927 research outputs found
Simple and Deterministic Matrix Sketching
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 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 [\|Ax\|^2 \ge \|Bx\|^2 \ge \|Ax\|^2 - \eps \|A\|_{f}^2 \.] Sketch
updates per row in 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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