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DTSTART;TZID=America/Los_Angeles:20220131T161500
DTEND;TZID=America/Los_Angeles:20220131T171500
DTSTAMP:20260413T115912
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SUMMARY:APPLIED MATH SEMINAR: Archetypal analysis by Professor Braxton Osting (University of Utah)
DESCRIPTION:Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed k\, the method finds a convex polytope with k vertices\, called archetype points\, such that the polytope is contained in the convex hull of the data and the mean squared distance between the data and the polytope is minimal. In this talk\, I’ll give an overview of the method and discuss connections to matrix factorization\, SVD/PCA\, and the k-means clustering method. I’ll discuss our recent results proving the consistency of archetypal analysis and describe probabilistic methods for approximate archetypal analysis. This is joint work with Ruijian Han\, Dong Wang\, Yiming Xu\, and Dominique Zosso.
URL:https://colleges.claremont.edu/ccms/event/applied-math-seminar-braxton-osting-university-of-utah/
LOCATION:CA
CATEGORIES:Applied Math Seminar
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DTSTART;TZID=America/Los_Angeles:20220201T123000
DTEND;TZID=America/Los_Angeles:20220201T132000
DTSTAMP:20260413T115912
CREATED:20220121T001428Z
LAST-MODIFIED:20220126T183034Z
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SUMMARY:Niho's last conjecture (Daniel Katz\, Cal State Northridge)
DESCRIPTION:A power permutation of a finite field F is a permutation of F whose functional form is x -> x^d for some exponent d.  Power permutations are used in cryptography\, and the exponent d must be chosen so that the permutation is highly nonlinear\, that is\, not easily approximated by linear functions.  The Walsh spectrum of a power permutation is a list of numbers measuring the correlation of our power permutation with the various linear functions. The last conjecture in Niho’s 1972 thesis considers a particular infinite family of highly nonlinear power permutations\, and states that each permutation in this family has a Walsh spectrum with at most five distinct values. Niho’s own techniques show that there are at most eight distinct values. Each of the eight candidate values corresponds to a possible number of distinct roots of a seventh degree polynomial on a subset of the finite field F called the unit circle. We use symmetry arguments to show that it is impossible to have four\, six\, or seven roots on the unit circle: this proves Niho’s last conjecture. This is joint work with Tor Helleseth and Chunlei Li.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-daniel-katz-cal-state-northridge/
LOCATION:On Zoom
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
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DTSTART;TZID=America/Los_Angeles:20220202T161500
DTEND;TZID=America/Los_Angeles:20220202T173000
DTSTAMP:20260413T115912
CREATED:20220128T183638Z
LAST-MODIFIED:20220131T193506Z
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SUMMARY:Exploiting metric structure for more accurate classification (Prof. Mike Izbicki)
DESCRIPTION:Title: Exploiting metric structure for more accurate classification \nSpeaker: Mike Izbicki\, Department of Mathematical Sciences\, Claremont McKenna College \nAbstract: Classification problems often have many semantically similar classes.  For example\, the famous ImageNet dataset contains classes for 80 different dog breeds\, 40 different bird species\, and 25 types of vehicles.  This semantic structure can be formalized using a metric space\, with semantic similarity of classes encoded by the distance function.  In this talk\, I’ll describe the “tree loss”\, which is the first technique with provable performance guarantees for exploiting this metric structure.  I’ll also show that the tree loss has better empirical performance than competing algorithms on image\, text\, and vector data. \n\nMike studies machine learning theory\, focusing on applications to natural language and social media.  He has been at CMC for 3 years now\, where he teaches computer and data science classes.  Prior to his academic career\, Mike spent 7 years in the US Navy.  Highlights include converting >10g of Uranium into pure energy as a nuclear submarine officer\, and doing [redacted] for the NSA.  After leaving the navy\, Mike went to North Korea to teach computer science as part of an academic exchange program designed to improve relations between the US and North Korea.  He earned his phd from UC Riverside.
URL:https://colleges.claremont.edu/ccms/event/exploiting-metric-structure-for-more-accurate-classification-prof-mike-izbicki/
LOCATION:Zoom meeting\, United States
CATEGORIES:Colloquium
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