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SUMMARY:A curious correspondence between sparse and low-rank matrices and 
 its myriad practical uses - Lawrence Saul (None / Other)
DTSTART:20250724T083000Z
DTEND:20250724T093000Z
UID:TALK234634@talks.cam.ac.uk
DESCRIPTION:We consider when a sparse nonnegative matrix can be recovered\
 , via a simple elementwise nonlinearity\, from a real-valued matrix of sig
 nificantly lower rank. We show that this question arises naturally in many
  problems of high dimensional data analysis\, and for a particular choice 
 of nonlinearity\, we describe an algorithm\, known as subzero matrix compl
 etion\, to discover these low-rank representations. As illustrative exampl
 es\, we use the algorithm to analyze the synaptic weight matrix of the fru
 it-fly connectome and the co-occurence statistics of words in natural lang
 uage. Finally\, we discuss the challenges of scaling this algorithm to ver
 y large matrices\, as well as recent progress on overcoming these challeng
 es.
LOCATION:External
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