Related papers: Robust CUR Decomposition: Theory and Imaging Appli…
Video decomposition is very important to extract moving foreground objects from complex backgrounds in computer vision, machine learning, and medical imaging, e.g., extracting moving contrast-filled vessels from the complex and noisy…
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…
Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…
Background foreground separation (BFS) is a popular computer vision problem where dynamic foreground objects are separated from the static background of a scene. Typically, this is performed using consumer cameras because of their low cost,…
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…
Principle Component Analysis PCA is a classical feature extraction and data representation technique widely used in pattern recognition. It is one of the most successful techniques in face recognition. But it has drawback of high…
Over the past years Robust PCA has been established as a standard tool for reliable low-rank approximation of matrices in the presence of outliers. Recently, the Robust PCA approach via nuclear norm minimization has been extended to…
Dynamic inner principal component analysis (DiPCA) is a powerful method for the analysis of time-dependent multivariate data. DiPCA extracts dynamic latent variables that capture the most dominant temporal trends by solving a large-scale,…
Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…
Calcium imaging is an essential tool to study the activity of neuronal populations. However, the high level of background fluorescence in images hinders the accurate identification of neurons and the extraction of neuronal activities. While…
In the context of online Robust Principle Component Analysis (RPCA) for the video foreground-background separation, we propose a compressive online RPCA with optical flow that separates recursively a sequence of frames into sparse…
We consider the problem of learning a linear factor model. We propose a regularized form of principal component analysis (PCA) and demonstrate through experiments with synthetic and real data the superiority of resulting estimates to those…
The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…
Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…
We derive a CUR matrix factorization based on the Discrete Empirical Interpolation Method (DEIM). For a given matrix $A$, such a factorization provides a low rank approximate decomposition of the form $A \approx C U R$, where $C$ and $R$…
The segmentation of animals from camera-trap images is a difficult task. To illustrate, there are various challenges due to environmental conditions and hardware limitation in these images. We proposed a multi-layer robust principal…
A common problem in large-scale data analysis is to approximate a matrix using a combination of specifically sampled rows and columns, known as CUR decomposition. Unfortunately, in many real-world environments, the ability to sample…
The CUR decomposition of an $m \times n$ matrix $A$ finds an $m \times c$ matrix $C$ with a subset of $c < n$ columns of $A,$ together with an $r \times n$ matrix $R$ with a subset of $r < m$ rows of $A,$ as well as a $c \times r$ low-rank…
Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…
Recently the sparse representation based classification (SRC) has been proposed for robust face recognition (FR). In SRC, the testing image is coded as a sparse linear combination of the training samples, and the representation fidelity is…