Linear discriminant analysis

About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.

Discriminant waveletfaces and nearest feature classifiers for face recognition

Abstract: Feature extraction, discriminant analysis, and classification rules are three crucial issues for face recognition. We present hybrid approaches to handle three issues together. For feature extraction, we apply the multiresolution wavelet transform to extract the waveletface. We also perform the linear discriminant analysis on waveletfaces to reinforce discriminant power. During classification, the nearest feature plane (NFP) and nearest feature space (NFS) classifiers are explored for robust decisions in presence of wide facial variations. Their relationships to conventional nearest neighbor and nearest feature line classifiers are demonstrated. In the experiments, the discriminant waveletface incorporated with the NFS classifier achieves the best face recognition performance.

Learning distance functions using equivalence relations

Abstract: We address the problem of learning distance metrics using side-information in the form of groups of "similar" points. We propose to use the RCA algorithm, which is a simple and efficient algorithm for learning a full ranked Mahalanobis metric (Shental et al., 2002). We first show that RCA obtains the solution to an interesting optimization problem, founded on an information theoretic basis. If the Mahalanobis matrix is allowed to be singular, we show that Fisher's linear discriminant followed by RCA is the optimal dimensionality reduction algorithm under the same criterion. We then show how this optimization problem is related to the criterion optimized by another recent algorithm for metric learning (Xing et al., 2002), which uses the same kind of side information. We empirically demonstrate that learning a distance metric using the RCA algorithm significantly improves clustering performance, similarly to the alternative algorithm. Since the RCA algorithm is much more efficient and cost effective than the alternative, as it only uses closed form expressions of the data, it seems like a preferable choice for the learning of full rank Mahalanobis distances.

Computer-aided tumor detection in endoscopic video using color wavelet features

Abstract: We present an approach to the detection of tumors in colonoscopic video. It is based on a new color feature extraction scheme to represent the different regions in the frame sequence. This scheme is built on the wavelet decomposition. The features named as color wavelet covariance (CWC) are based on the covariances of second-order textural measures and an optimum subset of them is proposed after the application of a selection algorithm. The proposed approach is supported by a linear discriminant analysis (LDA) procedure for the characterization of the image regions along the video frames. The whole methodology has been applied on real data sets of color colonoscopic videos. The performance in the detection of abnormal colonic regions corresponding to adenomatous polyps has been estimated high, reaching 97% specificity and 90% sensitivity.

Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Applications to Face and Palm Biometrics

Abstract: This paper develops an unsupervised discriminant projection (UDP) technique for dimensionality reduction of high-dimensional data in small sample size cases. UDP can be seen as a linear approximation of a multimanifolds-based learning framework which takes into account both the local and nonlocal quantities. UDP characterizes the local scatter as well as the nonlocal scatter, seeking to find a projection that simultaneously maximizes the nonlocal scatter and minimizes the local scatter. This characteristic makes UDP more intuitive and more powerful than the most up-to-date method, locality preserving projection (LPP), which considers only the local scatter for clustering or classification tasks. The proposed method is applied to face and palm biometrics and is examined using the Yale, FERET, and AR face image databases and the PolyU palmprint database. The experimental results show that UDP consistently outperforms LPP and PCA and outperforms LDA when the training sample size per class is small. This demonstrates that UDP is a good choice for real-world biometrics applications

Multiclass linear dimension reduction by weighted pairwise Fisher criteria

Abstract: We derive a class of computationally inexpensive linear dimension reduction criteria by introducing a weighted variant of the well-known K-class Fisher criterion associated with linear discriminant analysis (LDA). It can be seen that LDA weights contributions of individual class pairs according to the Euclidean distance of the respective class means. We generalize upon LDA by introducing a different weighting function.