Related papers: Generalized Image Reconstruction over T-Algebra

Continuing our previous research on color image compression, we move towards spectral image compression. This enormous amount of data needs more space to store and more time to transmit. To manage this sheer amount of data, researchers have…

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

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 arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an…

Principal Component analysis (PCA) is a useful statistical technique that is commonly used for multivariate analysis of correlated variables. It is usually applied as a dimension reduction method: the top principal components (PCs)…

We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA…

Principal component analysis (PCA) can be significantly limited when there is too few examples of the target data of interest. We propose a transfer learning approach to PCA (TL-PCA) where knowledge from a related source task is used in…

We present a new straightforward principal component analysis (PCA) method based on the diagonalization of the weighted variance-covariance matrix through two spectral decomposition methods: power iteration and Rayleigh quotient iteration.…

Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…

Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal…

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

We demonstrate that Principal Component Analysis (PCA), when applied in a structured manner, either to polar-transformed images or segment-wise to token sequences, enables extreme compression of neural models without sacrificing…

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

Principal Component Analysis (PCA) is a pivotal technique widely utilized in the realms of machine learning and data analysis. It aims to reduce the dimensionality of a dataset while minimizing the loss of information. In recent years,…

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…

Compressive imaging using coded apertures (CA) is a powerful technique that can be used to recover depth, light fields, hyperspectral images and other quantities from a single snapshot. The performance of compressive imaging systems based…

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…

High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…