Data visualization by nonlinear dimensionality reduction

被引：54
作者：
Gisbrecht, Andrej [1 ]
Hammer, Barbara [1 ]
机构：
[1] CITEC, Bielefeld, Germany
来源：
WILEY INTERDISCIPLINARY REVIEWS-DATA MINING AND KNOWLEDGE DISCOVERY | 2015年 / 5卷 / 02期
关键词：
GENERAL FRAMEWORK; NYSTROM METHOD; PROJECTION; PERSPECTIVE; EXPRESSION; SIMILARITY; METRICS; MAPS;
D O I：
10.1002/widm.1147
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
In this overview, commonly used dimensionality reduction techniques for data visualization and their properties are reviewed. Thereby, the focus lies on an intuitive understanding of the underlying mathematical principles rather than detailed algorithmic pipelines. Important mathematical properties of the technologies are summarized in the tabular form. The behavior of representative techniques is demonstrated for three benchmarks, followed by a short discussion on how to quantitatively evaluate these mappings. In addition, three currently active research topics are addressed: how to devise dimensionality reduction techniques for complex non-vectorial data sets, how to easily shape dimensionality reduction techniques according to the users preferences, and how to device models that are suited for big data sets. WIREs Data Mining Knowl Discov 2015, 5:51-73. doi: 10.1002/widm.1147 For further resources related to this article, please visit the .
引用
收藏
页码：51 / 73
页数：23
相关论文
共 98 条
[1]  
[Anonymous], 2013, PROC 30 INT C MACHIN
[2]  
[Anonymous], 1992, Neural computation and self-organizing maps: an introduction
[3]  
[Anonymous], 2003, Advances in Neural Information Processing Systems 15, DOI DOI 10.1109/34.682189
[4]  
[Anonymous], 2005, The Dissimilarity Representation for Pattern Recognition: Foundations And Applications (Machine Perception and Artificial Intelligence)
[5]  
[Anonymous], P EUR S ART NEUR NET
[6]   A HIERARCHICAL O(N-LOG-N) FORCE-CALCULATION ALGORITHM [J].
BARNES, J ;
HUT, P .
NATURE, 1986, 324 (6096) :446-449
[7]   A taxonomy for spatiotemporal connectionist networks revisited:: The unsupervised case [J].
Barreto, GD ;
Araújo, AFR .
NEURAL COMPUTATION, 2003, 15 (06) :1255-1320
[8]   Generalized discriminant analysis using a kernel approach [J].
Baudat, G ;
Anouar, FE .
NEURAL COMPUTATION, 2000, 12 (10) :2385-2404
[9]   QUANTIFYING THE NEIGHBORHOOD PRESERVATION OF SELF-ORGANIZING FEATURE MAPS [J].
BAUER, HU ;
PAWELZIK, KR .
IEEE TRANSACTIONS ON NEURAL NETWORKS, 1992, 3 (04) :570-579
[10]   Laplacian eigenmaps for dimensionality reduction and data representation [J].
Belkin, M ;
Niyogi, P .
NEURAL COMPUTATION, 2003, 15 (06) :1373-1396
12345678910