Category Archives: Algorithm

SVD and Eigenvectors for Big Data

People generally believe that a PC can handle SVD for matrices only up to thousands by thousands. Textbooks also suggest that it is not wise to compute singular vectors one by one. In this post, I’ll refute both statements. In particular, … Continue reading

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Faster Than SGD 1: Variance Reduction

SGD is well-known for large-scale optimization. In my mind, there are two (and only two) fundamental improvements since the original introduction of SGD: (1) variance reduction, and (2) acceleration. In this guest post at Princeton’s OptiML group, I’d love to conduct … Continue reading

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Faster Comp-Geometry via Optimization

If one wants to compute the minimum enclosing ball (MinEB) of a set of points, would you believe that the running time can be improved by a significant factor if we randomly rotate the space? While seemingly very counter-intuitive because a … Continue reading

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Spielman-Teng-A: A Local Clustering Algorithm for Massive Graphs and its Application to Nearly-Linear Time Graph Partitioning

Spielman-Teng’s 2004 paper [ST04] on almost-linear Laplacian linear solver has been divided and re-written into three very technically involved ones [ST08a], [ST08b] and [ST08c]. I am planning to write memos for all of them, while this post is the Part … Continue reading

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Spielman-Teng-B: Spectral Sparsification of Graphs (Part II)

Spielman-Teng’s 2004 paper [ST04] on almost-linear Laplacian linear solver has been divided and re-written into three very technically involved papers [ST08a], [ST08b] and [ST08c]. I am planning to write memos for all of them, while this post is the Part … Continue reading

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Spielman-Teng-B: Spectral Sparsification of Graphs (Part I)

Spielman-Teng’s 2004 paper [ST04] on almost-linear Laplacian linear solver has been divided and re-written into three very technically involved papers [ST08a], [ST08b] and [ST08c]. I am planning to write memos for all of them, while this post is the Part … Continue reading

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Constant Factor Approximation of Vertex-Cuts in Planar Graphs

There has been a long time I couldn’t remember to write memos for the papers I’ve read, and it’s time for me to come back to this blog, coz my memory is fading all the time and blogging is a … Continue reading

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