#### DMCA

## Efficient image classification via multiple rank regression (2013)

Venue: | IEEE Transactions on Image Processing |

Citations: | 4 - 2 self |

### Citations

13209 | Statistical Learning Theory
- Vapnik
- 1998
(Show Context)
Citation Context ...oth image processing and machine learning. In the literature, a lot of classification approaches have been proposed, such as K-Nearest Neighborhoods classifier (KNN) [4], Support Vector Machine (SVM) =-=[5]-=- and onedimensional Regression methods (for brief, denoted as 1DREG in the following) [6]. Some of them are similarity based, such as KNN. Some of them are margin based, such as SVM. Among these appro... |

5167 | An introduction to the bootstrap
- Efron, Tibshirani
- 1993
(Show Context)
Citation Context ...h column vector of MRR initialization corresponds to the weight of column vectors of X in following regression, we want these column vectors to be orthogonal. Finally, we use the bootstrap technology =-=[26]-=- to generate each column vector for initialization. More concretely, for each column, we randomly (uniformly) selected several rows, whose values are 1. The others are 0. Different from the above two ... |

1280 | A study of cross-validation and bootstrap for accuracy estimation and model selection
- Kohavi
- 1995
(Show Context)
Citation Context ...regularization. When α is large, we will neglect the requirement of regression. When it is small, the problem of over fitting will appear. In this paper, we determine it by five fold cross validation =-=[28]-=-. The experiments in Section V(E) will show numerical results with different α. See more details there. The second parameter is the rank of regression, i.e., k. Obviously, this parameter balances the ... |

611 |
der Malsburg. Face recognition by elastic bunch graph matching
- Wiskott, Fellous, et al.
- 1997
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Citation Context ...itting problem in regression [6]. To solve these problems, there have been many feature based methods, such as the elastic graph model which can remain spatial information in a compact dimensionality =-=[10]-=-–[12]. Recently, a lot of interests have been conducted on tensor-based approaches for matrix data analysis. Intrinsically, a matrix is a two-order tensor. Vasilescu and Terzopoulos have firstly propo... |

414 | Locality preserving projections.
- He, Niyogi
- 2003
(Show Context)
Citation Context ...hers have also extended a lot of traditional subspace learning methods, such as Principal Component Analysis (PCA) [14], Linear Discriminant Analysis (LDA) [15], Locality Preserving Projections (LPP) =-=[16]-=-, [17], etc, into their tensor counterparts [18]–[23]. Nevertheless, the purpose in designing these approaches is to learn subspaces of original matrix data. For matrix data classification, one possib... |

245 |
Principal Component Analysis, 2nd ed
- JOLLIFFE
- 2002
(Show Context)
Citation Context ...os have firstly proposed a novel tensor face for face recognition [13]. Other researchers have also extended a lot of traditional subspace learning methods, such as Principal Component Analysis (PCA) =-=[14]-=-, Linear Discriminant Analysis (LDA) [15], Locality Preserving Projections (LPP) [16], [17], etc, into their tensor counterparts [18]–[23]. Nevertheless, the purpose in designing these approaches is t... |

167 | High-dimensional data analysis: the curses and blessings of dimensionality. Available at http://wwwstat.stanford.edu/donoho/Lectures
- Donoho
- 2000
(Show Context)
Citation Context ... very high. For example, for a small image of resolution 100 × 100, the reformulated vector is 10 000 dimensional. The performances of these methods will degrade due to the increase of dimensionality =-=[7]-=-. (2) With the increase of dimensionality, the computational time will increase drastically. If the matrix scale is a little larger, traditional approaches can not be implemented in this scenario [8].... |

143 | Automatic classification of single facial images. - Lyons, Budynek, et al. - 1999 |

119 | Multilinear subspace analysis of image ensembles.
- Vasilescu, Terzopoulos
- 2003
(Show Context)
Citation Context ... conducted on tensor-based approaches for matrix data analysis. Intrinsically, a matrix is a two-order tensor. Vasilescu and Terzopoulos have firstly proposed a novel tensor face for face recognition =-=[13]-=-. Other researchers have also extended a lot of traditional subspace learning methods, such as Principal Component Analysis (PCA) [14], Linear Discriminant Analysis (LDA) [15], Locality Preserving Pro... |

106 |
Two-dimensional linear discriminant analysis. In:
- Ye, Janardan, et al.
- 2005
(Show Context)
Citation Context ... in using these methods is projecting matrix data into a subspace at first and then employing another classifier. Besides, among these approaches, Two-dimensional Linear Discriminant Analysis (2DLDA) =-=[19]-=- is a popular supervised tensor based approach. It uses label information 1057–7149/$31.00 © 2012 IEEE HOU et al.: EFFICIENT IMAGE CLASSIFICATION VIA MRR 341 Label Label Left Vectors Right Vectors 1D ... |

65 | Tensor Subspace Analysis". - He, Cai, et al. - 2005 |

53 | Learning a Spatially Smooth Subspace for Face Recognition,
- Cai, He, et al.
- 2007
(Show Context)
Citation Context ...f the matrix scale is a little larger, traditional approaches can not be implemented in this scenario [8]. (3) When a matrix is expanded as a vector, we would lose the correlations of the matrix data =-=[9]-=-. For example, the m × n matrix representation of an image suggests that the real number of freedom is far less than mn, which is revealed by representing an image as a mn-dimensional vector. This wil... |

48 | Multilinear discriminant analysis for face recognition.
- Yan, Xu, et al.
- 2007
(Show Context)
Citation Context ...k regression, tensor analysis. I. INTRODUCTION IMAGE DATA, or more commonly, tensor data, have beenemerged in various applications. For example, in biologic data mining, the data, such as face images =-=[1]-=-, palm images [2], or MRI data [3], are usually represented in the form of data matrices. Additionally, in video data mining, the data in each time frame is also a matrix. How to classify this kind of... |

38 | 2D-LDA: a statistical linear discriminant analysis for image matrix. - Li, Yuan - 2005 |

37 |
A survey of palmprint recognition”,
- Konga, Zhang, et al.
- 2009
(Show Context)
Citation Context ...sor analysis. I. INTRODUCTION IMAGE DATA, or more commonly, tensor data, have beenemerged in various applications. For example, in biologic data mining, the data, such as face images [1], palm images =-=[2]-=-, or MRI data [3], are usually represented in the form of data matrices. Additionally, in video data mining, the data in each time frame is also a matrix. How to classify this kind of data is one of t... |

32 | An efficient algorithm for large-scale discriminant analysis".
- Cai, He, et al.
- 2008
(Show Context)
Citation Context ... D. Parameter Determination There are mainly two important parameters in our MRR algorithm. The first one is regularization parameter α and the second is the rank of regression, i.e., k. As stated in =-=[27]-=-, parameter determination is still an open problem in the related fields. Thus, we determine parameters heuristically and empirically. For the first parameter α, it is used to balance the influence of... |

24 |
Generalized Bilinear Regression.
- Gabriel
- 1998
(Show Context)
Citation Context ... top procedure is traditional regression and the bottom is multiple rank regression. in manipulating matrix data. Moreover, Gabriel et al have analyzed the Generalized Bilinear Regression (GBR) model =-=[24]-=- mathematically. They have not used it in classifying matrix data. When these tensor-based approaches are employed to classify matrix data, their performances can also be improved since (1) Most of th... |

16 |
An Efficient and Effective Dimension Reduction Algorithm and its Theoretical Foundation”, Pattern Recognition,
- Ye, LDAQR
- 2004
(Show Context)
Citation Context ...ace for face recognition [13]. Other researchers have also extended a lot of traditional subspace learning methods, such as Principal Component Analysis (PCA) [14], Linear Discriminant Analysis (LDA) =-=[15]-=-, Locality Preserving Projections (LPP) [16], [17], etc, into their tensor counterparts [18]–[23]. Nevertheless, the purpose in designing these approaches is to learn subspaces of original matrix data... |

7 |
Extracting the optimal dimensionality for local tensor discriminant analysis
- Nie, Xiang, et al.
- 2009
(Show Context)
Citation Context ... learning methods, such as Principal Component Analysis (PCA) [14], Linear Discriminant Analysis (LDA) [15], Locality Preserving Projections (LPP) [16], [17], etc, into their tensor counterparts [18]–=-=[23]-=-. Nevertheless, the purpose in designing these approaches is to learn subspaces of original matrix data. For matrix data classification, one possible way in using these methods is projecting matrix da... |

6 | Enhancing bilinear subspace learning by element rearrangement
- Xu, Yan, et al.
- 1913
(Show Context)
Citation Context ... [7]. (2) With the increase of dimensionality, the computational time will increase drastically. If the matrix scale is a little larger, traditional approaches can not be implemented in this scenario =-=[8]-=-. (3) When a matrix is expanded as a vector, we would lose the correlations of the matrix data [9]. For example, the m × n matrix representation of an image suggests that the real number of freedom is... |

5 |
Discrete wavelet face graph matching
- Ma, Tang
- 2001
(Show Context)
Citation Context ...g problem in regression [6]. To solve these problems, there have been many feature based methods, such as the elastic graph model which can remain spatial information in a compact dimensionality [10]–=-=[12]-=-. Recently, a lot of interests have been conducted on tensor-based approaches for matrix data analysis. Intrinsically, a matrix is a two-order tensor. Vasilescu and Terzopoulos have firstly proposed a... |

4 |
3-D Brain MRI tissue classification on FPGAs
- Koo, Evans, et al.
- 2009
(Show Context)
Citation Context ...INTRODUCTION IMAGE DATA, or more commonly, tensor data, have beenemerged in various applications. For example, in biologic data mining, the data, such as face images [1], palm images [2], or MRI data =-=[3]-=-, are usually represented in the form of data matrices. Additionally, in video data mining, the data in each time frame is also a matrix. How to classify this kind of data is one of the most important... |

2 |
Orthogonal locality minimizing globality maximizing projections for feature extraction
- Nie, Xiang, et al.
- 2009
(Show Context)
Citation Context ...ave also extended a lot of traditional subspace learning methods, such as Principal Component Analysis (PCA) [14], Linear Discriminant Analysis (LDA) [15], Locality Preserving Projections (LPP) [16], =-=[17]-=-, etc, into their tensor counterparts [18]–[23]. Nevertheless, the purpose in designing these approaches is to learn subspaces of original matrix data. For matrix data classification, one possible way... |

1 |
Subspace learning based on tensor analysis,” Dept
- Cai, He, et al.
- 2005
(Show Context)
Citation Context ...space learning methods, such as Principal Component Analysis (PCA) [14], Linear Discriminant Analysis (LDA) [15], Locality Preserving Projections (LPP) [16], [17], etc, into their tensor counterparts =-=[18]-=-–[23]. Nevertheless, the purpose in designing these approaches is to learn subspaces of original matrix data. For matrix data classification, one possible way in using these methods is projecting matr... |

1 |
Efficient regularized least squares classification
- Zhang, Peng
(Show Context)
Citation Context ...ants, denoted as W = [w1, w2, . . . , wc] ∈ Rmn×c and b = [b1, b2, . . . , bc]T . In order to avoid over fitting, we often add a regularizer. The most commonly used one is the Tikhonov regularization =-=[25]-=-. Briefly, the objective function of 1DREG with Tikhonov regularization is L(W, b) = ∑li=1 ‖WT xi + b − yi‖2F + α‖W‖2F (2) where ‖ · ‖F is the Frobenius norm of a matrix. After some simple derivation,... |