Optimality driven nearest centroid classification from genomic data

Nearest-centroid classifiers have recently been successfully employed in high-dimensional applications, such as in genomics. A necessary step when building a classifier for high-dimensional data is feature selection. Feature selection is frequently carried out by computing univariate scores for each feature individually, without consideration for how a subset of features performs as a whole. We introduce a new feature selection approach for high-dimensional nearest centroid classifiers that instead is based on the theoretically optimal choice of a given number of features, which we determine directly here. This allows us to develop a new greedy algorithm to estimate this optimal nearest-centroid classifier with a given number of features. In addition, whereas the centroids are usually formed from maximum likelihood estimates, we investigate the applicability of high-dimensional shrinkage estimates of centroids. We apply the proposed method to clinical classification based on gene-expression microarrays, demonstrating that the proposed method can outperform existing nearest centroid classifiers.     

Optimal Aggregation of Binary Classifiers for Multiclass Cancer Diagnosis Using Gene Expression Profiles

Multiclass classification is one of the fundamental tasks in bioinformatics and typically arises in cancer diagnosis studies by gene expression profiling. There have been many studies of aggregating binary classifiers to construct a multiclass classifier based on one-versus-the-rest (1R), one-versus-one (11), or other coding strategies, as well as some comparison studies between them. However, the studies found that the best coding depends on each situation. Therefore, a new problem, which we call the ldquooptimal coding problem,rdquo has arisen: how can we determine which coding is the optimal one in each situation? To approach this optimal coding problem, we propose a novel framework for constructing a multiclass classifier, in which each binary classifier to be aggregated has a weight value to be optimally tuned based on the observed data. Although there is no a priori answer to the optimal coding problem, our weight tuning method can be a consistent answer to the problem. We apply this method to various classification problems including a synthesized data set and some cancer diagnosis data sets from gene expression profiling. The results demonstrate that, in most situations, our method can improve classification accuracy over simple voting heuristics and is better than or comparable to state-of-the-art multiclass predictors.     

Multiclass cancer classification by support vector machines with class-wise optimized genes and probability estimates

We investigate the multiclass classification of cancer microarray samples. In contrast to classification of two cancer types from gene expression data, multiclass classification of more than two cancer types are relatively hard and less studied problem. We used class-wise optimized genes with corresponding one-versus-all support vector machine (OVA-SVM) classifier to maximize the utilization of selected genes. Final prediction was made by using probability scores from all classifiers. We used three different methods of estimating probability from decision value. Among the three probability methods, Platt's approach was more consistent, whereas, isotonic approach performed better for datasets with unequal proportion of samples in different classes. Probability based decision does not only gives true and fair comparison between different one-versus-all (OVA) classifiers but also gives the possibility of using them for any post analysis. Several ensemble experiments, an example of post analysis, of the three probability methods were implemented to study their effect in improving the classification accuracy. We observe that ensemble did help in improving the predictive accuracy of cancer data sets especially involving unbalanced samples. Four-fold external stratified cross-validation experiment was performed on the six multiclass cancer datasets to obtain unbiased estimates of prediction accuracies. Analysis of class-wise frequently selected genes on two cancer datasets demonstrated that the approach was able to select important and relevant genes consistent to literature. This study demonstrates successful implementation of the framework of class-wise feature selection and multiclass classification for prediction of cancer subtypes on six datasets.     

Support vector machine implementations for classification & clustering

BACKGROUND: We describe Support Vector Machine (SVM) applications to classification and clustering of channel current data. SVMs are variational-calculus based methods that are constrained to have structural risk minimization (SRM), i.e., they provide noise tolerant solutions for pattern recognition. The SVM approach encapsulates a significant amount of model-fitting information in the choice of its kernel. In work thus far, novel, information-theoretic, kernels have been successfully employed for notably better performance over standard kernels. Currently there are two approaches for implementing multiclass SVMs. One is called external multi-class that arranges several binary classifiers as a decision tree such that they perform a single-class decision making function, with each leaf corresponding to a unique class. The second approach, namely internal-multiclass, involves solving a single optimization problem corresponding to the entire data set (with multiple hyperplanes). RESULTS: Each SVM approach encapsulates a significant amount of model-fitting information in its choice of kernel. In work thus far, novel, information-theoretic, kernels were successfully employed for notably better performance over standard kernels. Two SVM approaches to multiclass discrimination are described: (1) internal multiclass (with a single optimization), and (2) external multiclass (using an optimized decision tree). We describe benefits of the internal-SVM approach, along with further refinements to the internal-multiclass SVM algorithms that offer significant improvement in training time without sacrificing accuracy. In situations where the data isn't clearly separable, making for poor discrimination, signal clustering is used to provide robust and useful information--to this end, novel, SVM-based clustering methods are also described. As with the classification, there are Internal and External SVM Clustering algorithms, both of which are briefly described.     

Class prediction for high-dimensional class-imbalanced data

Background  

The goal of class prediction studies is to develop rules to accurately predict the class membership of new samples. The rules are derived using the values of the variables available for each subject: the main characteristic of high-dimensional data is that the number of variables greatly exceeds the number of samples. Frequently the classifiers are developed using class-imbalanced data, i.e., data sets where the number of samples in each class is not equal. Standard classification methods used on class-imbalanced data often produce classifiers that do not accurately predict the minority class; the prediction is biased towards the majority class. In this paper we investigate if the high-dimensionality poses additional challenges when dealing with class-imbalanced prediction. We evaluate the performance of six types of classifiers on class-imbalanced data, using simulated data and a publicly available data set from a breast cancer gene-expression microarray study. We also investigate the effectiveness of some strategies that are available to overcome the effect of class imbalance.     

Classification and Visualization Based on Derived Image Features: Application to Genetic Syndromes

Data transformations prior to analysis may be beneficial in classification tasks. In this article we investigate a set of such transformations on 2D graph-data derived from facial images and their effect on classification accuracy in a high-dimensional setting. These transformations are low-variance in the sense that each involves only a fixed small number of input features. We show that classification accuracy can be improved when penalized regression techniques are employed, as compared to a principal component analysis (PCA) pre-processing step. In our data example classification accuracy improves from 47% to 62% when switching from PCA to penalized regression. A second goal is to visualize the resulting classifiers. We develop importance plots highlighting the influence of coordinates in the original 2D space. Features used for classification are mapped to coordinates in the original images and combined into an importance measure for each pixel. These plots assist in assessing plausibility of classifiers, interpretation of classifiers, and determination of the relative importance of different features.     

Classification using partial least squares with penalized logistic regression

MOTIVATION: One important aspect of data-mining of microarray data is to discover the molecular variation among cancers. In microarray studies, the number n of samples is relatively small compared to the number p of genes per sample (usually in thousands). It is known that standard statistical methods in classification are efficient (i.e. in the present case, yield successful classifiers) particularly when n is (far) larger than p. This naturally calls for the use of a dimension reduction procedure together with the classification one. RESULTS: In this paper, the question of classification in such a high-dimensional setting is addressed. We view the classification problem as a regression one with few observations and many predictor variables. We propose a new method combining partial least squares (PLS) and Ridge penalized logistic regression. We review the existing methods based on PLS and/or penalized likelihood techniques, outline their interest in some cases and theoretically explain their sometimes poor behavior. Our procedure is compared with these other classifiers. The predictive performance of the resulting classification rule is illustrated on three data sets: Leukemia, Colon and Prostate.     

A comparative study of feature selection and multiclass classification methods for tissue classification based on gene expression

This paper studies the problem of building multiclass classifiers for tissue classification based on gene expression. The recent development of microarray technologies has enabled biologists to quantify gene expression of tens of thousands of genes in a single experiment. Biologists have begun collecting gene expression for a large number of samples. One of the urgent issues in the use of microarray data is to develop methods for characterizing samples based on their gene expression. The most basic step in the research direction is binary sample classification, which has been studied extensively over the past few years. This paper investigates the next step-multiclass classification of samples based on gene expression. The characteristics of expression data (e.g. large number of genes with small sample size) makes the classification problem more challenging. The process of building multiclass classifiers is divided into two components: (i) selection of the features (i.e. genes) to be used for training and testing and (ii) selection of the classification method. This paper compares various feature selection methods as well as various state-of-the-art classification methods on various multiclass gene expression datasets. Our study indicates that multiclass classification problem is much more difficult than the binary one for the gene expression datasets. The difficulty lies in the fact that the data are of high dimensionality and that the sample size is small. The classification accuracy appears to degrade very rapidly as the number of classes increases. In particular, the accuracy was very low regardless of the choices of the methods for large-class datasets (e.g. NCI60 and GCM). While increasing the number of samples is a plausible solution to the problem of accuracy degradation, it is important to develop algorithms that are able to analyze effectively multiple-class expression data for these special datasets.     

Using attribute behavior diversity to build accurate decision tree committees for microarray data

DNA microarrays (gene chips), frequently used in biological and medical studies, measure the expressions of thousands of genes per sample. Using microarray data to build accurate classifiers for diseases is an important task. This paper introduces an algorithm, called Committee of Decision Trees by Attribute Behavior Diversity (CABD), to build highly accurate ensembles of decision trees for such data. Since a committee's accuracy is greatly influenced by the diversity among its member classifiers, CABD uses two new ideas to "optimize" that diversity, namely (1) the concept of attribute behavior-based similarity between attributes, and (2) the concept of attribute usage diversity among trees. The ideas are effective for microarray data, since such data have many features and behavior similarity between genes can be high. Experiments on microarray data for six cancers show that CABD outperforms previous ensemble methods significantly and outperforms SVM, and show that the diversified features used by CABD's decision tree committee can be used to improve performance of other classifiers such as SVM. CABD has potential for other high-dimensional data, and its ideas may apply to ensembles of other classifier types.     

Avoiding model selection bias in small-sample genomic datasets

MOTIVATION: Genomic datasets generated by high-throughput technologies are typically characterized by a moderate number of samples and a large number of measurements per sample. As a consequence, classification models are commonly compared based on resampling techniques. This investigation discusses the conceptual difficulties involved in comparative classification studies. Conclusions derived from such studies are often optimistically biased, because the apparent differences in performance are usually not controlled in a statistically stringent framework taking into account the adopted sampling strategy. We investigate this problem by means of a comparison of various classifiers in the context of multiclass microarray data. RESULTS: Commonly used accuracy-based performance values, with or without confidence intervals, are inadequate for comparing classifiers for small-sample data. We present a statistical methodology that avoids bias in cross-validated model selection in the context of small-sample scenarios. This methodology is valid for both k-fold cross-validation and repeated random sampling.     

Multiclass Decision Forest--a novel pattern recognition method for multiclass classification in microarray data analysis

The wealth of knowledge imbedded in gene expression data from DNA microarrays portends rapid advances in both research and clinic. Turning the prodigious and noisy data into knowledge is a challenge to the field of bioinformatics, and development of classifiers using supervised learning techniques is the primary methodological approach for clinical application using gene expression data. In this paper, we present a novel classification method, multiclass Decision Forest (DF), that is the direct extension of the two-class DF previously developed in our lab. Central to DF is the synergistic combining of multiple heterogenic but comparable decision trees to reach a more accurate and robust classification model. The computationally inexpensive multiclass DF algorithm integrates gene selection and model development, and thus eliminates the bias of gene preselection in crossvalidation. Importantly, the method provides several statistical means for assessment of prediction accuracy, prediction confidence, and diagnostic capability. We demonstrate the method by application to gene expression data for 83 small round blue-cell tumors (SRBCTs) samples belonging to one of four different classes. Based on 500 runs of 10-fold crossvalidation, tumor prediction accuracy was approximately 97%, sensitivity was approximately 95%, diagnostic sensitivity was approximately 91%, and diagnostic accuracy was approximately 99.5%. Among 25 genes selected to distinguish tumor class, 12 have functional information in the literature implicating their involvement in cancer. The four types of SRBCTs samples are also distinguishable in a clustering analysis based on the expression profiles of these 25 genes. The results demonstrated that the multiclass DF is an effective classification method for analysis of gene expression data for the purpose of molecular diagnostics.     

A comparison of machine learning algorithms for chemical toxicity classification using a simulated multi-scale data model

Background  

Bioactivity profiling using high-throughput in vitro assays can reduce the cost and time required for toxicological screening of environmental chemicals and can also reduce the need for animal testing. Several public efforts are aimed at discovering patterns or classifiers in high-dimensional bioactivity space that predict tissue, organ or whole animal toxicological endpoints. Supervised machine learning is a powerful approach to discover combinatorial relationships in complex in vitro/in vivo datasets. We present a novel model to simulate complex chemical-toxicology data sets and use this model to evaluate the relative performance of different machine learning (ML) methods.     

Computational neuroanatomy and co-expression of genes in the adult mouse brain,analysis tools for the Allen Brain Atlas

We review quantitative methods and software developed to analyze genome-scale, brain-wide spatially-mapped gene-expression data. We expose new methods based on the underlying high-dimensional geometry of voxel space and gene space, and on simulations of the distribution of co-expression networks of a given size. We apply them to the Allen Atlas of the adult mouse brain, and to the co-expression network of a set of genes related to nicotine addiction retrieved from the NicSNP database. The computational methods are implemented in BrainGeneExpressionAnalysis (BGEA), a Matlab toolbox available for download.     

High-Dimensional Heteroscedastic Regression with an Application to eQTL Data Analysis

We consider the problem of high-dimensional regression under non-constant error variances. Despite being a common phenomenon in biological applications, heteroscedasticity has, so far, been largely ignored in high-dimensional analysis of genomic data sets. We propose a new methodology that allows non-constant error variances for high-dimensional estimation and model selection. Our method incorporates heteroscedasticity by simultaneously modeling both the mean and variance components via a novel doubly regularized approach. Extensive Monte Carlo simulations indicate that our proposed procedure can result in better estimation and variable selection than existing methods when heteroscedasticity arises from the presence of predictors explaining error variances and outliers. Further, we demonstrate the presence of heteroscedasticity in and apply our method to an expression quantitative trait loci (eQTLs) study of 112 yeast segregants. The new procedure can automatically account for heteroscedasticity in identifying the eQTLs that are associated with gene expression variations and lead to smaller prediction errors. These results demonstrate the importance of considering heteroscedasticity in eQTL data analysis.     

Multiclass molecular cancer classification by kernel subspace methods with effective kernel parameter selection

Microarray techniques provide new insights into molecular classification of cancer types, which is critical for cancer treatments and diagnosis. Recently, an increasing number of supervised machine learning methods have been applied to cancer classification problems using gene expression data. Support vector machines (SVMs), in particular, have become one of the most effective and leading methods. However, there exist few studies on the application of other kernel methods in the literature. We apply a kernel subspace (KS) method to multiclass cancer classification problems, and assess its validity by comparing it with multiclass SVMs. Our comparative study using seven multiclass cancer datasets demonstrates that the KS method has high performance that is comparable to multiclass SVMs. Furthermore, we propose an effective criterion for kernel parameter selection, which is shown to be useful for the computation of the KS method.     

Instance-based concept learning from multiclass DNA microarray data

Background  

Various statistical and machine learning methods have been successfully applied to the classification of DNA microarray data. Simple instance-based classifiers such as nearest neighbor (NN) approaches perform remarkably well in comparison to more complex models, and are currently experiencing a renaissance in the analysis of data sets from biology and biotechnology. While binary classification of microarray data has been extensively investigated, studies involving multiclass data are rare. The question remains open whether there exists a significant difference in performance between NN approaches and more complex multiclass methods. Comparative studies in this field commonly assess different models based on their classification accuracy only; however, this approach lacks the rigor needed to draw reliable conclusions and is inadequate for testing the null hypothesis of equal performance. Comparing novel classification models to existing approaches requires focusing on the significance of differences in performance.     

Boosting multiclass learning with repeating codes and weak detectors for protein subcellular localization

MOTIVATION: Determining locations of protein expression is essential to understand protein function. Advances in green fluorescence protein (GFP) fusion proteins and automated fluorescence microscopy allow for rapid acquisition of large collections of protein localization images. Recognition of these cell images requires an automated image analysis system. Approaches taken by previous work concentrated on designing a set of optimal features and then applying standard machine-learning algorithms. In fact, trends of recent advances in machine learning and computer vision can be applied to improve the performance. One trend is the advances in multiclass learning with error-correcting output codes (ECOC). Another trend is the use of a large number of weak detectors with boosting for detecting objects in images of real-world scenes. RESULTS: We take advantage of these advances to propose a new learning algorithm, AdaBoost.ERC, coupled with weak and strong detectors, to improve the performance of automatic recognition of protein subcellular locations in cell images. We prepared two image data sets of CHO and Vero cells and downloaded a HeLa cell image data set in the public domain to evaluate our new method. We show that AdaBoost.ERC outperforms other AdaBoost extensions. We demonstrate the benefit of weak detectors by showing significant performance improvements over classifiers using only strong detectors. We also empirically test our method's capability of generalizing to heterogeneous image collections. Compared with previous work, our method performs reasonably well for the HeLa cell images. AVAILABILITY: CHO and Vero cell images, their corresponding feature sets (SSLF and WSLF), our new learning algorithm, AdaBoost.ERC, and Supplementary Material are available at http://aiia.iis.sinica.edu.tw/     

Multiclass cancer classification using semisupervised ellipsoid ARTMAP and particle swarm optimization with gene expression data

It is crucial for cancer diagnosis and treatment to accurately identify the site of origin of a tumor. With the emergence and rapid advancement of DNA microarray technologies, constructing gene expression profiles for different cancer types has already become a promising means for cancer classification. In addition to research on binary classification such as normal versus tumor samples, which attracts numerous efforts from a variety of disciplines, the discrimination of multiple tumor types is also important. Meanwhile, the selection of genes which are relevant to a certain cancer type not only improves the performance of the classifiers, but also provides molecular insights for treatment and drug development. Here, we use semisupervised ellipsoid ARTMAP (ssEAM) for multiclass cancer discrimination and particle swarm optimization for informative gene selection. ssEAM is a neural network architecture rooted in adaptive resonance theory and suitable for classification tasks. ssEAM features fast, stable, and finite learning and creates hyperellipsoidal clusters, inducing complex nonlinear decision boundaries. PSO is an evolutionary algorithm-based technique for global optimization. A discrete binary version of PSO is employed to indicate whether genes are chosen or not. The effectiveness of ssEAM/PSO for multiclass cancer diagnosis is demonstrated by testing it on three publicly available multiple-class cancer data sets. ssEAM/PSO achieves competitive performance on all these data sets, with results comparable to or better than those obtained by other classifiers     

PSP_MCSVM: brainstorming consensus prediction of protein secondary structures using two-stage multiclass support vector machines

Secondary structure prediction is a crucial task for understanding the variety of protein structures and performed biological functions. Prediction of secondary structures for new proteins using their amino acid sequences is of fundamental importance in bioinformatics. We propose a novel technique to predict protein secondary structures based on position-specific scoring matrices (PSSMs) and physico-chemical properties of amino acids. It is a two stage approach involving multiclass support vector machines (SVMs) as classifiers for three different structural conformations, viz., helix, sheet and coil. In the first stage, PSSMs obtained from PSI-BLAST and five specially selected physicochemical properties of amino acids are fed into SVMs as features for sequence-to-structure prediction. Confidence values for forming helix, sheet and coil that are obtained from the first stage SVM are then used in the second stage SVM for performing structure-to-structure prediction. The two-stage cascaded classifiers (PSP_MCSVM) are trained with proteins from RS126 dataset. The classifiers are finally tested on target proteins of critical assessment of protein structure prediction experiment-9 (CASP9). PSP_MCSVM with brainstorming consensus procedure performs better than the prediction servers like Predator, DSC, SIMPA96, for randomly selected proteins from CASP9 targets. The overall performance is found to be comparable with the current state-of-the art. PSP_MCSVM source code, train-test datasets and supplementary files are available freely in public domain at: and     

Microarray-based expression profiling and informatics

Microarray-based expression profiling is a powerful technology for studying biological mechanisms and for developing clinically valuable predictive classifiers. The high-dimensional read-out for each sample assayed makes it possible to do new kinds of studies but also increases the risks of misleading conclusions. We review here the current state-of-the-art for design and analysis of microarray-based investigations.