Paper Info
Title
Principal Graphs and Manifolds
Abstract
In many physical statistical, biological and other investigations it is desirable to approximate a system of points by objects of lower dimension and/or complexity. For this purpose, Karl Pearson invented principal component analysis in 1901 and found 'lines and planes of closest fit to system of points'. The famous k-means algorithm solves the approximation problem too, but by finite sets instead of lines and planes. This chapter gives a brief practical introduction into the methods of construction of general principal objects, i.e. objects embedded in the 'middle' of the multidimensional data set. As a basis, the unifying framework of mean squared distance approximation of finite datasets is selected. Principal graphs and manifolds are constructed as generalisations of principal components and k-means principal points. For this purpose, the family of expectation/maximisation algorithms with nearest generalisations is presented. Construction of principal graphs with controlled complexity is based on the graph grammar approach.
Year
DOI
Venue
2008
10.4018/978-1-60566-766-9
Clinical Orthopaedics and Related Research
Keywords
Field
DocType
evolutionary computing,principal component analysis,k means,k means algorithm,principal component
Graph,Finite set,Square (algebra),Cardinal point,Principal geodesic analysis,Grammar,Artificial intelligence,Manifold,Machine learning,Mathematics,Principal component analysis
Journal
Volume
ISSN
Citations 
abs/0809.0
Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods and Techniques, Ch. 2, Information Science Reference, 2009. 28-59
5
PageRank 
References 
Authors
0.79
17
2
Name
Order
Citations
PageRank
Alexander N. Gorban1194.04
Andrei Yu. Zinovyev29311.87