Low-Rank Methods in Event Detection

We present low-rank methods for event detection. We assume that normal observation come from a low-rank subspace, prior to being corrupted by a uniformly distributed noise. Correspondingly, we aim at recovering a representation of the subspace, and perform event detection by running point-to-subspace distance query in `∞, for each incoming observation. In particular, we use a variant of matrix completion under interval uncertainty on a suitable flattening M ∈ Rm×n of the input data to obtain a low-rank model M ≈ L × R, L ∈ Rm×r, R ∈ Rr×n, r m. On-line, we compute the distance of each incoming x ∈ R to the space spanned by R. For the distance computation, we present a constant-time algorithm with a one-sided error bounded by a function of the number of coordinates employed. Our experimental evaluation illustrates the benefit of the approach proposed.