Related papers: A Compared Study Between Some Subspace Based Algor…

It has been shown that dimension reduction methods such as PCA may be inherently prone to unfairness and treat data from different sensitive groups such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing dimensionality…

Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…

Face recognition is the important field in machine learning and pattern recognition research area. It has a lot of applications in military, finance, public security, to name a few. In this paper, the combination of the tensor sparse PCA…

Kernel Principal Component Analysis (KPCA) is a popular dimensionality reduction technique with a wide range of applications. However, it suffers from the problem of poor scalability. Various approximation methods have been proposed in the…

Robust principal component analysis (RPCA) is a powerful method for learning low-rank feature representation of various visual data. However, for certain types as well as significant amount of error corruption, it fails to yield…

In order to process efficiently ever-higher dimensional data such as images, sentences, or audio recordings, one needs to find a proper way to reduce the dimensionality of such data. In this regard, SVD-based methods including PCA and…

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The…

We investigate whether the standard dimensionality reduction technique of PCA inadvertently produces data representations with different fidelity for two different populations. We show on several real-world data sets, PCA has higher…

Principal Component Analysis (PCA) is a widely utilized technique for dimensionality reduction; however, its inherent lack of interpretability-stemming from dense linear combinations of all feature-limits its applicability in many domains.…

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First,…

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,…

Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…

Because of high dimensionality, correlation among covariates, and noise contained in data, dimension reduction (DR) techniques are often employed to the application of machine learning algorithms. Principal Component Analysis (PCA), Linear…

We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…

Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…

Face detection and recognition has been prevalent with research scholars and diverse approaches have been incorporated till date to serve purpose. The rampant advent of biometric analysis systems, which may be full body scanners, or iris…

Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…

Developing a reliable and practical face recognition system is a long-standing goal in computer vision research. Existing literature suggests that pixel-wise face alignment is the key to achieve high-accuracy face recognition. By assuming a…

Motivated by the recently shown connection between self-attention and (kernel) principal component analysis (PCA), we revisit the fundamentals of PCA. Using the difference-of-convex (DC) framework, we present several novel formulations and…

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…