Low-Rank Methods in Event Detection
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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 ℓ^∞, for each incoming observation. In particular, we use a variant of matrix completion under interval uncertainty on a suitable flattening M ∈ R^m × n of the input data to obtain a low-rank model M ≈ L × R, L ∈ R^m × r, R ∈ R^r × n, r ≪ m. On-line, we compute the distance of each incoming x ∈ R^n 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.
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