Representative Previous Work

1. Representative Previous Work PCA LDA ISOMAP: Geodesic Distance Preserving J. Tenenbaum et al., 2000 LLE: Local Neighborhood Relationship Preserving S. Roweis & L. Saul, 2000 LE/LPP: Local Similarity Preserving, M. Belkin, P. Niyogi et al., 2001, 2003

2. Any common perspective to understand and explain these dimensionality reduction algorithms? Or any unified formulation that is shared by them? Any general tool to guide developing new algorithms for dimensionality reduction? Hundreds Dimensionality Reduction Algorithms Statistics-based Geometry-based … PCA/KPCA ISOMAP LLE LE/LPP … LDA/KDA Matrix Tensor

3. Our Answers Direct Graph Embedding Linearization Kernelization Original PCA & LDA, ISOMAP, LLE, Laplacian Eigenmap PCA, LDA, LPP KPCA, KDA Tensorization Type Formulation CSA, DATER Example S. Yan, D. Xu, H. Zhang and et al., CVPR, 2005, T-PAMI,2007

4. Direct Graph Embedding Intrinsic Graph: S, SP: Similarity matrix (graph edge) Similarity in high dimensional space L, B:Laplacian matrix from S, SP; Data in high-dimensional space and low-dimensional space (assumed as 1D space here): Penalty Graph

5. Direct Graph Embedding -- Continued Intrinsic Graph: S, SP: Similarity matrix (graph edge) L, B:Laplacian matrix from S, SP; Similarity in high dimensional space Data in high-dimensional space and low-dimensional space (assumed as 1D space here): Criterion to Preserve Graph Similarity: Penalty Graph Special case B isIdentity matrix (Scale normalization) Problem: It cannot handle new test data.

6. Linearization Intrinsic Graph Linear mapping function Penalty Graph Objective function in Linearization Problem: linear mapping function is not enough to preserve the real nonlinear structure?

7. Kernelization Intrinsic Graph Nonlinear mapping: the original input space to another higher dimensional Hilbert space. Penalty Graph Constraint: Kernel matrix: Objective function in Kernelization

8. Tensorization Low dimensional representation is obtained as: Intrinsic Graph Penalty Graph Objective function in Tensorization where

9. Common Formulation Intrinsic graph S, SP: Similarity matrix L, B:Laplacian matrix from S, SP; Penalty graph Direct Graph Embedding Linearization Kernelization Tensorization where

10. A General Framework for Dimensionality Reduction D: Direct Graph Embedding L:Linearization K: Kernelization T: Tensorization

11. New Dimensionality Reduction Algorithm: Marginal Fisher Analysis Important Information for face recognition: 1) Label information 2) Local manifold structure (neighborhood or margin) 1: ifxi is among the k1-nearest neighbors of xj in the same class; 0 :otherwise 1: if the pair (i,j) is among the k2 shortest pairs among the data set; 0: otherwise

12. Marginal Fisher Analysis: Advantage No Gaussian distribution assumption

13. Experiments: Face Recognition

14. Summary • Optimization framework that unifies previous dimensionality reduction algorithms as special cases. • A new dimensionality reduction algorithm: Marginal Fisher Analysis.

15. Event Recognition in News Video • Online and offline video search • 56 events are defined in LSCOM Airplane Flying Riot Existing Car Geometric and photometric variances Clutter background Complex camera motion and object motion More diverse !

16. Earth Mover’s Distance in Temporal Domain(T-MM, Under Review) Key Frames of two video clips in class “riot” EMD can efficiently utilize the information from multiple frames.

17. Multi-level Pyramid Matching (CVPR 2007, Under Review) • One Clip = several • subclips (stages of event evolution) . • No prior knowledge about the number of stages in an event, and videos of the same event may include a subset of stage only. Smoke Level-1 Fire Level-1 Level-0 Level-0 Fire Level-1 Smoke Level-1 Solution: Multi-level Pyramid Matching in Temporal Domain

18. Other Publications & Professional Activities Other Publications: • Kernel based Learning: Coupled Kernel-based Subspace Analysis: CVPR 2005 Fisher+Kernel Criterion for Discriminant Analysis: CVPR 2005 • Manifold Learning: Nonlinear Discriminant Analysis on Embedding Manifold : T-CSVT (Accepted) • Face Verification: Face Verification with Balanced Thresholds: T-IP (Accepted) • Multimedia: Insignificant Shadow Detection for Video Segmentation: T-CSVT 2005 Anchorperson extraction for Picture in Picture News Video: PRL 2005 Guest Editor: • Special issue on Video Analysis, Computer Vision and Image Understanding • Special issue on Video-based Object and Event Analysis, Pattern RecognitionLetters Book Editor: • Semantic Mining Technologies for Multimedia Databases Publisher: Idea Group Inc. (www.idea-group.com)

19. Future Work Machine Learning Event Recognition Biometric Computer Vision Pattern Recognition Multimedia Content Analysis Web Search Multimedia

20. Acknowledgement Shuicheng Yan UIUC Steve Lin Microsoft Lei Zhang Microsoft Hong-Jiang Zhang Microsoft Shih-Fu Chang Columbia Xuelong Li UK Xiaoou Tang Hong Kong Zhengkai Liu, USTC

21. Thank You very much!

22. What is Gabor Features? Gabor features can improve recognition performance in comparison to grayscale features. Chengjun Liu T-IP, 2002 Five Scales … Input: Grayscale Image Eight Orientations Output: 40 Gabor-filtered Images Gabor Wavelet Kernels

23. Pixel Rearrangement Pixel Rearrangement Sets of highly correlated pixels Columns of highly correlated pixels How to Utilize More Correlations? Potential Assumption in Previous Tensor-based Subspace Learning: Intra-tensor correlations: Correlations among the features within certain tensor dimensions, such as rows, columns and Gabor features…

24. Tensor Representation: Advantages • Enhanced Learnability • 2. Appreciable reductions in computational costs • 3. Large number of available projection directions • 4. Utilize the structure information

25. Connection to Previous Work –Tensorface (M. Vasilescu and D. Terzopoulos, 2002) From an algorithmic view or mathematics view, CSA and Tensorface are both variants of Rank-(R1,R2,…,Rn) decomposition.