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Open Problems in Spectral Dimensionality Reduction 2014 ed. [Mīkstie vāki]

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  • Formāts: Paperback / softback, 92 pages, height x width: 235x155 mm, weight: 1708 g, 15 Illustrations, color; 5 Illustrations, black and white; IX, 92 p. 20 illus., 15 illus. in color., 1 Paperback / softback
  • Sērija : SpringerBriefs in Computer Science
  • Izdošanas datums: 21-Jan-2014
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319039423
  • ISBN-13: 9783319039428
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Open Problems in Spectral Dimensionality Reduction 2014 ed.Palielināt
  • Formāts: Paperback / softback, 92 pages, height x width: 235x155 mm, weight: 1708 g, 15 Illustrations, color; 5 Illustrations, black and white; IX, 92 p. 20 illus., 15 illus. in color., 1 Paperback / softback
  • Sērija : SpringerBriefs in Computer Science
  • Izdošanas datums: 21-Jan-2014
  • Izdevniecība: Springer International Publishing AG
  • ISBN-10: 3319039423
  • ISBN-13: 9783319039428
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9783319039428.html
Keywords:
The last few years have seen a great increase in the amount of data available to scientists, yet many of the techniques used to analyse this data cannot cope with such large datasets. Therefore, strategies need to be employed as a pre-processing step to reduce the number of objects or measurements whilst retaining important information. Spectral dimensionality reduction is one such tool for the data processing pipeline. Numerous algorithms and improvements have been proposed for the purpose of performing spectral dimensionality reduction, yet there is still no gold standard technique. This book provides a survey and reference aimed at advanced undergraduate and postgraduate students as well as researchers, scientists, and engineers in a wide range of disciplines. Dimensionality reduction has proven useful in a wide range of problem domains and so this book will be applicable to anyone with a solid grounding in statistics and computer science seeking to apply spectral dimensionalit

y to their work.

IntroductionSpectral Dimensionality ReductionModelling the ManifoldIntrinsic DimensionalityIncorporating New PointsLarge Scale DataPostcript
1 Introduction
1(6)
1.1 Goals of the Book
2(1)
1.2 Relation to Existing Work
3(1)
1.3 Outline
4(3)
References
4(3)
2 Spectral Dimensionality Reduction
7(16)
2.1 A General Setting for Spectral Dimensionality Reduction
7(2)
2.2 Linear Spectral Dimensionality Reduction
9(2)
2.2.1 Principal Components Analysis (PCA)
9(1)
2.2.2 Classical Multidimensional Scaling (MDS)
10(1)
2.3 Nonlinear Spectral Dimensionality Reduction
11(9)
2.3.1 Isomap
12(1)
2.3.2 Maximum Variance Unfolding (MVU)
13(1)
2.3.3 Diffusion Maps
14(2)
2.3.4 Locally Linear Embedding (LLE)
16(1)
2.3.5 Laplacian Eigenmaps
17(2)
2.3.6 Local Tangent Space Alignment (LTSA)
19(1)
2.4 Kernel Formulation
20(1)
2.5 Summary
21(2)
References
21(2)
3 Modelling the Manifold
23(18)
3.1 Overview of Neighbourhood Graph Construction
24(1)
3.2 Building Neighbourhood Graphs
25(5)
3.2.1 Optimised Neighbourhood Methods
26(2)
3.2.2 Adaptive Estimation Methods
28(2)
3.3 Topological and Multi-manifold Considerations
30(4)
3.3.1 Manifolds with Loops
31(1)
3.3.2 Multiple Manifolds
32(2)
3.4 Noise and Outliers
34(4)
3.4.1 Pre-processing Methods
35(1)
3.4.2 Noise Handling Extensions
36(2)
3.5 Summary
38(3)
References
38(3)
4 Intrinsic Dimensionality
41(12)
4.1 Background
41(1)
4.2 Estimating Dimensionality: The Spectral Gap
42(2)
4.3 Estimating Dimensionality: Other Methods
44(5)
4.3.1 Global Estimators
44(3)
4.3.2 Local Estimators
47(2)
4.4 Choosing Techniques and Limitations
49(1)
4.5 Summary
50(3)
References
51(2)
5 Incorporating New Points
53(16)
5.1 Natural Incorporation
53(1)
5.2 Out-of-Sample Extensions
54(6)
5.2.1 The Nystrom Method
55(2)
5.2.2 Generalised
57(2)
5.2.3 Common Problems
59(1)
5.3 Pre-image
60(1)
5.4 Incremental Learning
61(5)
5.4.1 Incremental PCA
62(1)
5.4.2 Incremental Isomap
62(2)
5.4.3 Incremental LLE
64(1)
5.4.4 Incremental Laplacian Eigenmaps
64(1)
5.4.5 A Unified Framework
65(1)
5.5 Summary
66(3)
References
67(2)
6 Large Scale Data
69(14)
6.1 Computational Complexity and Bottlenecks
69(4)
6.1.1 Complexity of Spectral Dimensionality Reduction Algorithms
70(3)
6.1.2 Common Bottlenecks
73(1)
6.2 The Nystrom Method
73(2)
6.2.1 Sampling Methods
74(1)
6.3 Other Approximation Methods
75(3)
6.3.1 Isomap Variants
75(1)
6.3.2 Laplacian Eigenmap Variants
76(1)
6.3.3 Maximum Variance Unfolding Variants
77(1)
6.3.4 Diffusion Maps Variants
77(1)
6.4 Using Brute Force: GPU and Parallel Implementations
78(1)
6.5 Summary
79(4)
References
79(4)
7 Postscript
83(8)
7.1 Digging Deeper: How do You Measure Success?
83(2)
7.2 Beyond Spectral Dimensionality Reduction
85(1)
7.2.1 Manifold Learning and ANNs
85(1)
7.2.2 Beyond Dimensionality Reduction
85(1)
7.3 Implementations
86(1)
7.4 Conclusions
87(1)
7.5 Future Paths
88(1)
7.6 Summary
88(3)
References
89(2)
Index 91