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Linear Discriminant Analysis (LDA) is a fundamental method for classification. Its simple linear structure facilitates interpretation, and it is naturally suited to multi-class settings. LDA is also closely connected to several classical…
The use of quadratic discriminant analysis (QDA) or its regularized version (R-QDA) for classification is often not recommended, due to its well-acknowledged high sensitivity to the estimation noise of the covariance matrix. This becomes…
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two…
Probabilistic linear discriminant analysis (PLDA) has broad application in open-set verification tasks, such as speaker verification. A key concern for PLDA is that the model is too simple (linear Gaussian) to deal with complicated data;…
We introduce Deep Linear Discriminant Analysis (DeepLDA) which learns linearly separable latent representations in an end-to-end fashion. Classic LDA extracts features which preserve class separability and is used for dimensionality…
Principal Component Analysis (PCA) is one of the most important unsupervised methods to handle high-dimensional data. However, due to the high computational complexity of its eigen decomposition solution, it hard to apply PCA to the…
Canonical Correlation Analysis (CCA) is a linear representation learning method that seeks maximally correlated variables in multi-view data. Non-linear CCA extends this notion to a broader family of transformations, which are more powerful…
We revisit Deep Linear Discriminant Analysis (Deep LDA) from a likelihood-based perspective. While classical LDA is a simple Gaussian model with linear decision boundaries, attaching an LDA head to a neural encoder raises the question of…
We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single…
The heavy-tailed distributions of corrupted outliers and singular values of all channels in low-level vision have proven effective priors for many applications such as background modeling, photometric stereo and image alignment. And they…
This paper addresses classification problems with matrix-valued data, which commonly arise in applications such as neuroimaging and signal processing. Building on the assumption that the data from each class follows a matrix normal…
Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…
This Generalized Discriminant Analysis (GDA) has provided an extremely powerful approach to extracting non linear features. The network traffic data provided for the design of intrusion detection system always are large with ineffective…
Big data applications, such as medical imaging and genetics, typically generate datasets that consist of few observations n on many more variables p, a scenario that we denote as p>>n. Traditional data processing methods are often…
Multiplicative noise widely exists in radar images, medical images and other important fields' images. Compared to normal noises, multiplicative noise has a generally stronger effect on the visual expression of images. Aiming at the…
The development of computing has made credit scoring approaches possible, with various machine learning (ML) and deep learning (DL) techniques becoming more and more valuable. While complex models yield more accurate predictions, their…
We present an algorithm for L1-norm kernel PCA and provide a convergence analysis for it. While an optimal solution of L2-norm kernel PCA can be obtained through matrix decomposition, finding that of L1-norm kernel PCA is not trivial due to…
Linear and Quadratic Discriminant Analysis (LDA and QDA) are well-known classical methods but can heavily suffer from non-Gaussian distributions and/or contaminated datasets, mainly because of the underlying Gaussian assumption that is not…
In this paper a novel efficient method for representation of facial action units by encoding an image sequence as a fourth-order tensor is presented. The multilinear tensor-based extension of the biased discriminant analysis (BDA)…
In this paper, two novel methods: 2DR1-PCA and 2DL1-PCA are proposed for face recognition. Compared to the traditional 2DPCA algorithm, 2DR1-PCA and 2DL1-PCA are based on the R1 norm and L1 norm, respectively. The advantage of these…