Related papers: On Robust Probabilistic Principal Component Analys…
Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…
We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse…
Principal component analysis (PCA) is often used to analyze multivariate data together with cluster analysis, which depends on the number of principal components used. It is therefore important to determine the number of significant…
Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…
Principal component analysis (PCA) is a widely used technique for dimension reduction. As datasets continue to grow in size, distributed-PCA (DPCA) has become an active research area. A key challenge in DPCA lies in efficiently aggregating…
Previous versions of sparse principal component analysis (PCA) have presumed that the eigen-basis (a $p \times k$ matrix) is approximately sparse. We propose a method that presumes the $p \times k$ matrix becomes approximately sparse after…
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.…
Principal component analysis (PCA) is a longstanding and well-studied approach for dimension reduction. It rests upon the assumption that the underlying signal in the data has low rank, and thus can be well-summarized using a small number…
Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…
Sequential or online dimensional reduction is of interests due to the explosion of streaming data based applications and the requirement of adaptive statistical modeling, in many emerging fields, such as the modeling of energy end-use…
Principal Component Analysis (PCA) is well known for its capability of dimension reduction and data compression. However, when using PCA for compressing/reconstructing images, images need to be recast to vectors. The vectorization of images…
Multidimensional data is often associated with uncertainties that are not well-described by normal distributions. In this work, we describe how such distributions can be projected to a low-dimensional space using uncertainty-aware principal…
Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
A new look on the principal component analysis has been presented. Firstly, a geometric interpretation of determination coefficient was shown. In turn, the ability to represent the analyzed data and their interdependencies in the form of…
Principal component analysis (PCA) is an indispensable tool in many learning tasks that finds the best linear representation for data. Classically, principal components of a dataset are interpreted as the directions that preserve most of…
We study the fundamental problem of Principal Component Analysis in a statistical distributed setting in which each machine out of $m$ stores a sample of $n$ points sampled i.i.d. from a single unknown distribution. We study algorithms for…
Principal component analysis (PCA) is a classical feature extraction method, but it may be adversely affected by outliers, resulting in inaccurate learning of the projection matrix. This paper proposes a robust method to estimate both the…
Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse,…
This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…