Archetype Analysis PDF
Preview Archetype Analysis
Archetype Analysis: a framework for selecting representative objects Volker Roth, Department of Mathematics and Computer Science, University of Basel 1 IPAM MPSWS1 2016, V Roth Machine Learning: Supervised Setting Learning Machine Important ©20th Century Fox Film Corporation spam Letter −> Class Label Statistical Learning Theory Supervisor 2 IPAM MPSWS1 2016, V Roth Machine Learning: Uncertain Labels Sometimes even the best experts make errors. Labels might be uncertain or missing... 3 IPAM MPSWS1 2016, V Roth Machine Learning: Unsupervised Setting Learning Machine Maybe clustering is a good idea ©20th Century Fox Film Corporation (BayeDsaitaan −) >M oSdtreul cStuelreection Supervisor How many clusters? How sparse is the graph? 4 IPAM MPSWS1 2016, V Roth A Repeated Pattern: Search for Representative Observations m Corporation ©20th Century Fox Fil "most pAerrfcehcte ptoyspsiebsle form" ("Canlu asttteemrp−t )aPt rsoomtoettyhipneg"s ©20th Century Fox Film Corporation 5 IPAM MPSWS1 2016, V Roth Archetype Analysis: Biological Motivation Is there a theoretical foundation of the “archetype concept”? O. Shoval, H. Sheftel, G. Shinar, Y. Hart, O. Ramote, A. Mayo, E. Dekel, K. Kavanagh, U. Alon: Evolutionary Trade-Offs, Pareto (cid:59) Optimality, and the Geometry of Phenotype Space. Science, 2012 6 IPAM MPSWS1 2016, V Roth Archetypes and Evolutionary Trade-offs Shoval et al.: Evolutionary Trade-Offs, Pareto Optimality, and the Geometry of Phenotype Space. Science, 2012 7 IPAM MPSWS1 2016, V Roth Shoval et al.: Evolutionary Trade-Offs, Pareto Optimality, and the Geometry of Phenotype Space. Science, 2012 8 IPAM MPSWS1 2016, V Roth Gene Expression Space Human colon crypt cells fall in a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. Korem et al. 2015 9 IPAM MPSWS1 2016, V Roth Computational Archetype Selection Cutler &Breiman, Archetypal Analysis, Technometrics 1994. • n observations {x , . . . , x } ∈ Rp, as rows of data matrix X ∈ Rn×p 1 n • Aim: find K archetypes ⇒ Z ∈ RK×p; K (cid:28) n fixed. • Observations are convex mixtures of archetypes (cid:80)K x = Zta + (cid:15) , a ≥ 0 and a = 1. i i i ij ij j=1 10 IPAM MPSWS1 2016, V Roth
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