The Bhattacharyya space for feature selection and its application to texture segmentation
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Bhattacharyya distance
Feature vector
Feature (linguistics)
Texture (cosmology)
In this paper, we propose an error estimation method based on the Bhattacharyya distance for multimodal data. First, we try to find the empirical relationship between the classification error and the Bhattacharyya distance. Then, we investigate the possibility to derive the error estimation equation based on the Bhattacharyya distance for multimodal data. We assume that the distribution of multimodal data can be approximated as a mixture of several Gaussian distributions. Experimental results with remotely sensed data showed that there exist strong relationships between the Bhattacharyya distance and the classification error and that it is possible to predict the classification error using the Bhattacharyya distance for multimodal data.
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The Bhattacharyya distance provides valuable information in determining the effectiveness of a feature set and has been used as a separability measure for feature selection. In Lee (1997), it has been shown that it is feasible to predict the classification error accurately using the Bhattacharyya distance. The new formula makes it possible to estimate classification error between two classes within 1-2% margin. In this paper, we propose a new feature extraction method utilizing the result. Initially, we start with an arbitrary feature vector. Assuming that the feature vector is used for classification, we estimate the classification error using the error estimation formula. Then we move the feature vector slightly in the direction so that the estimated classification error is decreased most rapidly. This can be done by taking a gradient. Experiments show that the proposed method compares favorably with the conventional methods.
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Feature vector
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This paper studies statistics based scene change detection in the video streaming scenario,and three scene feature metrics including histogram distance,chi-square distance,and Bhattacharyya distance have been investigated.With the unique characteristics of triangular inequality and non-singularity,Bhattacharyya distance has been proposed as a viable scene change metrics.It outperforms much better than the other two in that it calculates and maximizes the feature vector distance between multi-modal clusters in a hyper-sphere space.The experiments are conducted and the precision recall statistics are compared,and the results support our analysis.
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Feature (linguistics)
Earth mover's distance
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Whenever a feature extracted from an image has a unimodal distribution, information about its covariance matrix can be exploited for content based retrieval using as dissimilarity measure, the Bhattacharyya distance. To reduce the amount of computations and the size of logical database entry, we approximate the Bhattacharyya distance, taking into account that most of the energy in the feature space is often restricted to a low dimensional subspace. The theory was tested for a database of 1188 textures derived from VisTex with the local texture being represented by a 15 dimensional MRSAR feature vector. The retrieval performance improved significantly, relative to the traditional Mahalanobis distance based approach, in spite of using only one or two dimensions in the approximation.
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Mahalanobis distance
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Feature (linguistics)
Rank (graph theory)
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Combined with the advantages of principal components analysis(PCA) and linear discriminant analysis(LDA),PCA-LDA on gender classification is presented.Feature sub-space of training samples is obtained by way of PCA,and feature sub-space from LDA is calculated on the basis of PCA.In the meanwhile,the two feature sub-spaces from PCA and LDA are fused,and the fusion feature space is acquired.After training samples and test samples are respectively projected towards the fusion feature space,recognition features are accordingly gained.Nearest neighbor rule is utilized in gender classification.Experimental results on ORL face database show that PCA-LDA is better than PCA in recognition performance,and is a valid method in gender classification.
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In pattern classification, the Bhattacharyya distance has been used as a class separability measure. Furthemore, it is recently reported that the Bhattacharyya distance can be used to estimate error of Gaussian ML classifier within 1-2% margin. In this paper, we propose a feature extraction method utilizing the Bhattacharyya distance. In the proposed method, we first predict the classification error with the error estimation equation based on the Bhauacharyya distance. Then we find the feature vector that minimizes the classification error using two search algorithms: sequential search and global search. Experimental reslts show that the proposed method compares favorably with conventional feature extraction methods. In addition, it is possible to determine how man, feature vectors arc needed for achieving the same classification accuracy as in the original space.
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A relationship between the probability of misrecognition and the expected Bhattacharyya distance is examined, and it is shown that the maximization of the mean Bhattacharyya distance minimizes an upper bound on the error probability.
Bhattacharyya distance
Probability of error
Maximization
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This paper studies statistics based scene change detection in the video streaming scenario, and three scene feature metrics including histogram distance, chi-square distance, and Bhattacharyya distance have been investigated. With the unique characteristics of triangular inequality and non-singularity, Bhattacharyya distance has been proposed as a viable scene change metrics. It outperforms much better than the other two in that it calculates and maximizes the feature vector distance between multi-modal clusters in a hyper-sphere space. The experiments are conducted and the precision recall statistics are compared, and the results support our analysis.
Bhattacharyya distance
Feature vector
Feature (linguistics)
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Bhattacharyya distance
Feature (linguistics)
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A clustering algorithm for Gaussian Probability Distribution Function (GPDF) data called Centroid Neural Network with a Bhattacharyya Kernel (BK-CNN) is proposed in this paper. The proposed BK-CNN is based on the unsupervised competitive Centroid Neural Network (CNN) and employs a kernel method for data projection. The kernel method adopted in the proposed BK-CNN is used to project data from the low dimensional input feature space into higher dimensional feature space so as the nonlinear problems associated with input space can be solved linearly in the feature space. In order to cluster the GPDF data, the Bhattacharyya kernel is used to measure the distance between two probability distributions for data projection. With the incorporation of the kernel method, the proposed BK-CNN is capable of dealing with nonlinear separation boundaries and can successfully allocate more code vector in the region that GPDF data are densely distributed. When applied to GPDF data in an image classification probleml, the experiment results show that the proposed BK-CNN algorithm gives 1.7%-4.3% improvements in average classification accuracy over other conventional algorithm such as k-means, Self-Organizing Map (SOM) and CNN algorithms with a Bhattacharyya distance, classed as Bk-Means, B-SOM, B-CNN algorithms.
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