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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.


Papers
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Journal ArticleDOI
TL;DR: This paper investigated several state-of-the-art machine-learning methods for automated classification of clustered microcalcifications (MCs), and formulated differentiation of malignant from benign MCs as a supervised learning problem, and applied these learning methods to develop the classification algorithm.
Abstract: In this paper, we investigate several state-of-the-art machine-learning methods for automated classification of clustered microcalcifications (MCs). The classifier is part of a computer-aided diagnosis (CADx) scheme that is aimed to assisting radiologists in making more accurate diagnoses of breast cancer on mammograms. The methods we considered were: support vector machine (SVM), kernel Fisher discriminant (KFD), relevance vector machine (RVM), and committee machines (ensemble averaging and AdaBoost), of which most have been developed recently in statistical learning theory. We formulated differentiation of malignant from benign MCs as a supervised learning problem, and applied these learning methods to develop the classification algorithm. As input, these methods used image features automatically extracted from clustered MCs. We tested these methods using a database of 697 clinical mammograms from 386 cases, which included a wide spectrum of difficult-to-classify cases. We analyzed the distribution of the cases in this database using the multidimensional scaling technique, which reveals that in the feature space the malignant cases are not trivially separable from the benign ones. We used receiver operating characteristic (ROC) analysis to evaluate and to compare classification performance by the different methods. In addition, we also investigated how to combine information from multiple-view mammograms of the same case so that the best decision can be made by a classifier. In our experiments, the kernel-based methods (i.e., SVM, KFD, and RVM) yielded the best performance (A/sub z/=0.85, SVM), significantly outperforming a well-established, clinically-proven CADx approach that is based on neural network (A/sub z/=0.80).

305 citations

Proceedings ArticleDOI
20 Jun 2009
TL;DR: The proposed MDA method is evaluated on the tasks of object recognition with image sets, including face recognition and object categorization, and seeks to learn an embedding space, where manifolds with different class labels are better separated, and local data compactness within each manifold is enhanced.
Abstract: This paper presents a novel discriminative learning method, called manifold discriminant analysis (MDA), to solve the problem of image set classification. By modeling each image set as a manifold, we formulate the problem as classification-oriented multi-manifolds learning. Aiming at maximizing “manifold margin”, MDA seeks to learn an embedding space, where manifolds with different class labels are better separated, and local data compactness within each manifold is enhanced. As a result, new testing manifold can be more reliably classified in the learned embedding space. The proposed method is evaluated on the tasks of object recognition with image sets, including face recognition and object categorization. Comprehensive comparisons and extensive experiments demonstrate the effectiveness of our method.

304 citations

Journal ArticleDOI
TL;DR: Re-examination of single channel EEG data obtained from normal human subjects suggests that the previous indication of low-dimensional structure was an artifact of autocorrelation in the oversampled signal, and discriminatory analysis indicates that the correlation dimension is a poor discriminator for distinguishing between EEGs recorded at rest and during periods of cognitive activity.

302 citations

Journal ArticleDOI
TL;DR: MCLUST is a software package for model-based clustering, density estimation and discriminant analysis interfaced to the S-PLUS commercial software and the R language that implements parameterized Gaussian hierarchical clustering algorithms and the EM algorithm for parameterizedGaussian mixture models with the possible addition of a Poisson noise term.
Abstract: MCLUST is a software package for model-based clustering, density estimation and discriminant analysis interfaced to the S-PLUS commercial software and the R language. It implements parameterized Gaussian hierarchical clustering algorithms and the EM algorithm for parameterized Gaussian mixture models with the possible addition of a Poisson noise term. Also included are functions that combine hierarchical clustering, EM and the Bayesian Information Criterion (BIC) in comprehensive strategies for clustering, density estimation, and discriminant analysis. MCLUST provides functionality for displaying and visualizing clustering and classification results. A web page with related links can be found at http://www.stat.washington.edu/mclust.

301 citations

Proceedings ArticleDOI
20 Jun 2011
TL;DR: It is shown that by introducing within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, the geometrical structure of data can be exploited.
Abstract: A convenient way of dealing with image sets is to represent them as points on Grassmannian manifolds. While several recent studies explored the applicability of discriminant analysis on such manifolds, the conventional formalism of discriminant analysis suffers from not considering the local structure of the data. We propose a discriminant analysis approach on Grassmannian manifolds, based on a graph-embedding framework. We show that by introducing within-class and between-class similarity graphs to characterise intra-class compactness and inter-class separability, the geometrical structure of data can be exploited. Experiments on several image datasets (PIE, BANCA, MoBo, ETH-80) show that the proposed algorithm obtains considerable improvements in discrimination accuracy, in comparison to three recent methods: Grassmann Discriminant Analysis (GDA), Kernel GDA, and the kernel version of Affine Hull Image Set Distance. We further propose a Grassmannian kernel, based on canonical correlation between subspaces, which can increase discrimination accuracy when used in combination with previous Grassmannian kernels.

300 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20251
20242
2023756
20221,711
2021678
2020815