927 research outputs found

    Simple and Deterministic Matrix Sketching

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    We adapt a well known streaming algorithm for approximating item frequencies to the matrix sketching setting. The algorithm receives the rows of a large matrix A∈RnΓ—mA \in \R^{n \times m} one after the other in a streaming fashion. It maintains a sketch matrix B \in \R^ {1/\eps \times m} such that for any unit vector xx [\|Ax\|^2 \ge \|Bx\|^2 \ge \|Ax\|^2 - \eps \|A\|_{f}^2 \.] Sketch updates per row in AA require O(m/\eps^2) operations in the worst case. A slight modification of the algorithm allows for an amortized update time of O(m/\eps) operations per row. The presented algorithm stands out in that it is: deterministic, simple to implement, and elementary to prove. It also experimentally produces more accurate sketches than widely used approaches while still being computationally competitive
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