Dimension Reduction by Mutual Information Discriminant Analysis

In the past few decades, researchers have proposed many discriminant analysis (DA) algorithms for the study of high-dimensional data in a variety of problems. Most DA algorithms for feature extraction are based on transformations that simultaneously maximize the between-class scatter and minimize the withinclass scatter matrices. This paper presents a novel DA algorithm for feature extraction using mutual information (MI). However, it is not always easy to obtain an accurate estimation for high-dimensional MI. In this paper, we propose an efficient method for feature extraction that is based on one-dimensional MI estimations. We will refer to this algorithm as mutual information discriminant analysis (MIDA). The performance of this proposed method was evaluated using UCI databases. The results indicate that MIDA provides robust performance over different data sets with different characteristics and that MIDA always performs better than, or at least comparable to, the best performing algorithms.Comment: 13pages, 3 tables, International Journal of Artificial Intelligence & Application

Eigenvector-based Dimensionality Reduction for Human Activity Recognition and Data Classification

In the context of appearance-based human motion compression, representation, and recognition, we have proposed a robust framework based on the eigenspace technique. First, the new appearance-based template matching approach which we named Motion Intensity Image for compressing a human motion video into a simple and concise, yet very expressive representation. Second, a learning strategy based on the eigenspace technique is employed for dimensionality reduction using each of PCA and FDA, while providing maximum data variance and maximum class separability, respectively. Third, a new compound eigenspace is introduced for multiple directed motion recognition that takes care also of the possible changes in scale. This method extracts two more features that are used to control the recognition process. A similarity measure, based on Euclidean distance, has been employed for matching dimensionally-reduced testing templates against a projected set of known motions templates. In the stream of nonlinear classification, we have introduced a new eigenvector-based recognition model, built upon the idea of the kernel technique. A practical study on the use of the kernel technique with 18 different functions has been carried out. We have shown in this study how crucial choosing the right kernel function is, for the success of the subsequent linear discrimination in the feature space for a particular problem. Second, building upon the theory of reproducing kernels, we have proposed a new robust nonparametric discriminant analysis approach with kernels. Our proposed technique can efficiently find a nonparametric kernel representation where linear discriminants can perform better. Data classification is achieved by integrating the linear version of the NDA with the kernel mapping. Based on the kernel trick, we have provided a new formulation for Fisher\u27s criterion, defined in terms of the Gram matrix only

Advances in Hyperspectral Image Classification Methods for Vegetation and Agricultural Cropland Studies

Hyperspectral data are becoming more widely available via sensors on airborne and unmanned aerial vehicle (UAV) platforms, as well as proximal platforms. While space-based hyperspectral data continue to be limited in availability, multiple spaceborne Earth-observing missions on traditional platforms are scheduled for launch, and companies are experimenting with small satellites for constellations to observe the Earth, as well as for planetary missions. Land cover mapping via classification is one of the most important applications of hyperspectral remote sensing and will increase in significance as time series of imagery are more readily available. However, while the narrow bands of hyperspectral data provide new opportunities for chemistry-based modeling and mapping, challenges remain. Hyperspectral data are high dimensional, and many bands are highly correlated or irrelevant for a given classification problem. For supervised classification methods, the quantity of training data is typically limited relative to the dimension of the input space. The resulting Hughes phenomenon, often referred to as the curse of dimensionality, increases potential for unstable parameter estimates, overfitting, and poor generalization of classifiers. This is particularly problematic for parametric approaches such as Gaussian maximum likelihoodbased classifiers that have been the backbone of pixel-based multispectral classification methods. This issue has motivated investigation of alternatives, including regularization of the class covariance matrices, ensembles of weak classifiers, development of feature selection and extraction methods, adoption of nonparametric classifiers, and exploration of methods to exploit unlabeled samples via semi-supervised and active learning. Data sets are also quite large, motivating computationally efficient algorithms and implementations. This chapter provides an overview of the recent advances in classification methods for mapping vegetation using hyperspectral data. Three data sets that are used in the hyperspectral classification literature (e.g., Botswana Hyperion satellite data and AVIRIS airborne data over both Kennedy Space Center and Indian Pines) are described in Section 3.2 and used to illustrate methods described in the chapter. An additional high-resolution hyperspectral data set acquired by a SpecTIR sensor on an airborne platform over the Indian Pines area is included to exemplify the use of new deep learning approaches, and a multiplatform example of airborne hyperspectral data is provided to demonstrate transfer learning in hyperspectral image classification. Classical approaches for supervised and unsupervised feature selection and extraction are reviewed in Section 3.3. In particular, nonlinearities exhibited in hyperspectral imagery have motivated development of nonlinear feature extraction methods in manifold learning, which are outlined in Section 3.3.1.4. Spatial context is also important in classification of both natural vegetation with complex textural patterns and large agricultural fields with significant local variability within fields. Approaches to exploit spatial features at both the pixel level (e.g., co-occurrencebased texture and extended morphological attribute profiles [EMAPs]) and integration of segmentation approaches (e.g., HSeg) are discussed in this context in Section 3.3.2. Recently, classification methods that leverage nonparametric methods originating in the machine learning community have grown in popularity. An overview of both widely used and newly emerging approaches, including support vector machines (SVMs), Gaussian mixture models, and deep learning based on convolutional neural networks is provided in Section 3.4. Strategies to exploit unlabeled samples, including active learning and metric learning, which combine feature extraction and augmentation of the pool of training samples in an active learning framework, are outlined in Section 3.5. Integration of image segmentation with classification to accommodate spatial coherence typically observed in vegetation is also explored, including as an integrated active learning system. Exploitation of multisensor strategies for augmenting the pool of training samples is investigated via a transfer learning framework in Section 3.5.1.2. Finally, we look to the future, considering opportunities soon to be provided by new paradigms, as hyperspectral sensing is becoming common at multiple scales from ground-based and airborne autonomous vehicles to manned aircraft and space-based platforms

Feature extraction and classification for hyperspectral remote sensing images

Recent advances in sensor technology have led to an increased availability of hyperspectral remote sensing data at very high both spectral and spatial resolutions. Many techniques are developed to explore the spectral information and the spatial information of these data. In particular, feature extraction (FE) aimed at reducing the dimensionality of hyperspectral data while keeping as much spectral information as possible is one of methods to preserve the spectral information, while morphological profile analysis is the most popular methods used to explore the spatial information. Hyperspectral sensors collect information as a set of images represented by hundreds of spectral bands. While offering much richer spectral information than regular RGB and multispectral images, the high dimensional hyperspectal data creates also a challenge for traditional spectral data processing techniques. Conventional classification methods perform poorly on hyperspectral data due to the curse of dimensionality (i.e. the Hughes phenomenon: for a limited number of training samples, the classification accuracy decreases as the dimension increases). Classification techniques in pattern recognition typically assume that there are enough training samples available to obtain reasonably accurate class descriptions in quantitative form. However, the assumption that enough training samples are available to accurately estimate the class description is frequently not satisfied for hyperspectral remote sensing data classification, because the cost of collecting ground-truth of observed data can be considerably difficult and expensive. In contrast, techniques making accurate estimation by using only small training samples can save time and cost considerably. The small sample size problem therefore becomes a very important issue for hyperspectral image classification. Very high-resolution remotely sensed images from urban areas have recently become available. The classification of such images is challenging because urban areas often comprise a large number of different surface materials, and consequently the heterogeneity of urban images is relatively high. Moreover, different information classes can be made up of spectrally similar surface materials. Therefore, it is important to combine spectral and spatial information to improve the classification accuracy. In particular, morphological profile analysis is one of the most popular methods to explore the spatial information of the high resolution remote sensing data. When using morphological profiles (MPs) to explore the spatial information for the classification of hyperspectral data, one should consider three important issues. Firstly, classical morphological openings and closings degrade the object boundaries and deform the object shapes, while the morphological profile by reconstruction leads to some unexpected and undesirable results (e.g. over-reconstruction). Secondly, the generated MPs produce high-dimensional data, which may contain redundant information and create a new challenge for conventional classification methods, especially for the classifiers which are not robust to the Hughes phenomenon. Last but not least, linear features, which are used to construct MPs, lose too much spectral information when extracted from the original hyperspectral data. In order to overcome these problems and improve the classification results, we develop effective feature extraction algorithms and combine morphological features for the classification of hyperspectral remote sensing data. The contributions of this thesis are as follows. As the first contribution of this thesis, a novel semi-supervised local discriminant analysis (SELD) method is proposed for feature extraction in hyperspectral remote sensing imagery, with improved performance in both ill-posed and poor-posed conditions. The proposed method combines unsupervised methods (Local Linear Feature Extraction Methods (LLFE)) and supervised method (Linear Discriminant Analysis (LDA)) in a novel framework without any free parameters. The underlying idea is to design an optimal projection matrix, which preserves the local neighborhood information inferred from unlabeled samples, while simultaneously maximizing the class discrimination of the data inferred from the labeled samples. Our second contribution is the application of morphological profiles with partial reconstruction to explore the spatial information in hyperspectral remote sensing data from the urban areas. Classical morphological openings and closings degrade the object boundaries and deform the object shapes. Morphological openings and closings by reconstruction can avoid this problem, but this process leads to some undesirable effects. Objects expected to disappear at a certain scale remain present when using morphological openings and closings by reconstruction, which means that object size is often incorrectly represented. Morphological profiles with partial reconstruction improve upon both classical MPs and MPs with reconstruction. The shapes of objects are better preserved than classical MPs and the size information is preserved better than in reconstruction MPs. A novel semi-supervised feature extraction framework for dimension reduction of generated morphological profiles is the third contribution of this thesis. The morphological profiles (MPs) with different structuring elements and a range of increasing sizes of morphological operators produce high-dimensional data. These high-dimensional data may contain redundant information and create a new challenge for conventional classification methods, especially for the classifiers which are not robust to the Hughes phenomenon. To the best of our knowledge the use of semi-supervised feature extraction methods for the generated morphological profiles has not been investigated yet. The proposed generalized semi-supervised local discriminant analysis (GSELD) is an extension of SELD with a data-driven parameter. In our fourth contribution, we propose a fast iterative kernel principal component analysis (FIKPCA) to extract features from hyperspectral images. In many applications, linear FE methods, which depend on linear projection, can result in loss of nonlinear properties of the original data after reduction of dimensionality. Traditional nonlinear methods will cause some problems on storage resources and computational load. The proposed method is a kernel version of the Candid Covariance-Free Incremental Principal Component Analysis, which estimates the eigenvectors through iteration. Without performing eigen decomposition on the Gram matrix, our approach can reduce the space complexity and time complexity greatly. Our last contribution constructs MPs with partial reconstruction on nonlinear features. Traditional linear features, on which the morphological profiles usually are built, lose too much spectral information. Nonlinear features are more suitable to describe higher order complex and nonlinear distributions. In particular, kernel principal components are among the nonlinear features we used to built MPs with partial reconstruction, which led to significant improvement in terms of classification accuracies. The experimental analysis performed with the novel techniques developed in this thesis demonstrates an improvement in terms of accuracies in different fields of application when compared to other state of the art methods

Bio-signal based control in assistive robots: a survey

Recently, bio-signal based control has been gradually deployed in biomedical devices and assistive robots for improving the quality of life of disabled and elderly people, among which electromyography (EMG) and electroencephalography (EEG) bio-signals are being used widely. This paper reviews the deployment of these bio-signals in the state of art of control systems. The main aim of this paper is to describe the techniques used for (i) collecting EMG and EEG signals and diving these signals into segments (data acquisition and data segmentation stage), (ii) dividing the important data and removing redundant data from the EMG and EEG segments (feature extraction stage), and (iii) identifying categories from the relevant data obtained in the previous stage (classification stage). Furthermore, this paper presents a summary of applications controlled through these two bio-signals and some research challenges in the creation of these control systems. Finally, a brief conclusion is summarized

Supervised Classification: Quite a Brief Overview

The original problem of supervised classification considers the task of automatically assigning objects to their respective classes on the basis of numerical measurements derived from these objects. Classifiers are the tools that implement the actual functional mapping from these measurements---also called features or inputs---to the so-called class label---or output. The fields of pattern recognition and machine learning study ways of constructing such classifiers. The main idea behind supervised methods is that of learning from examples: given a number of example input-output relations, to what extent can the general mapping be learned that takes any new and unseen feature vector to its correct class? This chapter provides a basic introduction to the underlying ideas of how to come to a supervised classification problem. In addition, it provides an overview of some specific classification techniques, delves into the issues of object representation and classifier evaluation, and (very) briefly covers some variations on the basic supervised classification task that may also be of interest to the practitioner

A Taxonomy of Big Data for Optimal Predictive Machine Learning and Data Mining

Big data comes in various ways, types, shapes, forms and sizes. Indeed, almost all areas of science, technology, medicine, public health, economics, business, linguistics and social science are bombarded by ever increasing flows of data begging to analyzed efficiently and effectively. In this paper, we propose a rough idea of a possible taxonomy of big data, along with some of the most commonly used tools for handling each particular category of bigness. The dimensionality p of the input space and the sample size n are usually the main ingredients in the characterization of data bigness. The specific statistical machine learning technique used to handle a particular big data set will depend on which category it falls in within the bigness taxonomy. Large p small n data sets for instance require a different set of tools from the large n small p variety. Among other tools, we discuss Preprocessing, Standardization, Imputation, Projection, Regularization, Penalization, Compression, Reduction, Selection, Kernelization, Hybridization, Parallelization, Aggregation, Randomization, Replication, Sequentialization. Indeed, it is important to emphasize right away that the so-called no free lunch theorem applies here, in the sense that there is no universally superior method that outperforms all other methods on all categories of bigness. It is also important to stress the fact that simplicity in the sense of Ockham's razor non plurality principle of parsimony tends to reign supreme when it comes to massive data. We conclude with a comparison of the predictive performance of some of the most commonly used methods on a few data sets.Comment: 18 pages, 2 figures 3 table