Deep neural networks (DNNs) have achieved exceptional performances in many tasks, particularly, in supervised classification tasks. However, achievements with supervised classification tasks are based on large datasets with well-separated classes. Typically, real-world applications involve wild datasets that include similar classes; thus, evaluating similarities between classes and understanding relations among classes are important. To address this issue, a similarity metric, ClassSim, based on the misclassification ratios of trained DNNs is proposed herein. We conducted image recognition experiments to demonstrate that the proposed method provides better similarities compared with existing methods and is useful for classification problems. Source code including all experimental results is available at this https URL
However, a method to estimate the similarities between classes has been proposed @cite_3 @cite_4 . In that method, images are divided into patches, and features are extracted from each patch using traditional methods, such as RGB color moment. In addition, to compute the distance between classes, we must assume that the images are generated from Gaussian mixture models (GMMs). Note that the number of GMM components must be determined manually relative to the number of target classes. In addition, the distance between classes expresses an inverse relation with similarities; they are not normalized, and their absolute values are meaningless. Here, two distances are involved, i.e., parametric distance (PD), which is the quadratic distance of the means and variances of a GMM, and an approximation of KL divergence. These two methods return similar results. Here, strong assumptions and simplifications were used to treat inter-class similarities realistically.
@cite_4 @cite_3
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Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM guarantees only convergence to a stationary point of the log-likelihood function, which could be arbitrarily worse than the optimal solution. Inspired by the relationship between the negative log-likelihood function and the Kullback-Leibler (KL) divergence, we propose an alternative formulation for estimating the GMM parameters using the sliced Wasserstein distance, which gives rise to a new algorithm. Specifically, we propose minimizing the sliced-Wasserstein distance between the mixture model and the data distribution with respect to the GMM parameters. In contrast to the KL-divergence, the energy landscape for the sliced-Wasserstein distance is more well-behaved and therefore more suitable for a stochastic gradient descent scheme to obtain the optimal GMM parameters. We show that our formulation results in parameter estimates that are more robust to random initializations and demonstrate that it can estimate high-dimensional data distributions more faithfully than the EM algorithm. In this paper, we propose a novel adaptive metric learning algorithm (AML) for visual saliency detection. A key observation is that the saliency of a superpixel can be estimated by the distance from the most certain foreground and background seeds. Instead of measuring distance on the Euclidean space, we present a learning method based on two complementary Mahalanobis distance metrics: 1) generic metric learning (GML) and 2) specific metric learning (SML). GML aims at the global distribution of the whole training set, while SML considers the specific structure of a single image. Considering that multiple similarity measures from different views may enhance the relevant information and alleviate the irrelevant one, we try to fuse the GML and SML together and experimentally find the combining result does work well. Different from the most existing methods which are directly based on low-level features, we devise a superpixelwise Fisher vector coding approach to better distinguish salient objects from the background. We also propose an accurate seeds selection mechanism and exploit contextual and multiscale information when constructing the final saliency map. Experimental results on various image sets show that the proposed AML performs favorably against the state-of-the-arts. A hierarchical Bayes Gaussian Mixture Model (HBGMM) with adaptive sparsity is proposed.We impose our hierarchical Bayes prior on the entries of precision matrices in GMM to encourage sparsity.Our adaptive sparsity can reduce the dimensionality of the parameters in GMM to be estimated.Our HBGMM method does not involve any hyperparameters to be estimated, i.e., it is hyperparameter-free. Gaussian Mixture Model (GMM) has been widely used in statistics for its great flexibility. However, parameter estimation for GMM with high dimensionality is a challenge because of the large number of parameters and the lack of observation data. In this paper, we propose an effective method named hierarchical Bayes based Adaptive Sparsity in Gaussian Mixture Model (ASGMM) to estimate the parameters in a GMM by incorporating a two-layer hierarchical Bayes based adaptive sparsity prior. The prior we impose on the precision matrices can encourage sparsity and hence reduce the dimensionality of the parameters to be estimated. In contrast to the l 1 -norm penalty or Laplace prior, our approach does not involve any hyperparameters that must be tuned, and the sparsity adapts to the observation data. The proposed method is achieved by three steps: first, we formulate an adaptive hierarchical Bayes model of the precision matrices in the GMM with a Jeffrey's noninformative hyperprior, which expresses scale-invariance and, more importantly, is hyperparameter-free and unbiased. Second, we perform a Cholesky decomposition on the precision matrices to impose the positive definite property. Finally, we exploit the expectation maximization (EM) algorithm to obtain the final estimated parameters in the GMM. Experimental results on synthetic and real-world datasets demonstrate that ASGMM cannot only adapt the sparsity of high-dimensional data with small estimated error, but also achieve better clustering performance comparing with several classical methods. This paper presents a new algorithm for the automatic recognition of object classes from images (categorization). Compact and yet discriminative appearance-based object class models are automatically learned from a set of training images. The method is simple and extremely fast, making it suitable for many applications such as semantic image retrieval, Web search, and interactive image editing. It classifies a region according to the proportions of different visual words (clusters in feature space). The specific visual words and the typical proportions in each object are learned from a segmented training set. The main contribution of this paper is twofold: i) an optimally compact visual dictionary is learned by pair-wise merging of visual words from an initially large dictionary. The final visual words are described by GMMs. ii) A novel statistical measure of discrimination is proposed which is optimized by each merge operation. High classification accuracy is demonstrated for nine object classes on photographs of real objects viewed under general lighting conditions, poses and viewpoints. The set of test images used for validation comprise: i) photographs acquired by us, ii) images from the Web and iii) images from the recently released Pascal dataset. The proposed algorithm performs well on both texture-rich objects (e.g. grass, sky, trees) and structure-rich ones (e.g. cars, bikes, planes)