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Multilinear Principal Component Analysis of Tensor Objects for Recognition

Multilinear Principal Component Analysis of Tensor Objects for Recognition. Haiping Lu , K.N. Plataniotis and A.N. Venetsanopoulos The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto. Motivation. Real data in pattern recognition

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Multilinear Principal Component Analysis of Tensor Objects for Recognition

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  1. Multilinear Principal Component Analysis of Tensor Objects for Recognition Haiping Lu, K.N. Plataniotis and A.N. Venetsanopoulos The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto International Conference on Pattern Recognition, Hong Kong, August 2006

  2. Motivation • Real data in pattern recognition • High-dimensional: dimensionality reduction • Multidimensional: tensors • PCA: reshape tensors into vectors • Multilinear algebra • 2DPCA, 3DPCA • Multifactor analysis • Objective: multilinear PCA for tensors International Conference on Pattern Recognition, Hong Kong, August 2006

  3. Overview • MPCA: natural extension of PCA • Multilinear singular value & eigentensor • Input: higher-order tensors • Application: gait recognition • Sample data set: 4th-order tensor • Gait sample: half gait cycle (normalized) • Recognition: outperforms baseline algorithm International Conference on Pattern Recognition, Hong Kong, August 2006

  4. Notations • Vector: lowercase boldface • Matrix: uppercase boldface • Tensor: calligraphic letter • n-mode product: • Scalar product: • Frobenius norm: • n-rank (n-mode vectors): International Conference on Pattern Recognition, Hong Kong, August 2006

  5. Higher-order SVD • Subtensors of the core tensorS • All-orthogonality • Ordered based on • : unitary International Conference on Pattern Recognition, Hong Kong, August 2006

  6. PCA with tensor notation • Basis vectors (PCs): columns of • PCA subspace: truncate  • Projection to feature space: International Conference on Pattern Recognition, Hong Kong, August 2006

  7. Multilinear PCA • Centered input tensor samples: • HOSVD: • Keep columns of  • n-mode singular value: • Basis tensor (eigentensor): • Projection: • MPCA features: International Conference on Pattern Recognition, Hong Kong, August 2006

  8. EigenTensorGait for recognition • Gait sample: half gait cycle (3rd-order) • To obtain samples: partition based on foreground pixels in silhouettes • Noise removal: best rank approximation • Temporal normalization: interpolation • Feature distance: sum of the absolute differences (equivalent to L1 norm) • Sequence matching: sum of min-dist International Conference on Pattern Recognition, Hong Kong, August 2006

  9. Best rank approximation The original silhouettes Best rank-(10,10,3) approximation International Conference on Pattern Recognition, Hong Kong, August 2006

  10. Experiments • Data: USF gait challenge data sets V.1.7 • Different conditions: surface, shoe, view • Sample size: 64x44x20 • Best results: • Performance measure: CMCs • Results: better overall recognition rate compared with baseline algorithm International Conference on Pattern Recognition, Hong Kong, August 2006

  11. Identification performance International Conference on Pattern Recognition, Hong Kong, August 2006

  12. MPCA CMC curves International Conference on Pattern Recognition, Hong Kong, August 2006

  13. Conclusions • MPCA: multilinear extension of PCA • Application of MPCA: EigenTensorGait • Half gait cycles as gait samples • Best rank approximation to reduce noise • Temporal normalization by interpolation • Future works • MPCA to other problems • Other multilinear extensions International Conference on Pattern Recognition, Hong Kong, August 2006

  14. Related work • Haiping Lu, K.N. Plataniotis and A.N. Venetsanopoulos, "Gait Recognition through MPCA plus LDA", in Proc. Biometrics Symposium 2006(BSYM 2006), Baltimore, US, September 2006. International Conference on Pattern Recognition, Hong Kong, August 2006

  15. Contact Information Haiping Lu Email: haiping@dsp.toronto.edu Academic website: http://www.dsp.toronto.edu/~haiping/ International Conference on Pattern Recognition, Hong Kong, August 2006

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