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## Face recognition using discriminatively trained orthogonal rank one tensor projections (2007)

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### Other Repositories/Bibliography

Venue: | In Proc. CVPR |

Citations: | 15 - 2 self |

### Citations

12873 | Statistical Learning Theory
- Vapnik
- 1998
(Show Context)
Citation Context ...e bias or discriminant ability, is the capacity of an algorithm to represent arbitrary class boundaries. It can be measured, for example, using Fisher’s criterion or the Vapnik-Chervonenkis dimension =-=[13]-=-. Generalization ability is a measure of the expected errors on data outside of the training set. It is most famously measured by classification margin [13]. While tradeoffs of these factors apply in ... |

2251 | Eigenfaces vs. Fisherfaces: recognition using class specific linear projection. TPAMI
- Belhumeur, Hespanha, et al.
- 1997
(Show Context)
Citation Context ...embedding of the original data into a lower dimensional space that preserves discriminant information and discards confounding information. Techniques such as EigenFaces (PCA) [12], FisherFaces (LDA) =-=[1]-=-, local discriminant embedding (LDE) [3], and variants of locality preserving projections (LPP) [8, 2], have proven to be effective to varying degrees. All these techniques must address three challeng... |

1345 |
Face recognition using eigenfaces
- Turk, Pentland
- 1991
(Show Context)
Citation Context ...is to find a projective embedding of the original data into a lower dimensional space that preserves discriminant information and discards confounding information. Techniques such as EigenFaces (PCA) =-=[12]-=-, FisherFaces (LDA) [1], local discriminant embedding (LDE) [3], and variants of locality preserving projections (LPP) [8, 2], have proven to be effective to varying degrees. All these techniques must... |

741 | From few to many: Illumination cone models for face recognition under variable lighting and pose
- Georghiades, Kriegman
- 2001
(Show Context)
Citation Context ...e proposed approach is extensively tested for face recognition on some widely used benchmark data sets such as the CMU PIE database [11], the Yale face database [1], the Extended Yale Face Database B =-=[6]-=- and the Olivetti Research Laboratory (ORL) database [10]. We refer them to be PIE, Yale, YaleB and ORL respectively. On all datasets, the gray-scale face images are cropped and aligned by fixing the ... |

385 | Parameterisation of a Stochastic Model for Human Face Identification
- Samaria, Harter
- 1994
(Show Context)
Citation Context ...nition on some widely used benchmark data sets such as the CMU PIE database [11], the Yale face database [1], the Extended Yale Face Database B [6] and the Olivetti Research Laboratory (ORL) database =-=[10]-=-. We refer them to be PIE, Yale, YaleB and ORL respectively. On all datasets, the gray-scale face images are cropped and aligned by fixing the eye locations, and then resized to 32 × 32 1 . No other p... |

379 | Face recognition using laplacianfaces
- He, Yan, et al.
- 2005
(Show Context)
Citation Context ...on and discards confounding information. Techniques such as EigenFaces (PCA) [12], FisherFaces (LDA) [1], local discriminant embedding (LDE) [3], and variants of locality preserving projections (LPP) =-=[8, 2]-=-, have proven to be effective to varying degrees. All these techniques must address three challenges: high dimensionality, learning capacity, and generalization ability. Learning capacity, sometimes c... |

361 | The CMU pose, illumination, and expression database
- Sim, Baker, et al.
- 2003
(Show Context)
Citation Context ...h varying dimensions, we first sort them according to discriminant power. Fig. 3 displays the discriminant power of the orthogonal rank one projections obtained on a training set from CMU PIE dataset =-=[11]-=-. The red curve shows the unsorted quotients, and the green curve displays the sorted quotients. We perform GLOCAL transform with 4 × 2 blocks to form a tensor of size 8 × 128, allowing a total of 128... |

121 | Orthogonal tensor decompositions
- Kolda
(Show Context)
Citation Context ...h pi is a column vector of dimension mi with the kth element pik, such that y = ∑ ...( ∑ ( ∑ xi0i1...in−1p0i0 )p1i1 ...)pn−1in−1 (1) in−1 i1 i0 The notation can be simplified using the k-mode product =-=[9, 14]-=-, i.e., Definition 2.2 The k-mode product of tensor X ∈ Rm0×...mk...×mn−1 and a matrix (i.e., an order 2 tensor) ′ mk×m B ∈ R k is a X ∈ Rm0×...mk×...×mn−1 → Y ∈ Rm0×...m′ k ×...×mn−1 mapping, i.e., Y... |

85 | Local discriminant embedding and its variants
- Chen, Liu
- 2005
(Show Context)
Citation Context ...wer dimensional space that preserves discriminant information and discards confounding information. Techniques such as EigenFaces (PCA) [12], FisherFaces (LDA) [1], local discriminant embedding (LDE) =-=[3]-=-, and variants of locality preserving projections (LPP) [8, 2], have proven to be effective to varying degrees. All these techniques must address three challenges: high dimensionality, learning capaci... |

80 | Orthogonal Laplacianfaces for face recognition
- Cai, He, et al.
- 2006
(Show Context)
Citation Context ...and OLPP are the best. ORO4×2 outperforms OLPP on Yale and ORL, and achieves equivalent results to that of OLPP on PIE. It is only inferior to OLPP on YaleB. • The locality preserving criterion (LPC) =-=[7, 2]-=-, and the local discriminant criterion(LDC) [3, 4] used in this paper are two criteria for selecting discriminant projections. It has been shown that LDC is superior to unsupervised LPC [3]. Our curre... |

64 | Tensor subspace analysis
- He, Cai, et al.
- 2005
(Show Context)
Citation Context ...y have been discarded. Vector based representations also ignore the spatial structure of image data which may be very useful for visual recognition. An alternative is to regard image data as a tensor =-=[7, 3, 14, 15]-=- (i.e., multiple dimensional arrays). With the tensor representation, discriminant multi-linear projections (e.g., bi-linear projections for 2 dimensional tensor) are pursued to construct the discrimi... |

44 | Optimal transformation for discriminant and principal component analysis - Duchene, Leclercq - 1988 |

9 | Rank-one projections with adaptive margins for face recognition
- Xu, Lin, et al.
- 2007
(Show Context)
Citation Context ...y have been discarded. Vector based representations also ignore the spatial structure of image data which may be very useful for visual recognition. An alternative is to regard image data as a tensor =-=[7, 3, 14, 15]-=- (i.e., multiple dimensional arrays). With the tensor representation, discriminant multi-linear projections (e.g., bi-linear projections for 2 dimensional tensor) are pursued to construct the discrimi... |

6 | Learning Effective Image Metrics from Few Pairwise Examples
- Chen, Liu, et al.
- 2005
(Show Context)
Citation Context .... In this new transformed space, our approach can now find a maximum of m ′ rank one projections. In this paper we explore second order tensors, in particular we use the GLOCAL transform motivated by =-=[4]-=-. The GLOCAL transform partitions a tensor of size m0 × non-overlapping blocks of size m1 into m ′ 1 = m0×m1 l0×l1 l0 × l1. The blocks are ordered by a raster scan. Each block i is then itself raster ... |

4 |
Coupled kernel-based subspace learning
- Yan, Xu, et al.
(Show Context)
Citation Context ...or LPP, 2DLDE and OLPP. Future work includes testing the proposed approach on higher order (≥ 3) tensor data, exploiting adaptive margins [14], and exploring nonlinear projections using kernel tricks =-=[15]-=-. We also plan to investigate both theoretically and empirically to better understand the pros and cons of the two discriminative criteria, supervised LPC and LDC, for the task of visual recognition. ... |