Related papers: An online algorithm for contrastive Principal Comp…

We study the fairness of dimensionality reduction methods for recommendations. We focus on the fundamental method of principal component analysis (PCA), which identifies latent components and produces a low-rank approximation via the…

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

Scaling methods have long been utilized to simplify and cluster high-dimensional data. However, the general latent spaces across all predefined groups derived from these methods sometimes do not fall into researchers' interest regarding…

In this paper we propose a novel optimization framework to systematically solve robust PCA problem with rigorous theoretical guarantee, based on which we investigate very computationally economic updating algorithms.

This paper proposes a novel dynamic forecasting method using a new supervised Principal Component Analysis (PCA) when a large number of predictors are available. The new supervised PCA provides an effective way to bridge the gap between…

Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of 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…

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…

Representation learning has significantly been developed with the advance of contrastive learning methods. Most of those methods have benefited from various data augmentations that are carefully designated to maintain their identities so…

Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…

The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such…

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or…

Conventional hyperparameter optimization methods are computationally intensive and hard to generalize to scenarios that require dynamically adapting hyperparameters, such as life-long learning. Here, we propose an online hyperparameter…

Principal component analysis (PCA) is by far the most widespread tool for unsupervised learning with high-dimensional data sets. Its application is popularly studied for the purpose of exploratory data analysis and online process…

Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…

Machine Learning models are prone to fail when test data are different from training data, a situation often encountered in real applications known as distribution shift. While still valid, the training-time knowledge becomes less…

Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…

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…

This paper uses network packet capture data to demonstrate how Robust Principal Component Analysis (RPCA) can be used in a new way to detect anomalies which serve as cyber-network attack indicators. The approach requires only a few…

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…