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Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…
Spectral clustering and Singular Value Decomposition (SVD) are both widely used technique for analyzing graph data. In this note, I will present their connections using simple linear algebra, aiming to provide some in-depth understanding…
In high-dimensional settings, Canonical Correlation Analysis (CCA) often fails, and existing sparse methods force an untenable choice between computational speed and statistical rigor. This work introduces a fast and provably consistent…
Singular Value Decomposition (SVD) and its close relative, Principal Component Analysis (PCA), are well-known linear matrix decomposition techniques that are widely used in applications such as dimension reduction and clustering. However,…
Numeric tabular datasets are the dominant data format in scientific practice, yet large language models lack native mechanisms for representing numeric datasets in a meaningful way across heterogeneous feature spaces. Existing approaches…
Massive data analysis calls for distributed algorithms and theories. We design a multi-round distributed algorithm for canonical correlation analysis. We construct principal directions through the convex formulation of canonical correlation…
In many biomedical research, multiple views of data (e.g., genomics, proteomics) are available, and a particular interest might be the detection of sample subgroups characterized by specific groups of variables. Biclustering methods are…
Multi-view clustering, a long-standing and important research problem, focuses on mining complementary information from diverse views. However, existing works often fuse multiple views' representations or handle clustering in a common…
The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first…
Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield…
These notes are an overview of some classical linear methods in Multivariate Data Analysis. This is a good old domain, well established since the 60's, and refreshed timely as a key step in statistical learning. It can be presented as part…
Multivariate Analysis (MVA) comprises a family of well-known methods for feature extraction which exploit correlations among input variables representing the data. One important property that is enjoyed by most such methods is uncorrelation…
In this work, travel destination and business location are taken as venues. Discovering a venue by a photo is very important for context-aware applications. Unfortunately, few efforts paid attention to complicated real images such as venue…
Multi-criteria Analysis (MCA) is used to rank alternatives based on various criteria. Key MCA methods, such as Multiple Criteria Decision Making (MCDM) methods, estimate parameters for criteria to compute the performance of each…
Formal Concept Analysis (FCA) is a mathematical framework for knowledge representation and discovery. It performs a hierarchical clustering over a set of objects described by attributes, resulting in conceptual structures in which objects…
This paper is concerned with the analysis of correlation between two high-dimensional data sets when there are only few correlated signal components but the number of samples is very small, possibly much smaller than the dimensions of the…
Multivariate Analysis (MVA) comprises a family of well-known methods for feature extraction that exploit correlations among input variables of the data representation. One important property that is enjoyed by most such methods is…
Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…
This paper provides a simple, yet reliable, alternative to the (Bayesian) estimation of large multivariate VARs with time variation in the conditional mean equations and/or in the covariance structure. With our new methodology, the original…
We propose a new high dimensional semiparametric principal component analysis (PCA) method, named Copula Component Analysis (COCA). The semiparametric model assumes that, after unspecified marginally monotone transformations, the…