BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:FI Computational Methods and Data Science Journal Club: Larry Saul
  (CCM)
DTSTART:20221213T200000Z
DTEND:20221213T220000Z
DTSTAMP:20260519T010500Z
UID:indico-event-3442@indico.flatironinstitute.org
CONTACT:ccaadmin@flatironinstitute.org
DESCRIPTION:Rescheduled from November 8thFI Computational Methods and Data
  Science Journal ClubFlatiron Institute\, 162 5th AvenueSpeaker: Larry Sa
 ul (CCM)Title: A geometrical connection between sparse and low-rank matric
 es and its uses for machine learningAbstract: Many problems in high dimens
 ional data analysis can be formulated as a search for structure in large m
 atrices. One important type of structure is sparsity\; for example\, when 
 a matrix is sparse\, with a large number of zero elements\, it can be stor
 ed in a highly compressed format. Another type of structure is linear depe
 ndence\; when a matrix is low-rank\, it can be expressed as the product of
  two smaller matrices. It is well known that neither one of these structur
 es implies the other. But can one find more subtle connections by looking 
 beyond the canonical decompositions of linear algebra?In this talk\, I wil
 l consider when a sparse nonnegative matrix can be recovered from a real-v
 alued matrix of significantly lower rank. Of particular interest is the se
 tting where the positive elements of the sparse matrix encode the similari
 ties of nearby points on a low dimensional manifold. The recovery can then
  be posed as a problem in manifold learning—namely\, how to learn a simi
 larity-preserving mapping of high dimensional inputs into a lower dimensio
 nal space. I will describe an algorithm for this problem based on a genera
 lized low-rank decomposition of sparse matrices. This decomposition has th
 e interesting property that it can be encoded by a neural network with one
  layer of rectified linear units\; since the algorithm discovers this enco
 ding\, it can also be viewed as a layerwise primitive for deep learning. F
 inally\, I will apply the algorithm to data sets where vector magnitudes a
 nd small cosine distances have interpretable meanings (e.g.\, the brightne
 ss of an image\, the similarity to other words). On these data sets\, the 
 algorithm is able to discover much lower dimensional representations that 
 preserve these meanings.Bio: Lawrence Saul is a Senior Research Scientist 
 in the Center for Computational Mathematics (CCM) at the Flatiron Institut
 e. He joined CCM in July 2022 as a group leader in machine learning\; prev
 iously\, he was a Professor and Vice Chair in the Department of Computer S
 cience and Engineering at UC San Diego. Attendee Instructions:FI employee
 s are welcome to attend in person. Please email ccaadmin@flatironinstitute
 .org for the Zoom link if you wish to attend remotely.Visitors (w/out an 
 FI badge) please email ccaadmin@flatironinstitute.org 24hrs in advance to 
 be registered to the building or to obtain Zoom information.Additional Inf
 ormation:COVID Policy: By making entry to our buildings all staff\, vendor
 s and guests will implicitly attest to being symptom/COVID free. Vaccinati
 on status will no longer be validated as a condition of entry. However\, a
 ll staff and affiliates are strongly encouraged to remain up to date with 
 their vaccination boosters\, according to their individual eligibility.Age
  Restriction: All employees\, visitors\, event attendees and vendors are r
 equired to be above the age of eighteen for entry into our building(s). Ph
 oto ID with birthdate will be required by security upon arrival to our bui
 lding. For nursing mothers\, please reach out to an admin to arrange an ex
 ception.\n\nhttps://indico.flatironinstitute.org/event/3442/
LOCATION:5th Floor Classroom/5-Flatiron Institute (162 5th Avenue)
URL:https://indico.flatironinstitute.org/event/3442/
END:VEVENT
END:VCALENDAR