manifold learning dimensionality reduction. outline introduction dim. reduction manifold isomap...
TRANSCRIPT
![Page 1: Manifold Learning Dimensionality Reduction. Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649ccf5503460f9499b616/html5/thumbnails/1.jpg)
Manifold LearningDimensionality Reduction
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Outline
Introduction Dim. Reduction Manifold
Isomap Overall procedure Approximating geodesic dist. Dijkstra’s algorithm
Reference
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Introduction (dim. reduction)
DimensionalityReduction
LinearPCAMDS
Non-linearIsomap(2000)
LLE(2000)SDE(2005)
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Introduction (dim. reduction)
Principal Component Analysis
x∑
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Introduction (dim. reduction)
DimensionalityReduction
LinearPCAMDS
Non-linearIsomap(2000)
LLE(2000)SDE(2005)
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Introduction (dim. reduction)
Multidimensional Scaling
ChicagoRaleigh
Boston Seattle S.F. Austin Orlando
Chicago 0
Raleigh 641 0
Boston 851 608 0
Seattle 1733 2363 2488 0
S.F. 1855 2406 2696 684 0
Austin 972 1167 1691 1764 1495 0
Orlando 994 520 1105 2565 2458 1015 0
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Introduction (dim. reduction)
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Introduction (dim. reduction)
DimensionalityReduction
LinearPCAMDS
Non-linearIsomap(2000)
LLE(2000)SDE(2005)
![Page 9: Manifold Learning Dimensionality Reduction. Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649ccf5503460f9499b616/html5/thumbnails/9.jpg)
Introduction (manifold)
Linear methods do nothing more than “globally transform”(rotate/translate..) data. Sometimes need to “unwrap” the data first
PCA
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Introduction (dim. reduction)
The task of dimensionality reduction is to find a small number of features to represent a large number of observed dimensions.
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Introduction (manifold)
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Introduction (manifold)
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Outline
Introduction Dim. Reduction Manifold
Isomap Overall procedure Approximating geodesic dist. Dijkstra’s algorithm
Reference
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Isomap (overall procedure)
Compute fully-connected neighborhood of points for each item (k nearest)
Calculate pairwise Euclidean distances within each neighborhood
Use Dijkstra’s Algorithm to compute shortest path from each point to non-neighboring points
Run MDS on resulting distance matrix
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Isomap (Approximating geodesic dist.)
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Isomap (Approximating geodesic dist.)
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Isomap (Approximating geodesic dist.)
is not much bigger than
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Isomap (Approximating geodesic dist.)
is not much bigger than
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Isomap (Approximating geodesic dist.)
is not much bigger than
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Isomap (Approximating geodesic dist.)
is not much bigger than
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Isomap (Approximating geodesic dist.)
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Isomap (Dijkstra’s Algorithm)
Greedy breadth-first algorithm to compute shortest path from one point to all other points
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Isomap (Dijkstra’s Algorithm)
Greedy breadth-first algorithm to compute shortest path from one point to all other points
![Page 24: Manifold Learning Dimensionality Reduction. Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649ccf5503460f9499b616/html5/thumbnails/24.jpg)
Isomap (Dijkstra’s Algorithm)
Greedy breadth-first algorithm to compute shortest path from one point to all other points
![Page 25: Manifold Learning Dimensionality Reduction. Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649ccf5503460f9499b616/html5/thumbnails/25.jpg)
Isomap (Dijkstra’s Algorithm)
Greedy breadth-first algorithm to compute shortest path from one point to all other points
![Page 26: Manifold Learning Dimensionality Reduction. Outline Introduction Dim. Reduction Manifold Isomap Overall procedure Approximating geodesic dist. Dijkstra’s](https://reader036.vdocuments.mx/reader036/viewer/2022062515/56649ccf5503460f9499b616/html5/thumbnails/26.jpg)
Isomap
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Isomap
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Reference
http://www.cs.unc.edu/Courses/comp290-090-s06/
http://www.cse.msu.edu/~lawhiu/manifold/