Аннотации:
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.