EPSRC Winter School in Mathematics for Data Modelling

Dimensionality Reduction

author: Neil Lawrence, University of Manchester

Description

This presentation discusses methods for dimensionality reduction.

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*Slides*
0:00	Dimensionality Reduction
1:11	Outline
1:43	Online Resources
2:21	- Motivation
2:22	High Dimensional Data - 1
3:16	High Dimensional Data - 2
3:22	High Dimensional Data - 1
3:26	High Dimensional Data - 2
3:30	High Dimensional Data - 3
4:12	High Dimensional Data - 4
4:19	Simple Model of Digit - 1
4:32	Simple Model of Digit - 2
4:34	Simple Model of Digit - 3
4:35	Simple Model of Digit - 4
4:36	Simple Model of Digit - 5
4:37	Simple Model of Digit - 6
4:38	Simple Model of Digit - 7
4:38	Simple Model of Digit - 8
4:39	Simple Model of Digit - 9
4:39	MATLAB Demo - 1
4:43	MATLAB Demo - 2
5:55	Simple Model of Digit - 9
5:56	Simple Model of Digit - 8
5:57	Simple Model of Digit - 9
5:58	Simple Model of Digit - 8
6:00	Simple Model of Digit - 9
6:10	Simple Model of Digit - 8
6:10	Simple Model of Digit - 9
6:12	MATLAB Demo - 2
6:36	MATLAB Demo - 3
7:16	Low Dimensional Manifolds
9:14	- Background
9:16	Notation
11:12	MATLAB Demo - 3
11:21	Notation
11:22	Reading Notation
12:36	- Distance Matching
12:47	Data Representation
13:41	Interpoint Distances for Rotated Sixes
16:00	Multidimensional Scaling
18:16	Feature Selection - 1
20:01	Feature Selection Derivation
22:11	Feature Selection Derivation II
23:07	Feature Selection Derivation III
25:43	Feature Selection - 1
25:45	Reconstruction from Latent Space - 1
26:18	Interpoint Distances for Rotated Sixes
26:20	Reconstruction from Latent Space - 1
26:43	Reconstruction from Latent Space - 2
27:33	Feature Selection - 2
28:18	Feature Selection - 2
28:25	Feature Selection - 3
28:27	Feature Selection - 2
28:30	Feature Selection - 3
28:32	Feature Selection - 2
28:33	Feature Selection - 3
28:36	Feature Extraction - 1
29:04	Feature Extraction - 2
29:05	Feature Extraction - 3
29:07	Feature Extraction - 4
29:10	Feature Extraction - 5
29:21	Feature Selection - 2
29:39	Feature Extraction - 1
29:40	Feature Extraction - 2
29:40	Feature Extraction - 3
29:41	Feature Extraction - 4
29:42	Feature Extraction - 5
29:43	Feature Extraction - 6
29:46	Feature Extraction - 7
29:58	Which Rotation?
30:31	Rotation Reconstruction from Latent Space - 1
30:33	Which Rotation?
30:45	Rotation Reconstruction from Latent Space - 1
31:05	Reconstruction from Latent Space - 1
31:11	Rotation Reconstruction from Latent Space - 1
31:39	Rotation Reconstruction from Latent Space - 2
31:49	Rotation Reconstruction from Latent Space - 1
31:53	Rotation Reconstruction from Latent Space - 2
32:25	Reminder: Principal Component Analysis
32:57	Principal Component Analysis
34:52	Lagrangian
36:00	Lagrange Multiplier
36:31	Lagrangian
36:35	Lagrange Multiplier
36:44	Principal Component Analysis
36:48	Lagrange Multiplier
36:52	Lagrangian
37:00	Lagrange Multiplier
37:19	Further Directions
38:32	Further Eigenvectors
39:42	Principal Coordinates Analysis
40:35	Feature Extraction - 7
40:38	Feature Selection - 1
41:39	Principal Coordinates Analysis
43:23	An Alternative Formalism - 1
44:35	An Alternative Formalism - 2
44:45	An Alternative Formalism - 1
44:47	An Alternative Formalism - 2
44:51	An Alternative Formalism - 3
44:54	An Alternative Formalism - 2
44:58	An Alternative Formalism - 3
45:34	Uq Diagonalizes the Inner Product Matrix - 1
45:58	Uq Diagonalizes the Inner Product Matrix - 2
46:17	Uq Diagonalizes the Inner Product Matrix - 3
46:32	Uq Diagonalizes the Inner Product Matrix - 4
46:54	Uq Diagonalizes the Inner Product Matrix - 5
47:01	Uq Diagonalizes the Inner Product Matrix - 6
47:31	Uq Diagonalizes the Inner Product Matrix - 7
47:42	Uq Diagonalizes the Inner Product Matrix - 8
47:53	Uq Diagonalizes the Inner Product Matrix - 9
47:54	Uq Diagonalizes the Inner Product Matrix - 10
47:56	Uq Diagonalizes the Inner Product Matrix - 11
47:59	Uq Diagonalizes the Inner Product Matrix - 12
48:26	Uq Diagonalizes the Inner Product Matrix - 13
48:27	Equivalent Eigenvalue Problems
49:37	The Covariance Interpretation

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