Name
Abstract | ||
|---|---|---|
Archetypal analysis (aa) proposed by Cutler and Breiman (1994) 7] estimates the principal convex hull (pch) of a data set. As such aa favors features that constitute representative 'corners' of the data, i.e., distinct aspects or archetypes. We currently show that aa enjoys the interpretability of clustering - without being limited to hard assignment and the uniqueness of svd - without being limited to orthogonal representations. In order to do large scale aa, we derive an efficient algorithm based on projected gradient as well as an initialization procedure we denote FurthestSum that is inspired by the FurthestFirst approach widely used for k-means (Hochbaum and Shmoys, 1985 14]). We generalize the aa procedure to kernel-aa in order to extract the principal convex hull in potential infinite Hilbert spaces and derive a relaxation of aa when the archetypes cannot be represented as convex combinations of the observed data. We further demonstrate that the aa model is relevant for feature extraction and dimensionality reduction for a large variety of machine learning problems taken from computer vision, neuroimaging, chemistry, text mining and collaborative filtering leading to highly interpretable representations of the dynamics in the data. Matlab code for the derived algorithms is available for download from www.mortenmorup.dk. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.neucom.2011.06.033 | Neurocomputing |
Keywords | Field | DocType |
aa model,furthestfirst approach,principal convex hull,initialization procedure,archetypal analysis,data mining,aa procedure,observed data,convex combination,large scale aa,large variety,kernel methods,non negative matrix factorization,clustering | Data mining,Dimensionality reduction,Convex hull,Artificial intelligence,Cluster analysis,Interpretability,Pattern recognition,Feature extraction,Non-negative matrix factorization,Initialization,Kernel method,Machine learning,Mathematics | Journal |
Volume | Issue | ISSN |
80 | C | 0925-2312 |
Citations | PageRank | References |
45 | 1.83 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Morten Mørup | 1 | 704 | 51.29 |
| Lars Kai Hansen | 2 | 2776 | 341.03 |