Related papers: Principal Loading Analysis
Partial Least Square (PLS) is a dimension reduction method used to remove multicollinearities in a regression model. However contrary to Principal Components Analysis (PCA) the PLS components are also choosen to be optimal for predicting…
Principal Component Analysis is a key technique for reducing the complexity of high-dimensional data while preserving its fundamental data structure, ensuring models remain stable and interpretable. This is achieved by transforming the…
Principal Subspace Analysis (PSA) -- and its sibling, Principal Component Analysis (PCA) -- is one of the most popular approaches for dimensionality reduction in signal processing and machine learning. But centralized PSA/PCA solutions are…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
Generalized principal component analysis (GLM-PCA) facilitates dimension reduction of non-normally distributed data. We provide a detailed derivation of GLM-PCA with a focus on optimization. We also demonstrate how to incorporate…
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…
Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…
Probabilistic linear discriminant analysis (PLDA) is commonly used in speaker verification systems to score the similarity of speaker embeddings. Recent studies improved the performance of PLDA in domain-matched conditions by diagonalizing…
Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…
Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…
We develop a new principal components analysis (PCA) type dimension reduction method for binary data. Different from the standard PCA which is defined on the observed data, the proposed PCA is defined on the logit transform of the success…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…
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…
In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program…
Of particular interest is to discover useful representations solely from observations in an unsupervised generative manner. However, the question of whether existing normalizing flows provide effective representations for downstream tasks…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
Motivation: Although principal component analysis is frequently applied to reduce the dimensionality of matrix data, the method is sensitive to noise and bias and has difficulty with comparability and interpretation. These issues are…
Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems. For these methods we assume observations are normally distributed within group. We estimate a mean and covariance matrix for each group and…
Clustering analysis is one of the most widely used statistical tools in many emerging areas such as microarray data analysis. For microarray and other high-dimensional data, the presence of many noise variables may mask underlying…