Related papers: A New Reduced-Rank Linear Discriminant Analysis Me…
Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…
Linear discriminant analysis (LDA) is a fundamental classification and dimension reduction method that achieves Bayes optimality under Gaussian mixture, but often struggles in high-dimensional settings where the covariance matrix cannot be…
Deep autoencoders are often extended with a supervised or adversarial loss to learn latent representations with desirable properties, such as greater predictivity of labels and outcomes or fairness with respects to a sensitive variable.…
Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…
Due to the rapid growth of smart agents such as weakly connected computational nodes and sensors, developing decentralized algorithms that can perform computations on local agents becomes a major research direction. This paper considers the…
Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…
In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…
We present a supervised dimensionality reduction technique called Convex Linear Discriminant Analysis (ConvexLDA). The proposed model optimizes a multi-objective cost function by balancing two complementary terms. The first term pulls the…
Dimensionality reduction represents a critical preprocessing step in order to increase the efficiency and the performance of many hyperspectral imaging algorithms. However, dimensionality reduction algorithms, such as the Principal…
Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…
Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is non-trivial to develop efficient statistical methods due to two main challenges. First, profiles are high-dimensional functional…
This paper proposes a new method and algorithm for predicting multivariate responses in a regression setting. Research into classification of High Dimension Low Sample Size (HDLSS) data, in particular microarray data, has made considerable…
Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…
This paper studies the dimension effect of the linear discriminant analysis (LDA) and the regularized linear discriminant analysis (RLDA) classifiers for large dimensional data where the observation dimension $p$ is of the same order as the…
Principal component analysis (PCA) is a widely used method for dimension reduction. In high dimensional data, the "signal" eigenvalues corresponding to weak principal components (PCs) do not necessarily separate from the bulk of the "noise"…
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas…
The performance of principal component analysis (PCA) suffers badly in the presence of outliers. This paper proposes two novel approaches for robust PCA based on semidefinite programming. The first method, maximum mean absolute deviation…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…