Лекции профессора А.Н.ГорбаняAlexander Gorban University of Leicester, UKhttps://lib.nsu.ru/xmlui/handle/nsu/40292024-03-29T10:26:57Z2024-03-29T10:26:57ZPrincipal Graphs and ManifoldsGorban, Alexander N.Zinovyev, Andrei Y.https://lib.nsu.ru/xmlui/handle/nsu/40322014-12-14T22:00:37Z2010-01-01T00:00:00ZPrincipal Graphs and Manifolds; Графы и многообразия
Gorban, Alexander N.; Zinovyev, Andrei Y.
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.
2010-01-01T00:00:00ZОбзор алгоритмов кластерного анализаWunsch, DonaldRui Xuhttps://lib.nsu.ru/xmlui/handle/nsu/40312014-12-14T22:00:34Z2005-05-01T00:00:00ZОбзор алгоритмов кластерного анализа; Survey of Clustering Algorithms
Wunsch, Donald; Rui Xu
Data analysis plays an indispensable role for understanding various phenomena. Cluster analysis, primitive exploration with little or no prior knowledge, consists of research developed across a wide variety of communities. The diversity, on one hand, equips us with many tools. On the other hand, the profusion of options causes confusion. We survey clustering algorithms for data sets appearing in statistics, computer science, and machine learning, and illustrate their applications in some benchmark data sets, the traveling salesman problem, and bioinformatics, a new field attracting intensive efforts. Several tightly related topics, proximity measure, and cluster validation, are also discussed.
keywords: {data analysis;pattern classification;pattern clustering;benchmark data sets;bioinformatics;cluster analysis;data analysis;traveling salesman problem;Application software;Bioinformatics;Clustering algorithms;Computer science;Data analysis;Humans;Machine learning;Machine learning algorithms;Statistics;Traveling salesman problems;Adaptive resonance theory (ART);cluster validation;clustering;clustering algorithm;neural networks;proximity;self-organizing feature map (SOFM);Algorithms;Computer Simulation;Models, Statistical;Neural Networks (Computer);Numerical Analysis, Computer-Assisted;Pattern Recognition, Automated;Signal Processing, Computer-Assisted;Stochastic Processes},
2005-05-01T00:00:00ZСовременные проблемы информатики и классический кластер-анализГорбань, Александр Николаевичhttps://lib.nsu.ru/xmlui/handle/nsu/40302014-12-14T22:00:37Z2014-12-01T00:00:00ZСовременные проблемы информатики и классический кластер-анализ
Горбань, Александр Николаевич
Презентации лекций
2014-12-01T00:00:00Z