Fisher Discriminant Analysis with New Between-class Scatter Matrix for Audio Signal Classification

This research features a new method for automatic face recognition robust to variations in lighting, facial expression and eyewear. The new algorithm named SKKUfaces (Sungkyunkwan University faces) employs PCA (Principal Component Analysis) and FLD (Fisher's Linear Discriminant) in series similarly to Fisherfaces. The fundamental difference is that SKKUfaces effectively eliminates, in the reduced PCA subspace, portions of the subspace that are responsible for variations in lighting and facial expression and then applies FLD to the resulting subspace. This results in superb discriminating power for pattern classification and excellent recognition accuracy. We also propose an efficient method to compute the between-class scatter and within-class scatter matrices for the FLD analysis. We have evaluated the performance of SKKUfaces using YALE and SKKU facial databases. Experimental results show that the SKKUface method is computationally efficient and achieves much better recognition accuracy than the Fisherface method [1] especially for facial images with variations in lighting and eyewear.

The goal of this paper is to present a new fuzzy logic-based feature extraction method, called Fuzzy Generalized Two-Dimensional Fisher's Linear Discriminant (FG-2DFLD) method for face recognition. More specifically, the FG-2DFLD method is an extension of the G-2DFLD method. In FG-2DFLD method, we introduced fuzzy membership values to all the training samples and incorporated them into the within-class and between-class scatter matrices along the row and column directions. The class-wise mean images are also generated by considering the membership values. The fuzzy k-nearest neighbour (FKNN) algorithm is applied for generating the corresponding degrees of class membership. Finally, the feature matrix generated by solving the eigenvalue problem of these scatter matrices actually provide better discrimination information as supported by the simulation results on the AT&T (formally known as ORL) and UMIST face databases using a radial basis function (RBF) neural network.

We introduce two enhanced Fisher linear discriminant (FLD) models (EFM) in order to improve the generalization ability of the standard FLD based classifiers such as Fisherfaces. Similar to Fisherfaces, both EFM models apply first principal component analysis (PCA) for dimensionality reduction before proceeding with FLD type of analysis. EFM-1 implements the dimensionality reduction with the goal to balance between the need that the selected eigenvalues account for most of the spectral energy of the raw data and the requirement that the eigenvalues of the within-class scatter matrix in the reduced PCA subspace are not too small. EFM-2 implements the dimensionality reduction as Fisherfaces do. It proceeds with the whitening of the within-class scatter matrix in the reduced PCA subspace and then chooses a small set of features (corresponding to the eigenvectors of the within-class scatter matrix) so that the smaller trailing eigenvalues are not included in further computation of the between-class scatter matrix. Experimental data using a large set of faces-1,107 images drawn from 369 subjects and including duplicates acquired at a later time under different illumination-from the FERET database shows that the EFM models outperform the standard FLD based methods.

With a wide variety of applications for audio classification, multimedia content analysis has become crucial in the educational field as online lectures are being increasingly practiced. The breaks pause and non-stationeries present in the audio signals make segmentation and classification of the signal quite a challenging and demanding process. This motivates building a package that aims to analyze the multimedia content for achieving novel means to classify audio into different categories specific to an application. Although work on audio classification exists, a majority of it attempts to classify the audio into predefined categories like silence and music. Our package is an attempt to obtain maximum accuracy in classifying the data into whatever categories are specified by the input data. Various simple features including, the average crossing rate, spectral features, energy function are extricated. This paper presents an approach to achieve efficient segmentation, feature extraction, and classification of audio signals.

The Fisher's discriminant ratio has been used as a class separability criterion and implemented in a k-means clustering algorithm for performing simultaneous feature selection and data set trimming on a set of 221 HIV-1 protease inhibitors. The total number of molecular descriptors computed for each inhibitor is 43, and they are scaled to lie between 1 and 0 before being subjected to the feature selection process. Since the purpose is to select some of the most class sensitive descriptors, several feature evaluation indices such as the Shannon entropy, the linear regression of selected descriptors on the pKi of selected inhibitors, and a stepwise variable selection program are used to filter them. While the Shannon entropy provides the information content for each descriptor computed, more class sensitive descriptors are searched by both the linear regression and stepwise variable selection procedures. The inhibitors are divided into several different numbers of classes. They are subsequently divided into five classes due to the fact that the best feature selection result is obtained by the division. Most of the good features selected are the topological descriptors, and they are correlated well with the pKi values. The outliers or the inhibitors with less class-sensitive descriptor values computed for each selected descriptor are identified and gathered by the k-means clustering algorithm. These are the trimmed inhibitors, while the remaining ones are retained or selected. We find that 44% or 98 inhibitors can be retained when the number of good descriptors selected for clustering is three. The descriptor values of these selected inhibitors are far more class sensitive than the original ones as evidenced by substantial increasing in statistical significance when they are subjected to both the SYBYL CoMFA PLS and Cerius2 PLS regression analyses.

Kernel approaches for fault detection and classification in PARR-2

Linear discriminant analysis (LDA) is a classical method for discriminative dimensionality reduction. The original LDA may degrade in its performance for non-Gaussian data, and may be unable to extract sufficient features to satisfactorily explain the data when the number of classes is small. Two prominent extensions to address these problems are subclass discriminant analysis (SDA) and mixture subclass discriminant analysis (MSDA). They divide every class into subclasses and re-define the within-class and between-class scatter matrices on the basis of subclass. In this paper we study the issue of how to obtain subclasses more effectively in order to achieve higher class separation. We observe that there is significant overlap between models of the subclasses, which we hypothesise is undesirable. In order to reduce their overlap we propose an extension of LDA, separability oriented subclass discriminant analysis (SSDA), which employs hierarchical clustering to divide a class into subclasses using a separability oriented criterion, before applying LDA optimisation using re-defined scatter matrices. Extensive experiments have shown that SSDA has better performance than LDA, SDA and MSDA in most cases. Additional experiments have further shown that SSDA can project data into LDA space that has higher class separation than LDA, SDA and MSDA in most cases.

A discriminant bispectrum feature for surface electromyogram signal classification

Audio signal classification is usually done using conventional signal features such as mel-frequency cepstrum coefficients (MFCC), line spectral frequencies (LSF), and short time energy (STM). Learned dictionaries have been shown to have promising capability for creating sparse representation of a signal and hence have a potential to be used for the extraction of signal features. In this paper, we consider to use sparse features for audio classification from music and speech data. We use the K-SVD algorithm to learn separate dictionaries for the speech and music signals to represent their respective subspaces and use them to extract sparse features for each class of signals using Orthogonal Matching Pursuit (OMP). Based on these sparse features, Support Vector Machines (SVM) are used for speech and music classification. The same signals were also classified using SVM based on the conventional MFCC coefficients and the classification results were compared to those of sparse coefficients. It was found that at lower signal to noise ratio (SNR), sparse coefficients give far better signal classification results as compared to the MFCC based classification.

This correspondence proposes a new technique for signal classification and jamming detection in wide-band (WB) radios. Theory of compressed sensing is exploited to recover the sparsely populated WB spectrum from sub-Nyquist samples, thus reducing the very high-rate sampling requirements at the receiver analog to digital converter. From the recovered WB, key spectral features of each narrow-band (NB) signal are extracted. These spectral features are then used to train a simple yet powerful classifier, the naive Bayes classifier (NBC). The trained NBC is then used not only to classify various NB signals into their respective modulations but also to detect the jamming on different NB signals, which are the main contributions of this letter. The proposed algorithm is then evaluated under different empirical setups and is shown to perform better when compared to a recently proposed feature-based jamming detection algorithm.

This research explores the possibility of monitoring apoptosis and classifying clusters of apoptotic cells based on the changes in ultrasound backscatter signals from the tissues. The backscatter from normal and apoptotic cells, using a high frequency ultrasound instrument are modeled through an autoregressive (AR) modeling technique. The proper model order is calculated by tracking the error criteria in the reconstruction of the original signal. The AR model coefficients, which are assumed to contain the main statistical features of the signal, are passed as the input to linear and nonlinear machine classifiers (Fisher linear discriminant, conditional Gaussian classifier, Naive Bayes classifier and neural networks with nonlinear activation functions). In addition, an adaptive signal segmentation method (least squares lattice filter) is used to differentiate the data from layers of different cell types into stationary parts ready for modeling and classification.

In this paper, we study the performance of variants of well-known Convolutional Neural Network (CNN) architectures on different audio tasks. We show that tuning the Receptive Field (RF) of CNNs is crucial to their generalization. An insufficient RF limits the CNN's ability to fit the training data. In contrast, CNNs with an excessive RF tend to over-fit the training data and fail to generalize to unseen testing data. As state-of-the-art CNN architectures - in computer vision and other domains - tend to go deeper in terms of number of layers, their RF size increases and therefore they degrade in performance in several audio classification and tagging tasks. We study well-known CNN architectures and how their building blocks affect their receptive field. We propose several systematic approaches to control the RF of CNNs and systematically test the resulting architectures on different audio classification and tagging tasks and datasets. The experiments show that regularizing the RF of CNNs using our proposed approaches can drastically improve the generalization of models, out-performing complex architectures and pre-trained models on larger datasets. The proposed CNNs achieve state-of-the-art results in multiple tasks, from acoustic scene classification to emotion and theme detection in music to instrument recognition, as demonstrated by top ranks in several pertinent challenges (DCASE, MediaEval).

In this paper, according to the concept of generalized Fisher (1938) discriminant (GFD) presented by Foley and Sammon (1975) , the generalized kernel function Fisher discriminant (GKFD) is investigated and proved based on the linear Fisher discriminant (LFD) and kernel function Fisher discriminant (KFD). It generalizes the solution of two-class pattern recognition nonlinearly, and the decision function is obtained. In the process of decision, the competition principle is used, each test sample is determined as the class with the largest decision function value, and a valid approach is provided for multi-class pattern recognition. The GKFD has the characteristic of solid theory foundation and strong generalization capability, which embraces important meanings and application merits in multi-class pattern recognition.

Fisher discrimination based low rank matrix recovery for face recognition

This work introduces two novel approaches for feature extraction applied to video-based Arabic sign language recognition, namely, motion representation through motion estimation and motion representation through motion residuals. In the former, motion estimation is used to compute the motion vectors of a video-based deaf sign or gesture. In the preprocessing stage for feature extraction, the horizontal and vertical components of such vectors are rearranged into intensity images and transformed into the frequency domain. In the second approach, motion is represented through motion residuals. The residuals are then thresholded and transformed into the frequency domain. Since in both approaches the temporal dimension of the video-based gesture needs to be preserved, hidden Markov models are used for classification tasks. Additionally, this paper proposes to project the motion information in the time domain through either telescopic motion vector composition or polar accumulated differences of motion residuals. The feature vectors are then extracted from the projected motion information. After that, model parameters can be evaluated by using simple classifiers such as Fisher's linear discriminant. The paper reports on the classification accuracy of the proposed solutions. Comparisons with existing work reveal that up to 39% of the misclassifications have been corrected.