## Phenotyping using Tensor Factorization

Less is More: Compact Matrix Decomposition for Large Sparse GraphsProceedings of the 2007 SIAM International Conference on Data Mining (SDM), Minneapolis, Minnesota, Apr 2007. (Best research paper award)

Errata: Figure 5:ApprMultiplication algorithm is updated by adding line 8 and 12, which only keeps the matching columns in C_d (line 8) and scaling factor for those columns is 1 (line 12: this is redundant in the implementation since the scaling factor is 1 but I specify out there for clarification purpose). Thank Sebastian Köhler, Ces Bertino and Jeffrey T. Johns for spotting that.

[paper][presentation][code]

Jimeng Sun, Dacheng Tao, Christos Faloutsos. Beyond Streams and Graphs: Dynamic Tensor Analysis, Proceedings of the Twelfth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (SIGKDD), Philadelphia, Pennsylvia, USA, August 20-23, 2006 [abstract][pdf][bib][ppt][codetensor toolbox required]

Spiros Papadimitriou, Jimeng Sun, Christos Faloutsos. Streaming Pattern Discovery in Multiple Time-Series, Proceedings of the Very Large Data Bases Conference (VLDB), Trondheim, Norway, 2005 [abstract][pdf][bib][code]
Errata: 1) On the top of left column of P6, Algorithm TrackW requires a 3 step to orthogonalize $\vec{w}_i, 1\le i\le k$ by fixing $\vec{w}_1$, i.e., to apply Gram Schimdt orthogonalization with initial vector $\vec{w}_1$ (keep the principal direction unchanged).
2) Lemma 4.1 the last term \|\vec{y}_t\| should be squared, i.e., \|\vec{y}_t\|^2.