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## Face Video Retrieval with Image Query via Hashing across Euclidean Space and Riemannian Manifold

### Citations

1025 | Approximate nearest neighbors: Towards removing the curse of dimensionality
- Indyk, Motwani
- 1998
(Show Context)
Citation Context ...cted to have potential application in more general object retrieval tasks. 2.2. Single Modality Hash Learning The pioneering hash learning method, i.e., the wellknown Locality Sensitive Hashing (LSH) =-=[19]-=-, is based on random projections. Although the asymptotic property is theoretically guaranteed, as a data-independent method, LSH still requires long codes to achieve satisfactory precision in practic... |

353 | Canonical correlation analysis: An overview with application to learning methods
- Hardoon, Szedmak, et al.
(Show Context)
Citation Context ...space. 4.2. Hash Learning Architecture As xi and Yi are heterogeneous, it is not trivial to embed them into a common Hamming space directly. To this end, we devise a two-step architecture inspired by =-=[16]-=- [18] to fill the heterogeneous gap and accomplish the common embedding (see Fig. 2). Specifically, in the first step, on the Riemannian manifold side, we propose to map the Riemannian manifold Sym+d ... |

335 | Generalized discriminant analysis using a kernel approach
- Baudat, Anouar
- 2000
(Show Context)
Citation Context ...he aforementioned two mappings, i.e., ϕ(xi) : R d →He, and η(Yi) : Sym + d →Hr, are usually implicit in practice. Hence, taking the Euclidean space mapping ϕ(·) as an example, we use the kernel trick =-=[4]-=- by expressing the weight vector wke as a linear combination of all the training samples in the mapped Hilbert space He as wke = N ∑ i=1 ukie ϕ(xi), (6) where ukie is the i th expansion coefficient. T... |

296 | Convergence of a block coordinate descent method for nondifferentiable minimization
- Tseng
(Show Context)
Citation Context ...jective function, here we try to seek a local optima to obtain good hash codes, which are capable of yielding desirable results. In particular, we exploit an iterative block coordinate descent method =-=[34]-=- to go down the objective function. The whole optimization procedure is formulated in Algorithm 1. Here we describe it step by step. First of all (line 1), the aforementioned two mappings, i.e., ϕ(xi)... |

283 | Spectral hashing
- Weiss, Torralba, et al.
- 2008
(Show Context)
Citation Context ...formation to achieve compact hash codes for specific datasets. This new direction is referred to as Hash Function Learning (HFL). Representative unsupervised HFL methods include Spectral Hashing (SH) =-=[41]-=-, Anchor Graph Hashing (AGH) [24], Iterative Quantization hashing (ITQ) [12], etc. More recently, semi-supervised and supervised HFL methods are gradually coming into view, such as Semi-Supervised Has... |

258 | Random features for large-scale kernel machines
- Rahimi, Recht
- 2007
(Show Context)
Citation Context ...ethods often scale imperfectly with large data size. Fortunately, a series of mathematically principled solutions, e.g., linear random projections [1], low-rank approximation [9], and random features =-=[28]-=-, have been well established that are just tailored to the further need of scalability. Moreover, observed from experimental results in Section 5, only a couple of hundred training samples can achieve... |

188 | On the nyström method for approximating a gram matrix for improved kernel-based learning
- Drineas, Mahoney
(Show Context)
Citation Context ...ity: Inevitably, kernel methods often scale imperfectly with large data size. Fortunately, a series of mathematically principled solutions, e.g., linear random projections [1], low-rank approximation =-=[9]-=-, and random features [28], have been well established that are just tailored to the further need of scalability. Moreover, observed from experimental results in Section 5, only a couple of hundred tr... |

170 | Human detection via classification on riemannian manifold. CVPR
- Tuzel, Porikli, et al.
- 2007
(Show Context)
Citation Context ...ifold Sym+d spanned by d× d Symmetric Positive Definite (SPD) matrices. Prior to our study here, covariance matrix has been used to characterize local regions within an image, named region covariance =-=[35]-=-, and apply to tasks like human detection. However, region covariance is computed within a local region for a single image, whereas our video covariance is the statistic among all frames for a whole v... |

164 |
Face recognition using temporal image sequence.
- Yamaguchi, Fukui, et al.
- 1998
(Show Context)
Citation Context ... thousands of frames. Alternatively, a more promising strategy is to model the video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces =-=[42]-=- [21] [40] [38], affine subspace [7] [17], or covariance matrix [39] [25] [36]. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann mani... |

157 | Iterative quantization: A procrustean approach to learning binary codes
- Gong, Lazebnik
- 2011
(Show Context)
Citation Context ...ction is referred to as Hash Function Learning (HFL). Representative unsupervised HFL methods include Spectral Hashing (SH) [41], Anchor Graph Hashing (AGH) [24], Iterative Quantization hashing (ITQ) =-=[12]-=-, etc. More recently, semi-supervised and supervised HFL methods are gradually coming into view, such as Semi-Supervised Hashing (SSH) [37], Kernel-based Supervised Hashing (KSH) [23], Discriminative ... |

130 | Discriminative learning and recognition of image set classes using canonical correlations
- Kim, Kittler, et al.
(Show Context)
Citation Context ...sands of frames. Alternatively, a more promising strategy is to model the video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces [42] =-=[21]-=- [40] [38], affine subspace [7] [17], or covariance matrix [39] [25] [36]. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann manifold ... |

108 | Hashing with graphs.
- Liu, Wang, et al.
- 2011
(Show Context)
Citation Context ... codes for specific datasets. This new direction is referred to as Hash Function Learning (HFL). Representative unsupervised HFL methods include Spectral Hashing (SH) [41], Anchor Graph Hashing (AGH) =-=[24]-=-, Iterative Quantization hashing (ITQ) [12], etc. More recently, semi-supervised and supervised HFL methods are gradually coming into view, such as Semi-Supervised Hashing (SSH) [37], Kernel-based Sup... |

107 | Histograms of oriented optical flow and binet-cauchy kernels on nonlinear dynamical systems for the recognition of human actions,”
- Chaudhry, Ravichandran, et al.
- 2009
(Show Context)
Citation Context ...designed for Hilbert space with manifold valued data; 2) as evidenced by the theory of kernel methods in Euclidean space, it yields a much richer representation of the original data distribution [13] =-=[8]-=- [14] [39] [36] [20] [15]. On the Euclidean space side, we can also map the Euclidean space Rd to another RKHS He via ϕ(xi) : R d →He without loss of generality. After the first-step mappings, gap bet... |

92 | Person spotting: video shot retrieval for face sets.
- Sivic, Everingham, et al.
- 2005
(Show Context)
Citation Context ... the video player can jump to the next shot containing a specific character; retrieving all the shots containing a particular family member from thousands of short videos captured by a digital camera =-=[33]-=-; and rapid locating and tracking suspects from masses of city surveillance videos (e.g., Boston marathon bombings event). For more intuitive understanding, we show a conceptual sample of TV-Series ch... |

91 | Semi-supervised hashing for scalable image retrieval.
- Wang, Kumar, et al.
- 2010
(Show Context)
Citation Context ...d LSH [19] 0.2086 0.2092 0.1963 0.1994 0.1508 0.1517 0.1568 0.1578 SH [41] 0.2652 0.2665 0.2623 0.2673 0.2046 0.2237 0.2177 0.2222 ITQ [12] 0.3025 0.2989 0.3029 0.3060 0.1848 0.1972 0.2265 0.2457 SSH =-=[37]-=- 0.2855 0.2662 0.2584 0.2586 0.2193 0.2202 0.2141 0.2120 DBC [30] 0.4495 0.4235 0.4005 0.3867 0.3858 0.4460 0.4707 0.4547 KSH [23] 0.4366 0.4454 0.4567 0.4604 0.3542 0.4149 0.4385 0.4517 SITQ [12] 0.3... |

84 | Supervised hashing with kernels.
- Liu, Wang, et al.
- 2012
(Show Context)
Citation Context ...on hashing (ITQ) [12], etc. More recently, semi-supervised and supervised HFL methods are gradually coming into view, such as Semi-Supervised Hashing (SSH) [37], Kernel-based Supervised Hashing (KSH) =-=[23]-=-, Discriminative Binary Codes (DBC) [30], and Supervised Iterative Quantization hashing (SITQ) [12], etc. These supervised paradigms move us toward higher performance in practical applications, such a... |

77 | Automatic face recognition for film character retrieval in feature-length films
- Arandjelović, Zisserman
- 2005
(Show Context)
Citation Context ...duce the relevant single modality and multiple modalities hash learning methods, respectively. 2.1. Face Video Retrieval Recent years have witnessed more and more studies on face video retrieval [33] =-=[2]-=- [3] [10] [31]. Arandjelović and Zisserman [2] [3] built an end-to-end system to retrieve film shots, given one or more query face images. They proposed to obtain an identity preserving and variation... |

76 | Face Recognition Based on Image Sets.
- Cevikalp, Triggs
- 2010
(Show Context)
Citation Context ...a more promising strategy is to model the video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces [42] [21] [40] [38], affine subspace =-=[7]-=- [17], or covariance matrix [39] [25] [36]. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann manifold and Symmetric Positive Definite... |

75 | Manifold-Manifold Distance with Application to Face Recognition Based on Image Set,‖ - Wang, Shan, et al. - 2008 |

74 | Grassmann discriminant analysis: A unifying view on subspace-based learning
- Hamm, Lee
- 2008
(Show Context)
Citation Context ...thms designed for Hilbert space with manifold valued data; 2) as evidenced by the theory of kernel methods in Euclidean space, it yields a much richer representation of the original data distribution =-=[13]-=- [8] [14] [39] [36] [20] [15]. On the Euclidean space side, we can also map the Euclidean space Rd to another RKHS He via ϕ(xi) : R d →He without loss of generality. After the first-step mappings, gap... |

64 | Sampling techniques for kernel methods
- Achlioptas, McSherry, et al.
- 2001
(Show Context)
Citation Context ...y material). Kernel Scalability: Inevitably, kernel methods often scale imperfectly with large data size. Fortunately, a series of mathematically principled solutions, e.g., linear random projections =-=[1]-=-, low-rank approximation [9], and random features [28], have been well established that are just tailored to the further need of scalability. Moreover, observed from experimental results in Section 5,... |

50 | Manifold Discriminant Analysis‖.
- Wang, Chen
- 2009
(Show Context)
Citation Context ...rames. Alternatively, a more promising strategy is to model the video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces [42] [21] [40] =-=[38]-=-, affine subspace [7] [17], or covariance matrix [39] [25] [36]. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann manifold and Symmet... |

45 |
Covariance discriminative learning: A natural and efficient approach to image set classification.
- Wang, Guo, et al.
- 2012
(Show Context)
Citation Context ... model the video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces [42] [21] [40] [38], affine subspace [7] [17], or covariance matrix =-=[39]-=- [25] [36]. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann manifold and Symmetric Positive Definite (SPD) matrix manifold, respecti... |

42 | Sparse Approximated Nearest Points for Image Set Classification
- Hu, Mian, et al.
- 2011
(Show Context)
Citation Context ...re promising strategy is to model the video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces [42] [21] [40] [38], affine subspace [7] =-=[17]-=-, or covariance matrix [39] [25] [36]. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann manifold and Symmetric Positive Definite (SPD... |

41 | Data fusion through cross-modality metric learning using similarity-sensitive hashing,” in CVPR,
- Bronstein, Bronstein, et al.
- 2010
(Show Context)
Citation Context ...uclidean space v.s. Riemannian manifold. To our best knowledge, off-the-shelf hash learning methods fail to work in this case. Hashing methods even specifically dealing with multiple modalities cases =-=[6]-=- [22] [43] [29] [44] [26] also can only handle the case where different modalities are all represented in Euclidean spaces (See Fig. 2), but not the case addressed in this paper. To break the above li... |

41 |
Generalized multiview analysis: A discriminative latent space
- Sharma, Kumar, et al.
- 2012
(Show Context)
Citation Context ...y reasonable explicit or implicit kernel for both spaces. After the computation of two kernel matrices, i.e., Ke and Kr, we use Kernelized Generalized Multiview Marginal 4762 Fisher Analysis (KGMMFA) =-=[32]-=- or Kernelized Canonical Correlation Analysis (KCCA) [16] to embed the two Hilbert spaces (i.e.,He andHr) into a common Euclidean space for hash codes initialization (line 2∼line 4). After the initial... |

39 | Attribute discovery via predictable discriminative binary codes. - Rastegari, Farhadi, et al. - 2012 |

37 |
Graph embedding discriminant analysis on Grassmannian manifolds for improved image set matching. In: Computer Vision and Pattern Recognition.
- Harandi, Shirazi, et al.
- 2011
(Show Context)
Citation Context ...gned for Hilbert space with manifold valued data; 2) as evidenced by the theory of kernel methods in Euclidean space, it yields a much richer representation of the original data distribution [13] [8] =-=[14]-=- [39] [36] [20] [15]. On the Euclidean space side, we can also map the Euclidean space Rd to another RKHS He via ϕ(xi) : R d →He without loss of generality. After the first-step mappings, gap between ... |

33 | Transfer learning in sign language
- Farhadi, Forsyth, et al.
- 2007
(Show Context)
Citation Context ...ne each hash function (i.e., each bit) as a split in the Hilbert space, we want the splits to be as stable as possible. Intuitively, a split is stable when it has large margins from samples around it =-=[11]-=-. Think about such a disillusionary situation where a split crosses an area with dense samples, many actually neighboring samples will be inevitably assigned different hash values. In a nutshell, simi... |

32 | Kernel methods on the Riemannian manifold of symmetric positive definite matrices.
- Jayasumana, Hartley, et al.
- 2013
(Show Context)
Citation Context ...t space with manifold valued data; 2) as evidenced by the theory of kernel methods in Euclidean space, it yields a much richer representation of the original data distribution [13] [8] [14] [39] [36] =-=[20]-=- [15]. On the Euclidean space side, we can also map the Euclidean space Rd to another RKHS He via ϕ(xi) : R d →He without loss of generality. After the first-step mappings, gap between the two origina... |

23 | Learning hash functions for crossview similarity search,”
- Kumar, Udupa
- 2011
(Show Context)
Citation Context ...dean space v.s. Riemannian manifold. To our best knowledge, off-the-shelf hash learning methods fail to work in this case. Hashing methods even specifically dealing with multiple modalities cases [6] =-=[22]-=- [43] [29] [44] [26] also can only handle the case where different modalities are all represented in Euclidean spaces (See Fig. 2), but not the case addressed in this paper. To break the above limitat... |

22 | A probabilistic model for multimodal hash function learning.
- Zhen, Yeung
- 2012
(Show Context)
Citation Context ... Riemannian manifold. To our best knowledge, off-the-shelf hash learning methods fail to work in this case. Hashing methods even specifically dealing with multiple modalities cases [6] [22] [43] [29] =-=[44]-=- [26] also can only handle the case where different modalities are all represented in Euclidean spaces (See Fig. 2), but not the case addressed in this paper. To break the above limitation, this paper... |

17 | Kernel Learning for Extrinsic Classification of Manifold Features
- Vemulapalli, Pillai, et al.
- 2013
(Show Context)
Citation Context ... video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces [42] [21] [40] [38], affine subspace [7] [17], or covariance matrix [39] [25] =-=[36]-=-. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann manifold and Symmetric Positive Definite (SPD) matrix manifold, respectively. Comp... |

16 |
Semisupervised Learning with Constraints for Person Identification in Multimedia Data
- Bäuml, Tapaswi, et al.
- 2013
(Show Context)
Citation Context ...it also contains a sizable number of face close-up shots (an average of 116px face size). We use the extracted face videos represented by block Discrete Cosine Transformation (DCT) feature as used in =-=[5]-=-. More specifically, each face frame is represented with a 240-d DCT feature, and thus forms a 240×240 covariance video representation. Faces are aligned and normalized without special preprocessing, ... |

16 |
Kernel analysis over riemannian manifolds for visual recognition of actions, pedestrians and textures.
- Harandi, Sanderson, et al.
- 2012
(Show Context)
Citation Context ...ce with manifold valued data; 2) as evidenced by the theory of kernel methods in Euclidean space, it yields a much richer representation of the original data distribution [13] [8] [14] [39] [36] [20] =-=[15]-=-. On the Euclidean space side, we can also map the Euclidean space Rd to another RKHS He via ϕ(xi) : R d →He without loss of generality. After the first-step mappings, gap between the two original het... |

15 |
Hello! My name is... Buffy”—automatic naming of characters in TV video
- Everingham, Sivic, et al.
- 2006
(Show Context)
Citation Context ... relevant single modality and multiple modalities hash learning methods, respectively. 2.1. Face Video Retrieval Recent years have witnessed more and more studies on face video retrieval [33] [2] [3] =-=[10]-=- [31]. Arandjelović and Zisserman [2] [3] built an end-to-end system to retrieve film shots, given one or more query face images. They proposed to obtain an identity preserving and variation insensit... |

13 | Image set classification using holistic multiple order statistics features and localized multi-kernel metric learning”, in
- Lu, Wang, et al.
- 2013
(Show Context)
Citation Context ...l the video frames collectively. Recently, promising methods represent all the frames by single or mixture of linear subspaces [42] [21] [40] [38], affine subspace [7] [17], or covariance matrix [39] =-=[25]-=- [36]. These representations all reside on some specific Riemannian manifolds, namely Grassmann manifold, affine Grassmann manifold and Symmetric Positive Definite (SPD) matrix manifold, respectively.... |

10 | Predictable dual-view hashing,”
- Rastegari, Choi, et al.
- 2013
(Show Context)
Citation Context ... v.s. Riemannian manifold. To our best knowledge, off-the-shelf hash learning methods fail to work in this case. Hashing methods even specifically dealing with multiple modalities cases [6] [22] [43] =-=[29]-=- [44] [26] also can only handle the case where different modalities are all represented in Euclidean spaces (See Fig. 2), but not the case addressed in this paper. To break the above limitation, this ... |

8 | Learning euclidean-to-riemannian metric for point-to-set classification
- Huang, Wang, et al.
- 2014
(Show Context)
Citation Context .... 4.2. Hash Learning Architecture As xi and Yi are heterogeneous, it is not trivial to embed them into a common Hamming space directly. To this end, we devise a two-step architecture inspired by [16] =-=[18]-=- to fill the heterogeneous gap and accomplish the common embedding (see Fig. 2). Specifically, in the first step, on the Riemannian manifold side, we propose to map the Riemannian manifold Sym+d into ... |

8 | Face recognition and retrieval in video
- Shan
- 2010
(Show Context)
Citation Context ... method over the state-of-the-art competitive hash learning methods. 1. Introduction Face video retrieval in general is to retrieve video shots containing particular person given one image of him/her =-=[31]-=-. It is an appealing research direction with increasing demands, especially in the era of social networking, when more and more videos are continuously uploaded to the Internet via video blogs, social... |

8 |
Parametric local multimodal hashing for cross-view similarity search
- Zhai, Chang, et al.
- 2013
(Show Context)
Citation Context ...space v.s. Riemannian manifold. To our best knowledge, off-the-shelf hash learning methods fail to work in this case. Hashing methods even specifically dealing with multiple modalities cases [6] [22] =-=[43]-=- [29] [44] [26] also can only handle the case where different modalities are all represented in Euclidean spaces (See Fig. 2), but not the case addressed in this paper. To break the above limitation, ... |

4 | On film character retrieval in feature-length films
- Arandjelović, Zisserman
- 2006
(Show Context)
Citation Context ... the relevant single modality and multiple modalities hash learning methods, respectively. 2.1. Face Video Retrieval Recent years have witnessed more and more studies on face video retrieval [33] [2] =-=[3]-=- [10] [31]. Arandjelović and Zisserman [2] [3] built an end-to-end system to retrieve film shots, given one or more query face images. They proposed to obtain an identity preserving and variation ins... |

4 | Multimodal similarity-preserving hashing
- Masci, Bronstein, et al.
(Show Context)
Citation Context ...annian manifold. To our best knowledge, off-the-shelf hash learning methods fail to work in this case. Hashing methods even specifically dealing with multiple modalities cases [6] [22] [43] [29] [44] =-=[26]-=- also can only handle the case where different modalities are all represented in Euclidean spaces (See Fig. 2), but not the case addressed in this paper. To break the above limitation, this paper prop... |

4 | Domain adaptive classification.
- Mirrashed, Rastegari
- 2013
(Show Context)
Citation Context ...by using Be as training labels to train the Riemannian manifold side SVMs with kernel matrix Kr, and vice versa. This strategy was proven to be effective especially for pairwise training samples [29] =-=[27]-=-. Third, update the current value of B∗ to reflect the hash codes that these SVMs actually yield. Fourth, Be and Br are mixed together to be optimized with Eqn. (5) for promoting the inter-space discr... |