Related papers: Few-Round Distributed Principal Component Analysis…
Auxiliary information is frequently utilized in survey sampling to improve the efficiency of estimators of the finite population mean. However, the simultaneous use of multiple auxiliary variables often induces multicollinearity, which…
In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations…
We consider the problem of decomposing a large covariance matrix into the sum of a low-rank matrix and a diagonally dominant matrix, and we call this problem the "Diagonally-Dominant Principal Component Analysis (DD-PCA)". DD-PCA is an…
Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA…
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…
For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a…
We introduce a variant of (sparse) PCA in which the set of feasible support sets is determined by a graph. In particular, we consider the following setting: given a directed acyclic graph $G$ on $p$ vertices corresponding to variables, the…
In this paper, we tackle a significant challenge in PCA: heterogeneity. When data are collected from different sources with heterogeneous trends while still sharing some congruency, it is critical to extract shared knowledge while retaining…
The divide and conquer strategy, which breaks a massive data set into a se- ries of manageable data blocks, and then combines the independent results of data blocks to obtain a final decision, has been recognized as a state-of-the-art…
Sparse principal component analysis (PCA) aims at mapping large dimensional data to a linear subspace of lower dimension. By imposing loading vectors to be sparse, it performs the double duty of dimension reduction and variable selection.…
A key motivation in the development of Distributed Model Predictive Control (DMPC) is to accelerate centralized Model Predictive Control (MPC) for large-scale systems. DMPC has the prospect of scaling well by parallelizing computations…
As the size of modern data sets exceeds the disk and memory capacities of a single computer, machine learning practitioners have resorted to parallel and distributed computing. Given that optimization is one of the pillars of machine…
This work obtains novel finite sample guarantees for Principal Component Analysis (PCA). These hold even when the corrupting noise is non-isotropic, and a part (or all of it) is data-dependent. Because of the latter, in general, the noise…
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…
Recent years have witnessed an increasing popularity of algorithm design for distributed data, largely due to the fact that massive datasets are often collected and stored in different locations. In the distributed setting communication…
We introduce Principal Component Analysis guided Quantile Sampling (PCA QS), a novel sampling framework designed to preserve both the statistical and geometric structure of large scale datasets. Unlike conventional PCA, which reduces…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
We consider the problem of learning a mixture of Random Utility Models (RUMs). Despite the success of RUMs in various domains and the versatility of mixture RUMs to capture the heterogeneity in preferences, there has been only limited…
This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the…