Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

A review on the combination of binary classifiers in multiclass problems

Several real problems involve the classification of data into categories or classes. Given a data set containing data whose classes are known, Machine Learning algorithms can be employed for the induction of a classifier able to predict the class of new data from the same domain, performing the desired discrimination. Some learning techniques are originally conceived for the solution of problems with only two classes, also named binary classification problems. However, many problems require the discrimination of examples into more than two categories or classes. This paper presents a survey on the main strategies for the generalization of binary classifiers to problems with more than two classes, known as multiclass classification problems. The focus is on strategies that decompose the original multiclass problem into multiple binary subtasks, whose outputs are combined to obtain the final prediction.

HIERARCHICAL DECOMPOSITION OF MULTICLASS PROBLEMS

Several popular Machine Learning techniques are originally designed for the solution of two-class problems. However, several classification problems have more than two classes. One approach to deal with multiclass problems using binary classifiers is to decompose the multiclass problem into multiple binary sub-problems disposed in a binary tree. This approach requires a binary partition of the classes for each node of the tree, which defines the tree structure. This paper presents two algorithms to determine the tree structure taking into account information collected from the used dataset. This approach allows the tree structure to be determined automatically for any multiclass dataset.

Multiclass Classification of SRBCTs

A novel approach to multiclass tumor classification using Artificial Neural Networks (ANNs) was introduced in a recent paper cite{Khan2001}. The method successfully classified and diagnosed small, round blue cell tumors (SRBCTs) of childhood into four distinct categories, neuroblastoma (NB), rhabdomyosarcoma (RMS), non-Hodgkin lymphoma (NHL) and the Ewing family of tumors (EWS), using cDNA gene expression profiles of samples that included both tumor biopsy material and cell lines. We report that using an approach similar to the one reported by Yeang et al cite{Yeang2001}, i.e. multiclass classification by combining outputs of binary classifiers, we achieved equal accuracy with much fewer features. We report the performances of 3 binary classifiers (k-nearest neighbors (kNN), weighted-voting (WV), and support vector machines (SVM)) with 3 feature selection techniques (Golub's Signal to Noise (SN) ratios cite{Golub99}, Fisher scores (FSc) and Mukherjee's SVM feature selection (SVMFS))cite{Sayan98}.

Building binary-tree-based multiclass classifiers using separability measures

Various popular machine learning techniques, like support vector machines, are originally conceived for the solution of two-class (binary) classification problems. However, a large number of real problems present more than two classes. A common approach to generalize binary learning techniques to solve problems with more than two classes, also known as multiclass classification problems, consists of hierarchically decomposing the multiclass problem into multiple binary sub-problems, whose outputs are combined to define the predicted class. This strategy results in a tree of binary classifiers, where each internal node corresponds to a binary classifier distinguishing two groups of classes and the leaf nodes correspond to the problem classes. This paper investigates how measures of the separability between classes can be employed in the construction of binary-tree-based multiclass classifiers, adapting the decompositions performed to each particular multiclass problem. (C) 2010 Elsevier B.V. All rights reserved.

Pruning methods to MLP neural networks considering proportional apparent error rate for classification problems with unbalanced data

This article deals with classification problems involving unequal probabilities in each class and discusses metrics to systems that use multilayer perceptrons neural networks (MLP) for the task of classifying new patterns. In addition we propose three new pruning methods that were compared to other seven existing methods in the literature for MLP networks. All pruning algorithms presented in this paper have been modified by the authors to do pruning of neurons, in order to produce fully connected MLP networks but being small in its intermediary layer. Experiments were carried out involving the E. coli unbalanced classification problem and ten pruning methods. The proposed methods had obtained good results, actually, better results than another pruning methods previously defined at the MLP neural network area. (C) 2014 Elsevier Ltd. All rights reserved.

Using the EM Algorithm to Train Neural Networks: Misconceptions and a New Algorithm for Multiclass Classification

The expectation-maximization (EM) algorithm has been of considerable interest in recent years as the basis for various algorithms in application areas of neural networks such as pattern recognition. However, there exists some misconceptions concerning its application to neural networks. In this paper, we clarify these misconceptions and consider how the EM algorithm can be adopted to train multilayer perceptron (MLP) and mixture of experts (ME) networks in applications to multiclass classification. We identify some situations where the application of the EM algorithm to train MLP networks may be of limited value and discuss some ways of handling the difficulties. For ME networks, it is reported in the literature that networks trained by the EM algorithm using iteratively reweighted least squares (IRLS) algorithm in the inner loop of the M-step, often performed poorly in multiclass classification. However, we found that the convergence of the IRLS algorithm is stable and that the log likelihood is monotonic increasing when a learning rate smaller than one is adopted. Also, we propose the use of an expectation-conditional maximization (ECM) algorithm to train ME networks. Its performance is demonstrated to be superior to the IRLS algorithm on some simulated and real data sets.

Tensor-Train decomposition for image classification problems

In these last years a great effort has been put in the development of new techniques for automatic object classification, also due to the consequences in many applications such as medical imaging or driverless cars. To this end, several mathematical models have been developed from logistic regression to neural networks. A crucial aspect of these so called classification algorithms is the use of algebraic tools to represent and approximate the input data. In this thesis, we examine two different models for image classification based on a particular tensor decomposition named Tensor-Train (TT) decomposition. The use of tensor approaches preserves the multidimensional structure of the data and the neighboring relations among pixels. Furthermore the Tensor-Train, differently from other tensor decompositions, does not suffer from the curse of dimensionality making it an extremely powerful strategy when dealing with high-dimensional data. It also allows data compression when combined with truncation strategies that reduce memory requirements without spoiling classification performance. The first model we propose is based on a direct decomposition of the database by means of the TT decomposition to find basis vectors used to classify a new object. The second model is a tensor dictionary learning model, based on the TT decomposition where the terms of the decomposition are estimated using a proximal alternating linearized minimization algorithm with a spectral stepsize.

Subclass problem-dependent design for error-correcting output codes

A common way to model multiclass classification problems is by means of Error-Correcting Output Codes (ECOCs). Given a multiclass problem, the ECOC technique designs a code word for each class, where each position of the code identifies the membership of the class for a given binary problem. A classification decision is obtained by assigning the label of the class with the closest code. One of the main requirements of the ECOC design is that the base classifier is capable of splitting each subgroup of classes from each binary problem. However, we cannot guarantee that a linear classifier model convex regions. Furthermore, nonlinear classifiers also fail to manage some type of surfaces. In this paper, we present a novel strategy to model multiclass classification problems using subclass information in the ECOC framework. Complex problems are solved by splitting the original set of classes into subclasses and embedding the binary problems in a problem-dependent ECOC design. Experimental results show that the proposed splitting procedure yields a better performance when the class overlap or the distribution of the training objects conceal the decision boundaries for the base classifier. The results are even more significant when one has a sufficiently large training size.

Evolutionary tuning of SVM parameter values in multiclass problems

Support vector machines (SVMs) were originally formulated for the solution of binary classification problems. In multiclass problems, a decomposition approach is often employed, in which the multiclass problem is divided into multiple binary subproblems, whose results are combined. Generally, the performance of SVM classifiers is affected by the selection of values for their parameters. This paper investigates the use of genetic algorithms (GAs) to tune the parameters of the binary SVMs in common multiclass decompositions. The developed GA may search for a set of parameter values common to all binary classifiers or for differentiated values for each binary classifier. (C) 2008 Elsevier B.V. All rights reserved.

Improving Multiclass Text Classification with the Support Vector Machine

We compare Naive Bayes and Support Vector Machines on the task of multiclass text classification. Using a variety of approaches to combine the underlying binary classifiers, we find that SVMs substantially outperform Naive Bayes. We present full multiclass results on two well-known text data sets, including the lowest error to date on both data sets. We develop a new indicator of binary performance to show that the SVM's lower multiclass error is a result of its improved binary performance. Furthermore, we demonstrate and explore the surprising result that one-vs-all classification performs favorably compared to other approaches even though it has no error-correcting properties.

Multiclass Adaboost Based on an Ensemble of Binary Adaboosts

This paper presents a multi-class AdaBoost based on incorporating an ensemble of binary AdaBoosts which is organized as Binary Decision Tree (BDT). It is proved that binary AdaBoost is extremely successful in producing accurate classification but it does not perform very well for multi-class problems. To avoid this performance degradation, the multi-class problem is divided into a number of binary problems and binary AdaBoost classifiers are invoked to solve these classification problems. This approach is tested with a dataset consisting of 6500 binary images of traffic signs. Haar-like features of these images are computed and the multi-class AdaBoost classifier is invoked to classify them. A classification rate of 96.7% and 95.7% is achieved for the traffic sign boarders and pictograms, respectively. The proposed approach is also evaluated using a number of standard datasets such as Iris, Wine, Yeast, etc. The performance of the proposed BDT classifier is quite high as compared with the state of the art and it converges very fast to a solution which indicates it as a reliable classifier.

Pre-processing for noise detection in gene expression classification data

Due to the imprecise nature of biological experiments, biological data is often characterized by the presence of redundant and noisy data. This may be due to errors that occurred during data collection, such as contaminations in laboratorial samples. It is the case of gene expression data, where the equipments and tools currently used frequently produce noisy biological data. Machine Learning algorithms have been successfully used in gene expression data analysis. Although many Machine Learning algorithms can deal with noise, detecting and removing noisy instances from the training data set can help the induction of the target hypothesis. This paper evaluates the use of distance-based pre-processing techniques for noise detection in gene expression data classification problems. This evaluation analyzes the effectiveness of the techniques investigated in removing noisy data, measured by the accuracy obtained by different Machine Learning classifiers over the pre-processed data.

Effect of training-sample size and classification difficulty on the accuracy of genomic predictors.

Introduction: As part of the MicroArray Quality Control (MAQC)-II project, this analysis examines how the choice of univariate feature-selection methods and classification algorithms may influence the performance of genomic predictors under varying degrees of prediction difficulty represented by three clinically relevant endpoints. Methods: We used gene-expression data from 230 breast cancers (grouped into training and independent validation sets), and we examined 40 predictors (five univariate feature-selection methods combined with eight different classifiers) for each of the three endpoints. Their classification performance was estimated on the training set by using two different resampling methods and compared with the accuracy observed in the independent validation set. Results: A ranking of the three classification problems was obtained, and the performance of 120 models was estimated and assessed on an independent validation set. The bootstrapping estimates were closer to the validation performance than were the cross-validation estimates. The required sample size for each endpoint was estimated, and both gene-level and pathway-level analyses were performed on the obtained models. Conclusions: We showed that genomic predictor accuracy is determined largely by an interplay between sample size and classification difficulty. Variations on univariate feature-selection methods and choice of classification algorithm have only a modest impact on predictor performance, and several statistically equally good predictors can be developed for any given classification problem.

An Automatic Approach for Learning and Tuning Gaussian Interval Type-2 Fuzzy Membership Functions Applied to Lung CAD Classification System

The potential of type-2 fuzzy sets for managing high levels of uncertainty in the subjective knowledge of experts or of numerical information has focused on control and pattern classification systems in recent years. One of the main challenges in designing a type-2 fuzzy logic system is how to estimate the parameters of type-2 fuzzy membership function (T2MF) and the Footprint of Uncertainty (FOU) from imperfect and noisy datasets. This paper presents an automatic approach for learning and tuning Gaussian interval type-2 membership functions (IT2MFs) with application to multi-dimensional pattern classification problems. T2MFs and their FOUs are tuned according to the uncertainties in the training dataset by a combination of genetic algorithm (GA) and crossvalidation techniques. In our GA-based approach, the structure of the chromosome has fewer genes than other GA methods and chromosome initialization is more precise. The proposed approach addresses the application of the interval type-2 fuzzy logic system (IT2FLS) for the problem of nodule classification in a lung Computer Aided Detection (CAD) system. The designed IT2FLS is compared with its type-1 fuzzy logic system (T1FLS) counterpart. The results demonstrate that the IT2FLS outperforms the T1FLS by more than 30% in terms of classification accuracy.