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Title: Fast Implementation of Linear Discriminant Analysis
Keywords: Dimensionality reduction, Linear Discrimination Analysis, null space based LDA, orthogonal LDA, QR , SVD,
Issue Date: 5-Aug-2009
Citation: GOH SIONG THYE (2009-08-05). Fast Implementation of Linear Discriminant Analysis. ScholarBank@NUS Repository.
Abstract: Dimensionality reduction has become a ubiquitous preprocessing step in many applications. Linear discriminant analysis (LDA) has been known to be one of the most optimal dimensionality reduction methods for classification. However, a main disadvantage of LDA is that the so-called "total scatter matrix" must be nonsingular. But, in many applications, the scatter matrices can be singular since the data points are from a very high-dimensional space and thus usually the number of the data samples is smaller than the data dimension. This is known as the undersampled problem. Many generalized LDA methods have been proposed in the past to overcome this singularity problem. There is a commonality for these generalized LDA methods, that is, they compute the optimal linear transformations by computing some eigen-decompositions and involving some matrix inversions. However, the eigen-decomposition is computationally expensive, and the involvement of matrix inverses may lead to that the methods are not numerically stable if the associated matrices are ill-conditioned. Hence, many existing LDA methods have high computational cost and potentially numerical instability problems. In this thesis, we present new methods to compute Orthogonal LDA and Null space based LDA for undersampled problem which do not involve expensive operations such as SVD and computing inverse. It is computed solely using QR decomposition. Effectiveness of the new implementations are performed using real world data.
Appears in Collections:Master's Theses (Open)

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