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Coherence Pursuit: Fast, Simple, and Robust Subspace Recovery

ICML 2017 · Learning theory and algorithms › Matrix and tensor methods · approach: Sparse and robust PCA · 10 citations (OpenAlex)

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Measured effects reported in the paper

What was changedWhereMeasuredEffect
Use single-step Coherence Pursuit (one Gram matrix multiplication with p-norm ranking) instead of iterative robust PCA solversrobust PCA subspace recovery · Running time, m=n=10000run time (s): 27 s vs 401 s (FMS), 3547 s (OP), 598 s (R1-PCA)Helped
Adopt the l1-norm (p=1) ranking for CoP when outliers are repeated (ablation)CoP with linearly dependent outliers · Repeated outliers illustration (r=5, n1=50, n2=500)separation of inlier vs outlier scores in pMixed
Use l2-norm (p=2) instead of l1 for ranking coherence (ablation)CoP · Theoretical sufficient conditions (Lemmas 1-2)outlier toleranceHelped
Adaptive column sampling (Algorithm 2) for subspace identification with random projectionCoP · Subspace identification stepredundant column samplingHelped
Use CoP as error-correction step on subspace clustering output (Hopkins155 traffic)subspace clustering error correction · Hopkins155 traffic sequences, 20% initial clustering errorclustering errorHelped

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