21 research outputs found
Graph Scaling Cut with L1-Norm for Classification of Hyperspectral Images
In this paper, we propose an L1 normalized graph based dimensionality
reduction method for Hyperspectral images, called as L1-Scaling Cut (L1-SC).
The underlying idea of this method is to generate the optimal projection matrix
by retaining the original distribution of the data. Though L2-norm is generally
preferred for computation, it is sensitive to noise and outliers. However,
L1-norm is robust to them. Therefore, we obtain the optimal projection matrix
by maximizing the ratio of between-class dispersion to within-class dispersion
using L1-norm. Furthermore, an iterative algorithm is described to solve the
optimization problem. The experimental results of the HSI classification
confirm the effectiveness of the proposed L1-SC method on both noisy and
noiseless data.Comment: European Signal Processing Conference 201
Discriminant Analysis via Joint Euler Transform and ℓ2, 1-Norm
Linear discriminant analysis (LDA) has been widely used for face recognition. However, when identifying faces in the wild, the existence of outliers that deviate significantly from the rest of the data can arbitrarily skew the desired solution. This usually deteriorates LDA’s performance dramatically, thus preventing it from mass deployment in real-world applications. To handle this problem, we propose an effective distance metric learning method-based LDA, namely, Euler LDA-L21 (e-LDA-L21). e-LDA-L21 is carried out in two stages, in which each image is mapped into a complex space by Euler transform in the first stage and the ℓ2,1 -norm is adopted as the distance metric in the second stage. This not only reveals nonlinear features but also exploits the geometric structure of data. To solve e-LDA-L21 efficiently, we propose an iterative algorithm, which is a closed-form solution at each iteration with convergence guaranteed. Finally, we extend e-LDA-L21 to Euler 2DLDA-L21 (e-2DLDA-L21) which further exploits the spatial information embedded in image pixels. Experimental results on several face databases demonstrate its superiority over the state-of-the-art algorithms
Semi-supervised tensor-based graph embedding learning and its application to visual discriminant tracking
An appearance model adaptable to changes in object appearance is critical in visual object tracking. In
this paper, we treat an image patch as a 2-order tensor which preserves the original image structure. We design
two graphs for characterizing the intrinsic local geometrical structure of the tensor samples of the object and the
background. Graph embedding is used to reduce the dimensions of the tensors while preserving the structure of
the graphs. Then, a discriminant embedding space is constructed. We prove two propositions for finding the
transformation matrices which are used to map the original tensor samples to the tensor-based graph embedding
space. In order to encode more discriminant information in the embedding space, we propose a transfer-learningbased
semi-supervised strategy to iteratively adjust the embedding space into which discriminative information
obtained from earlier times is transferred. We apply the proposed semi-supervised tensor-based graph
embedding learning algorithm to visual tracking. The new tracking algorithm captures an object’s appearance
characteristics during tracking and uses a particle filter to estimate the optimal object state. Experimental results
on the CVPR 2013 benchmark dataset demonstrate the effectiveness of the proposed tracking algorithm
Linear discriminant analysis using rotational invariant L-1 norm
Linear discriminant analysis (LDA) is a well-known scheme for supervised subspace learning. It has been widely used in the applications of computer vision and pattern recognition. However, an intrinsic limitation of LDA is the sensitivity to the presence of outliers, due to using the Frobenius norm to measure the inter-class and intra-class distances. In this paper, we propose a novel rotational invariant L-1 norm (i.e., R-1 norm) based discriminant criterion (referred to as DCL1), which better characterizes the intra-class compactness and the inter-class separability by using the rotational invariant L-1 norm instead of the Frobenius norm. Based on the DCL1, three subspace learning algorithms (i.e., 1DL(1), 2DL(1), and TDL1) are developed for vector-based, matrix-based, and tensor-based representations of data, respectively. They are capable of reducing the influence of outliers substantially, resulting in a robust classification. Theoretical analysis and experimental evaluations demonstrate the promise and effectiveness of the proposed DCL1 and its algorithms. (C) 2010 Elsevier B.V. All rights reserved
Regularized Bilinear Discriminant Analysis for Multivariate Time Series Data
In recent years, the methods on matrix-based or bilinear discriminant
analysis (BLDA) have received much attention. Despite their advantages, it has
been reported that the traditional vector-based regularized LDA (RLDA) is still
quite competitive and could outperform BLDA on some benchmark datasets.
Nevertheless, it is also noted that this finding is mainly limited to image
data. In this paper, we propose regularized BLDA (RBLDA) and further explore
the comparison between RLDA and RBLDA on another type of matrix data, namely
multivariate time series (MTS). Unlike image data, MTS typically consists of
multiple variables measured at different time points. Although many methods for
MTS data classification exist within the literature, there is relatively little
work in exploring the matrix data structure of MTS data. Moreover, the existing
BLDA can not be performed when one of its within-class matrices is singular. To
address the two problems, we propose RBLDA for MTS data classification, where
each of the two within-class matrices is regularized via one parameter. We
develop an efficient implementation of RBLDA and an efficient model selection
algorithm with which the cross validation procedure for RBLDA can be performed
efficiently. Experiments on a number of real MTS data sets are conducted to
evaluate the proposed algorithm and compare RBLDA with several closely related
methods, including RLDA and BLDA. The results reveal that RBLDA achieves the
best overall recognition performance and the proposed model selection algorithm
is efficient; Moreover, RBLDA can produce better visualization of MTS data than
RLDA.Comment: 14 pages, 2 figure