Related papers: PCA Reduced Gaussian Mixture Models with Applicati…

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Dimensionality reduction is a main step in the learning process which plays an essential role in many applications. The most popular methods in this field like SVD, PCA, and LDA, only can be applied to data with vector format. This means…

Dimensionality reduction algorithms are standard tools in a researcher's toolbox. Dimensionality reduction algorithms are frequently used to augment downstream tasks such as machine learning, data science, and also are exploratory methods…

Gaussian Graphical models (GGM) are widely used to estimate the network structures in many applications ranging from biology to finance. In practice, data is often corrupted by latent confounders which biases inference of the underlying…

We consider maximum likelihood estimation for Gaussian Mixture Models (Gmms). This task is almost invariably solved (in theory and practice) via the Expectation Maximization (EM) algorithm. EM owes its success to various factors, of which…

The Expectation-Maximization (EM) algorithm is a fundamental tool in unsupervised machine learning. It is often used as an efficient way to solve Maximum Likelihood (ML) estimation problems, especially for models with latent variables. It…

Gaussian mixture models (GMMs) are fundamental statistical tools for modeling heterogeneous data. Due to the nonconcavity of the likelihood function, the Expectation-Maximization (EM) algorithm is widely used for parameter estimation of…

Superpixel segmentation algorithms are to partition an image into perceptually coherence atomic regions by assigning every pixel a superpixel label. Those algorithms have been wildly used as a preprocessing step in computer vision works, as…

Recent advances in 3D Gaussian splatting have significantly improved real-time novel view synthesis, yet insufficient geometric constraints during scene optimization often result in blurred reconstructions of fine-grained details,…

Principal component analysis (PCA) is one of the most popular dimension reduction techniques in statistics and is especially powerful when a multivariate distribution is concentrated near a lower-dimensional subspace. Multivariate extreme…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from…

This paper presents a computational framework for the Principal Geodesic Analysis of merge trees (MT-PGA), a novel adaptation of the celebrated Principal Component Analysis (PCA) framework [87] to the Wasserstein metric space of merge trees…

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

In this paper, we develop an algorithm for federated principal component analysis (PCA) with emphases on both communication efficiency and data privacy. Generally speaking, federated PCA algorithms based on direct adaptations of classic…

In this paper we propose a new iterative algorithm to solve the fair PCA (FPCA) problem. We start with the max-min fair PCA formulation originally proposed in [1] and derive a simple and efficient iterative algorithm which is based on the…

We consider the dimensionality-reduction problem (finding a subspace approximation of observed data) for contaminated data in the high dimensional regime, where the number of observations is of the same magnitude as the number of variables…

Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic…

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…