A widely-used tool for binary classification is the Support Vector Machine (SVM), a supervised learning technique that finds the maximum margin linear separator between the two classes. While SVMs have been well studied in the batch (offline) setting
, there is considerably less work on the streaming (online) setting, which requires only a single pass over the data using sub-linear space. Existing streaming algorithms are not yet competitive with the batch implementation. In this paper, we use the formulation of the SVM as a minimum enclosing ball (MEB) problem to provide a streaming SVM algorithm based off of the blurred ball cover originally proposed by Agarwal and Sharathkumar. Our implementation consistently outperforms existing streaming SVM approaches and provides higher accuracies than libSVM on several datasets, thus making it competitive with the standard SVM batch implementation.
The analysis of several algorithms and data structures can be framed as a peeling process on a random hypergraph: vertices with degree less than k and their adjacent edges are removed until no vertices of degree less than k are left. Often the questi
on is whether the remaining hypergraph, the k-core, is empty or not. In some settings, it may be possible to remove either vertices or edges from the hypergraph before peeling, at some cost. For example, in hashing applications where keys correspond to edges and buckets to vertices, one might use an additional side data structure, commonly referred to as a stash, to separately handle some keys in order to avoid collisions. The natural question in such cases is to find the minimum number of edges (or vertices) that need to be stashed in order to realize an empty k-core. We show that both these problems are NP-complete for all $k geq 2$ on graphs and regular hypergraphs, with the sole exception being that the edge variant of stashing is solvable in polynomial time for $k = 2$ on standard (2-uniform) graphs.
