In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the Principle Component Analysis (PCA) of any $n\times d$ matrix, using one pass over the stream of its rows. Our solution uses coresets: a scaled subset of the $n$ rows that approximates their sum of squared distances to \emph{every} $k$-dimensional \emph{affine} subspace. An open theoretical problem has been to compute such a coreset that is independent of both $n$ and $d$. An open practical problem has been to compute a non-trivial approximation to the PCA of very large but sparse databases such as the Wikipedia document-term matrix in a reasonable time. We answer both of these questions affirmatively. Our main technical result is a new framework for deterministic coreset constructions based on a reduction to the problem of counting items in a stream.

Coresets are one of the central methods to facilitate the analysis of large data. We continue a recent line of research applying the theory of coresets to logistic regression. First, we show the negative result that no strongly sublinear sized coresets exist for logistic regression. To deal with intractable worst-case instances we introduce a complexity measure $\mu(X)$, which quantifies the hardness of compressing a data set for logistic regression.

To speed up ACL, this paper proposes a robustness-aware coreset selection (RCS) method.

In large-scale applications, datasets often contain billions of high-dimensional points. Grouping similar data points into clusters is crucial for understanding and organizing datasets.

In online learning literature, stochastic and adversarial settings are two of the most well-studied cases.

In online learning literature, stochastic and adversarial settings are two of the most well-studied cases.

Classically, sketching has been applied to design low-memory algorithms in the streaming setting, when the input is presented to the algorithm as a sequence of updates.