and noisy. However, existing methods for data analysis are able to cope with only some of these challenges. In this paper, we address all of these challenges with a unified method: nonnegative matrix factorization via the L2,1-norm (NMF-L2,1). While L2,1-norm minimization is applied to both the error function and the regularization term, our method is robust to outliers and noise in the data and generates sparse results. The application of our method to plant and tumor gene expression data demonstrates that NMF-L2,1 can extract more characteristic genes than other existing state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Identification of disease-causing genes is a fundamental challenge for human health studies. The phenotypic similarity among diseases may reflect the interactions at the molecular level, and phenotype comparison can be used to predict disease candidate genes. Online Mendelian Inheritance in Man (OMIM) is a database of human genetic diseases and related genes that has become an authoritative source of disease phenotypes. However, disease phenotypes have been described by free text; thus, standardization of phenotypic descriptions is needed before diseases can be compared. Several disease phenotype networks have been established in OMIM using different standardization methods. Two of these networks are important for phenotypic similarity analysis: the first and most commonly used network (mimMiner) is standardized by medical subject heading, and the other network (resnikHPO) is the first to be standardized by human phenotype ontology. This paper comprehensively evaluates for the first time the accuracy of these two networks in gene prioritization based on protein–protein interactions using large-scale, leave-one-out cross-validation experiments. The results show that both networks can effectively prioritize disease-causing genes, and the approach that relates two diseases using a logistic function improves prioritization performance. Tanimoto, one of four methods for normalizing resnikHPO, generates a symmetric network and it performs similarly to mimMiner. Furthermore, an integration of these two networks outperforms either network alone in gene prioritization, indicating that these two disease networks are complementary. [ABSTRACT FROM AUTHOR]

The maximal information coefficient (MIC) captures dependences between paired variables, including both functional and non-functional relationships. In this paper, we develop a new method, ChiMIC, to calculate the MIC values. The ChiMIC algorithm uses the chi-square test to terminate grid optimization and then removes the restriction of maximal grid size limitation of original ApproxMaxMI algorithm. Computational experiments show that ChiMIC algorithm can maintain same MIC values for noiseless functional relationships, but gives much smaller MIC values for independent variables. For noise functional relationship, the ChiMIC algorithm can reach the optimal partition much faster. Furthermore, the MCN values based on MIC calculated by ChiMIC can capture the complexity of functional relationships in a better way, and the statistical powers of MIC calculated by ChiMIC are higher than those calculated by ApproxMaxMI. Moreover, the computational costs of ChiMIC are much less than those of ApproxMaxMI. We apply the MIC values tofeature selection and obtain better classification accuracy using features selected by the MIC values from ChiMIC. [ABSTRACT FROM AUTHOR]

The identification of a subset of genes having the ability to capture the necessary information to distinguish classes of patients is crucial in bioinformatics applications. Ensemble and bagging methods have been shown to work effectively in the process of gene selection and classification. Testament to that is random forest which combines random decision trees with bagging to improve overall feature selection and classification accuracy. Surprisingly, the adoption of these methods in support vector machines has only recently received attention but mostly on classification not gene selection. This paper introduces an ensemble SVM-Recursive Feature Elimination (ESVM-RFE) for gene selection that follows the concepts of ensemble and bagging used in random forest but adopts the backward elimination strategy which is the rationale of RFE algorithm. The rationale behind this is, building ensemble SVM models using randomly drawn bootstrap samples from the training set, will produce different feature rankings which will be subsequently aggregated as one feature ranking. As a result, the decision for elimination of features is based upon the ranking of multiple SVM models instead of choosing one particular model. Moreover, this approach will address the problem of imbalanced datasets by constructing a nearly balanced bootstrap sample. Our experiments show that ESVM-RFE for gene selection substantially increased the classification performance on five microarray datasets compared to state-of-the-art methods. Experiments on the childhood leukaemia dataset show that an average 9% better accuracy is achieved by ESVM-RFE over SVM-RFE, and 5% over random forest based approach. The selected genes by the ESVM-RFE algorithm were further explored with Singular Value Decomposition (SVD) which reveals significant clusters with the selected data. [ABSTRACT FROM AUTHOR]

Cancer classification and feature (gene) selection plays an important role in knowledge discovery in genomic data. Although logistic regression is one of the most popular classification methods, it does not induce feature selection. In this paper, we presented a new hybrid L1/2 +2 regularization (HLR) function, a linear combination of L1/2 and L2 penalties, to select the relevant gene in the logistic regression. The HLR approach inherits some fascinating characteristics from L1/2 (sparsity) and L2 (grouping effect where highly correlated variables are in or out a model together) penalties. We also proposed a novel univariate HLR thresholding approach to update the estimated coefficients and developed the coordinate descent algorithm for the HLR penalized logistic regression model. The empirical results and simulations indicate that the proposed method is highly competitive amongst several state-of-the-art methods. [ABSTRACT FROM AUTHOR]