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.

Robust Sparse Linear Discriminant Analysis

Abstract: Linear discriminant analysis (LDA) is a very popular supervised feature extraction method and has been extended to different variants. However, classical LDA has the following problems: 1) The obtained discriminant projection does not have good interpretability for features; 2) LDA is sensitive to noise; and 3) LDA is sensitive to the selection of number of projection directions. In this paper, a novel feature extraction method called robust sparse linear discriminant analysis (RSLDA) is proposed to solve the above problems. Specifically, RSLDA adaptively selects the most discriminative features for discriminant analysis by introducing the $l_{2,1}$ norm. An orthogonal matrix and a sparse matrix are also simultaneously introduced to guarantee that the extracted features can hold the main energy of the original data and enhance the robustness to noise, and thus RSLDA has the potential to perform better than other discriminant methods. Extensive experiments on six databases demonstrate that the proposed method achieves the competitive performance compared with other state-of-the-art feature extraction methods. Moreover, the proposed method is robust to the noisy data.

Model-based Methods of Classification: Using the mclust Software in Chemometrics

Abstract: Due to recent advances in methods and software for model-based clustering, and to the interpretability of the results, clustering procedures based on probability models are increasingly preferred over heuristic methods. The clustering process estimates a model for the data that allows for overlapping clusters, producing a probabilistic clustering that quantifies the uncertainty of observations belonging to components of the mixture. The resulting clustering model can also be used for some other important problems in multivariate analysis, including density estimation and discriminant analysis. Examples of the use of model-based clustering and classification techniques in chemometric studies include multivariate image analysis, magnetic resonance imaging, microarray image segmentation, statistical process control, and food authenticity. We review model-based clustering and related methods for density estimation and discriminant analysis, and show how the R package mclust can be applied in each instance.

Dynamics of Facial Expression Extracted Automatically from Video

Abstract: We present a systematic comparison of machine learning methods applied to the problem of fully automatic recognition of facial expressions, including AdaBoost, support vector machines, and linear discriminant analysis. Each video-frame is first scanned in real-time to detect approximately upright-frontal faces. The faces found are scaled into image patches of equal size, convolved with a bank of Gabor energy filters, and then passed to a recognition engine that codes facial expressions into 7 dimensions in real time: neutral, anger, disgust, fear, joy, sadness, surprise. We report results on a series of experiments comparing spatial frequency ranges, feature selection techniques, and recognition engines. Best results were obtained by selecting a subset of Gabor filters using AdaBoost and then training Support Vector Machines on the outputs of the filters selected by AdaBoost. The generalization performance to new subjects for a 7-way forced choice was 93% or more correct on two publicly available datasets, the best performance reported so far on these datasets. Surprisingly, registration of internal facial features was not necessary, even though the face detector does not provide precisely registered images. The outputs of the classifier change smoothly as a function of time and thus can be used for unobtrusive motion capture. We developed an end-to-end system that provides facial expression codes at 24 frames per second and animates a computer generated character. In real-time this expression mirror operates down to resolutions of 16 pixels from eye to eye. We also applied the system to fully automated facial action coding.

Genetic algorithms applications in the analysis of insolvency risk

Abstract: This study analyses the comparison between a traditional statistical methodology for bankruptcy classification and prediction, i.e. linear discriminant analysis (LDA), and an artificial intelligence algorithm known as Genetic Algorithm (GA). The study was carried out at Centrale dei Bilanci, in Turin, Italy, analysing 1920 unsound and 1920 sound industrial Italian companies from 1982–1995. This paper follows our earlier examination of neural networks (NN) (see Altman et al., 1994 . Corporate distress diagnosis: Comparisons using discriminant analysis and neural network. Journal of Banking and Finance XVIII, 505–529). The experiments on GA were oriented along two different lines: the genetic generation of linear functions and the genetic generation of scores based on rules. The two types of experiments showed GA to be a very effective instrument for insolvency diagnosis, even if the results obtained with LDA analysis perhaps proved to be superior to those obtained from GA. Of particular interest, it should be noted that the results of GA were obtained in less time and with more limited contributions from the financial analyst than the LDA. Of additional interest is the relevance for credit risk management of financial institutions.