Related papers: Streaming PCA and Subspace Tracking: The Missing D…
We study principal component analysis (PCA), where given a dataset in $\mathbb{R}^d$ from a distribution, the task is to find a unit vector $v$ that approximately maximizes the variance of the distribution after being projected along $v$.…
The problem of choosing appropriate values for missing data is often encountered in the data science. We describe a novel method containing both traditional mathematics and machine learning elements for prediction (imputation) of missing…
In an era of ubiquitous large-scale streaming data, the availability of data far exceeds the capacity of expert human analysts. In many settings, such data is either discarded or stored unprocessed in datacenters. This paper proposes a…
Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{\`e}s, Wright, Li, and Ma…
Subspace tracking is a fundamental problem in signal processing, where the goal is to estimate and track the underlying subspace that spans a sequence of data streams over time. In high-dimensional settings, data samples are often corrupted…
Low-precision streaming PCA estimates the top principal component in a streaming setting under limited precision. We establish an information-theoretic lower bound on the quantization resolution required to achieve a target accuracy for the…
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…
Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…
We propose a novel statistical inference framework for streaming principal component analysis (PCA) using Oja's algorithm, enabling the construction of confidence intervals for individual entries of the estimated eigenvector. Most existing…
Linear subspace models are pervasive in computational sciences and particularly used for large datasets which are often incomplete due to privacy issues or sampling constraints. Therefore, a critical problem is developing an efficient…
This work studies the robust subspace tracking (ST) problem. Robust ST can be simply understood as a (slow) time-varying subspace extension of robust PCA. It assumes that the true data lies in a low-dimensional subspace that is either fixed…
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.…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
Classical machine learning algorithms often face scalability bottlenecks when they are applied to large-scale data. Such algorithms were designed to work with small data that is assumed to fit in the memory of one machine. In this report,…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
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…
Piecewise Linear Approximation (PLA) is a well-established tool to reduce the size of the representation of time series by approximating the series by a sequence of line segments while keeping the error introduced by the approximation…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…
Privacy-preserving data mining has become an important topic. People have built several multi-party-computation (MPC)-based frameworks to provide theoretically guaranteed privacy, the poor performance of real-world algorithms have always…