Related papers: Dual Principal Component Pursuit: Probability Anal…
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…
We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…
Dimension-reduction techniques can greatly improve statistical inference in astronomy. A standard approach is to use Principal Components Analysis (PCA). In this work we apply a recently-developed technique, diffusion maps, to astronomical…
Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…
Density-based clustering algorithms are widely used for discovering clusters in pattern recognition and machine learning since they can deal with non-hyperspherical clusters and are robustness to handle outliers. However, the runtime of…
Principal component analysis (PCA), along with its extensions to manifolds and outlier contaminated data, have been indispensable in computer vision and machine learning. In this work, we present a unifying formalism for PCA and its…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets.…
In real world, our datasets often contain outliers. Moreover, the outliers can seriously affect the final machine learning result. Most existing algorithms for handling outliers take high time complexities (e.g. quadratic or cubic…
In this paper, we propose and analyze a fast two-point gradient algorithm for solving nonlinear ill-posed problems, which is based on the sequential subspace optimization method. A complete convergence analysis is provided under the…
Given a data matrix $\mathbf{A} \in \mathbb{R}^{n \times d}$, principal component projection (PCP) and principal component regression (PCR), i.e. projection and regression restricted to the top-eigenspace of $\mathbf{A}$, are fundamental…
The subspace approximation problem with outliers, for given $n$ points in $d$ dimensions $x_{1},\ldots, x_{n} \in R^{d}$, an integer $1 \leq k \leq d$, and an outlier parameter $0 \leq \alpha \leq 1$, is to find a $k$-dimensional linear…
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…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
Overparameterization in deep learning is powerful: Very large models fit the training data perfectly and yet often generalize well. This realization brought back the study of linear models for regression, including ordinary least squares…
The probabilistic principal component analysis (PPCA) is built upon a global linear mapping, with which it is insufficient to model complex data variation. This paper proposes a mixture of bilateral-projection probabilistic principal…
This paper investigates the intrinsic group structures within the framework of large-dimensional approximate factor models, which portrays homogeneous effects of the common factors on the individuals that fall into the same group. To this…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Partial least squares regression (PLSR) has been a popular technique to explore the linear relationship between two datasets. However, most of algorithm implementations of PLSR may only achieve a suboptimal solution through an optimization…