Fisher Linear Discriminant Criterion Research Articles

Supervised Kernel Principal Component Analysis by Most Expressive Feature Reordering

The presented paper is concerned with feature space derivation through feature selection. The selection is performed on results of kernel Principal Component Analysis (kPCA) of input data samples. Several criteria that drive feature selection process are introduced and their performance is assessed and compared against the reference approach, which is a combination of kPCA and most expressive feature reordering based on the Fisher linear discriminant criterion. It has been shown that some of the proposed modifications result in generating feature spaces with noticeably better (at the level of approximately 4%) class discrimination properties.

Automated Classification of Normal and Leukemic B Cells on the ImageStream® Imaging Flow Cytometer Using Immunocytomorphological Image Characteristics

Leukemic B cells can be distinguished from normal B cells based on their surface staining patterns and their morphology, but the differences can be subtle and the abnormal events rare. In order to reliably differentiate normal from leukemic B cells, objective quantitation of large data sets is required. This is accomplished with the ImageStream cytometer, which automatically acquires multispectral images of thousands of individual cells in flow at very high speeds. The associated IDEAS data analysis software measures hundreds of photometric and morphometric features per cell, thereby enabling simultaneous immunophenotyping and morphology-based measurements. The features quantify individual image characteristics such as shape, size, signal strength and texture. We have leveraged these features by implementing an automated classification routine that identifies the feature combination that best separates different cell types of interest. Our automated classification routine utilizes a modification of Fisher's Linear Discriminant criterion to measure discrimination power between two or more populations of cells. The classifier generates a composite feature consisting of a weighted linear combination of basic image features that provides maximum discrimination. Thus, our method transforms a multi-parameter classification task that can be difficult to conceptualize into a classification based on a single composite feature that can be readily conceptualized and visualized using a simple histogram output. Since the composite feature is generated from, and tested and optimized on, large numbers of cells, we obtain results that are highly objective, repeatable, statistically significant and scalable with data size. We used this classification approach to study normal and tumor cells of the hematopoietic lineage with the goal of improving diagnosis of hematological disorders. Here we show the results of using automated classification to distinguish the subtle differences between B cells of CLL patients and those of normal patients. We also used the classifier to distinguish B-cell ALL from B-cell CLL. In both cases, we used a combination of shape, size, texture and signal strength features from the SSC, brightfield and nuclear imagery generated by the ImageStream system. The data presented demonstrate the application of a novel automated cell classification method to the discrimination of normal and tumor cells within large and heterogeneous cell samples.

A kernel optimization method based on the localized kernel Fisher criterion

It is widely recognized that whether the selected kernel matches the data determines the performance of kernel-based methods. Ideally it is expected that the data is linearly separable in the kernel induced feature space, therefore, Fisher linear discriminant criterion can be used as a cost function to optimize the kernel function. However, the data may not be linearly separable even after kernel transformation in many applications, e.g., the data may exist as multimodally distributed structure, in this case, a nonlinear classifier is preferred, and obviously Fisher criterion is not a suitable choice as kernel optimization rule. Motivated by this issue, we propose a localized kernel Fisher criterion, instead of traditional Fisher criterion, as the kernel optimization rule to increase the local margins between embedded classes in kernel induced feature space. Experimental results based on some benchmark data and measured radar high-resolution range profile (HRRP) data show that the classification performance can be improved by using the proposed method.

Comparisons of Four Feature Extraction Approaches Based on Fisher's Linear Discriminant Criterion in Radar Target Recognition

In this paper, the goal is to produce a highly separable and small-dimensional feature set for improving the target recognition strategy called Invariant Feature-based Method (IFM), which uses the conventional principal component analysis to reduce redundant information and feature space dimension. To meet this end, the principal component analysis is replaced with Fisher's linear discriminant criterion, originally developed for discriminating various patterns. Among the various versions of Fisher's criterion, four computationally efficient techniques including classical linear discriminant vectors (CLDV), classical linear discriminant vectors with whitening process (CLDVW), and weighted pairwise Fisher criteria vectors (WPFCV), weighted pairwise Fisher criteria vectors with whitening process (WPFCVW) are considered. It is shown that among the four techniques, CLDVW and WPFCVW outperform CLDV, WPFCV, and the conventional principal component analysis. In addition, an optimum number of feature dimension for Fisher's criterion combined with IFM is experimentally derived, and associated theoretical background is discussed.

Discriminative Common Vector Method With Kernels

In some pattern recognition tasks, the dimension of the sample space is larger than the number of samples in the training set. This is known as the "small sample size problem". Linear discriminant analysis (LDA) techniques cannot be applied directly to the small sample size case. The small sample size problem is also encountered when kernel approaches are used for recognition. In this paper, we attempt to answer the question of "How should one choose the optimal projection vectors for feature extraction in the small sample size case?" Based on our findings, we propose a new method called the kernel discriminative common vector method. In this method, we first nonlinearly map the original input space to an implicit higher dimensional feature space, in which the data are hoped to be linearly separable. Then, the optimal projection vectors are computed in this transformed space. The proposed method yields an optimal solution for maximizing a modified Fisher's linear discriminant criterion, discussed in the paper. Thus, under certain conditions, a 100% recognition rate is guaranteed for the training set samples. Experiments on test data also show that, in many situations, the generalization performance of the proposed method compares favorably with other kernel approaches.

An efficient approach to machine health diagnosis based on harmonic wavelet packet transform

This paper presents an efficient approach to machine condition monitoring and health diagnosis, based on the Discrete Harmonic Wavelet Packet Transform (DHWPT). Specifically, vibration signals measured from a bearing test bed were decomposed into a number of frequency sub-bands, and key features associated with each sub-band were selected, based on the Fisher linear discriminant criterion. The key features were then used as inputs to a neural network classifiers for assessing the system's health status. Comparing to the conventional approach where statistical parameters from raw vibration signals are used, the presented approach enables higher signal-to-noise ratios and consequently, more effective and intelligent use of the available sensor information, leading to more accurate system health evaluation.

Discriminative common vectors for face recognition

In face recognition tasks, the dimension of the sample space is typically larger than the number of the samples in the training set. As a consequence, the within-class scatter matrix is singular and the Linear Discriminant Analysis (LDA) method cannot be applied directly. This problem is known as the "small sample size" problem. In this paper, we propose a new face recognition method called the Discriminative Common Vector method based on a variation of Fisher's Linear Discriminant Analysis for the small sample size case. Two different algorithms are given to extract the discriminative common vectors representing each person in the training set of the face database. One algorithm uses the within-class scatter matrix of the samples in the training set while the other uses the subspace methods and the Gram-Schmidt orthogonalization procedure to obtain the discriminative common vectors. Then, the discriminative common vectors are used for classification of new faces. The proposed method yields an optimal solution for maximizing the modified Fisher's Linear Discriminant criterion given in the paper. Our test results show that the Discriminative Common Vector method is superior to other methods in terms of recognition accuracy, efficiency, and numerical stability.