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. Scalable image search based on visual similarity has been an active topic of research in recent years. State-of-the-art solutions often use hashing methods to embed high-dimensional image features into Hamming space, where search can be performed in real-time based on Hamming distance of compact hash codes. Unlike traditional metrics (e.g., Euclidean) that offer continuous distances, the Hamming distances are discrete integer values. As a consequence, there are often a large number of images sharing equal Hamming distances to a query, which largely hurts search results where fine-grained ranking is very important. This paper introduces an approach that enables query-adaptive ranking of the returned images with equal Hamming distances to the queries. This is achieved by firstly offline learning bitwise weights of the hash codes for a diverse set of predefined semantic concept classes. We formulate the weight learning process as a quadratic programming problem that minimizes intra-class distance while preserving inter-class relationship captured by original raw image features. Query-adaptive weights are then computed online by evaluating the proximity between a query and the semantic concept classes. With the query-adaptive bitwise weights, returned images can be easily ordered by weighted Hamming distance at a finer-grained hash code level rather than the original Hamming distance level. Experiments on a Flickr image dataset show clear improvements from our proposed approach. This paper presents a method named Discriminant Analysis on Riemannian manifold of Gaussian distributions (DARG) to solve the problem of face recognition with image sets. Our goal is to capture the underlying data distribution in each set and thus facilitate more robust classification. To this end, we represent image set as Gaussian Mixture Model (GMM) comprising a number of Gaussian components with prior probabilities and seek to discriminate Gaussian components from different classes. In the light of information geometry, the Gaussians lie on a specific Riemannian manifold. To encode such Riemannian geometry properly, we investigate several distances between Gaussians and further derive a series of provably positive definite probabilistic kernels. Through these kernels, a weighted Kernel Discriminant Analysis is finally devised which treats the Gaussians in GMMs as samples and their prior probabilities as sample weights. The proposed method is evaluated by face identification and verification tasks on four most challenging and largest databases, YouTube Celebrities, COX, YouTube Face DB and Point-and-Shoot Challenge, to demonstrate its superiority over the state-of-the-art. Modeling image similarity for browsing and searching in voluminous image databases is a challenging task of nearly all content-based image retrieval systems. One promising way of defining image similarity consists in applying distance-based similarity measures on compact image representations. Beyond feature histograms and feature signatures, more general feature representations are mixture models of which the Gaussian mixture model is the most prominent one. This feature representation can be compared by employing approximations of the Kullback-Leibler Divergence. Although several of those approximations have been successfully applied to model image similarity, their applicability to mixture models based on high-dimensional feature descriptors is questionable. In this paper, we thus introduce the Signature Quadratic Form Distance to measure the distance between two Gaussian mixture models of high-dimensional feature descriptors. We show the analytical computation of the proposed Gaussian Quadratic Form Distance and evaluate its retrieval performance by making use of different benchmark image databases. The restoration of clean remote sensing images from the degraded images is usually an ill-posed problem. A feasible solution for the problem is incorporating various priors into restoration procedure as constrained conditions. Recently, the patch-based Gaussian mixture model (GMM) priors became popular. However, the learning of patch-based GMM priors usually assumes the components of the GMM are independent and identically distributed (i.i.d.). The assumption means that two components could model the same training samples, and thus a possible decrease in model’s description ability. This work presents a new learning method to diversify the patch-based GMM priors through modeling the GMM’s parameters as a determinantal point process (DPP). The introduction of DPP allows us to specify a preference for diversity in patch-based GMM using a positive definite kernel function and thus to increase the model’s description ability for a given model complexity. Furthermore, under the expected patch log-likelihood (EPLL) restoration framework, we further introduce the diversified patch-based GMM priors into remote sensing literature and develop new remote sensing image restoration algorithms. The extensive experiments for denoising and deblurring of remote sensing images demonstrated that the proposed algorithms produced better restoration results than other methods that already proven to perform well in the literature. Along with the arrival of multimedia time, multimedia data has replaced textual data to transfer information in various fields. As an important form of multimedia data, images have been widely utilized by many applications, such as face recognition and image classification. Therefore, how to accurately annotate each image from a large set of images is of vital importance but challenging. To perform these tasks well, it is crucial to extract suitable features to character the visual contents of images and learn an appropriate distance metric to measure similarities between all images. Unfortunately, existing feature operators, such as histogram of gradient, local binary pattern, and color histogram, care more about the visual character of images and lack the ability to distinguish semantic information. Similarities between those features cannot reflect the real category correlations due to the well-known semantic gap. In order to solve this problem, this paper proposes a regularized distance metric framework called semantic discriminative metric learning (SDML). SDML combines geometric mean with normalized divergences and separates images from different classes simultaneously. The learned distance metric can treat all images from different classes equally. And distinctions between similar classes with entirely different semantic contents are emphasized by SDML. This procedure ensures the consistency between dissimilarities and semantic distinctions and avoids inaccuracy similarities incurred by unbalanced locations of samples. Various experiments on benchmark image datasets show the excellent performance of the novel method. Natural image modeling plays a key role in many vision problems such as image denoising. Image priors are widely used to regularize the denoising process, which is an illposed inverse problem. One category of denoising methods exploit the priors (e.g., TV, sparsity) learned from external clean images to reconstruct the given noisy image, while another category of methods exploit the internal prior (e.g., self-similarity) to reconstruct the latent image. Though the internal prior based methods have achieved impressive denoising results, the improvement of visual quality will become very difficult with the increase of noise level. In this paper, we propose to exploit image external patch prior and internal self-similarity prior jointly, and develop an external patch prior guided internal clustering algorithm for image denoising. It is known that natural image patches form multiple subspaces. By utilizing Gaussian mixture models (GMMs) learning, image similar patches can be clustered and the subspaces can be learned. The learned GMMs from clean images are then used to guide the clustering of noisypatches of the input noisy images, followed by a low-rank approximation process to estimate the latent subspace for image recovery. Numerical experiments show that the proposed method outperforms many state-of-the-art denoising algorithms such as BM3D and WNNM. A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new "normalized information distance," based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class and it minorizes every computable distance in the class (that is, it is universal in that it discovers all computable similarities). We demonstrate that it is a metric and call it the similarity metric . This theory forms the foundation for a new practical tool. To evidence generality and robustness, we give two distinctive applications in widely divergent areas using standard compression programs like gzip and GenCompress. First, we compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we fully automatically compute the language tree of 52 different languages. Patch based image modeling has achieved a great success in low level vision such as image denoising. In particular, the use of image nonlocal self-similarity (NSS) prior, which refers to the fact that a local patch often has many nonlocal similar patches to it across the image, has significantly enhanced the denoising performance. However, in most existing methods only the NSS of input degraded image is exploited, while how to utilize the NSS of clean natural images is still an open problem. In this paper, we propose a patch group (PG) based NSS prior learning scheme to learn explicit NSS models from natural images for high performance denoising. PGs are extracted from training images by putting nonlocal similar patches into groups, and a PG based Gaussian Mixture Model (PG-GMM) learning algorithm is developed to learn the NSS prior. We demonstrate that, owe to the learned PG-GMM, a simple weighted sparse coding model, which has a closed-form solution, can be used to perform image denoising effectively, resulting in high PSNR measure, fast speed, and particularly the best visual quality among all competing methods. Image-generating machine learning models are typically trained with loss functions based on distance in the image space. This often leads to over-smoothed results. We propose a class of loss functions, which we call deep perceptual similarity metrics (DeePSiM), that mitigate this problem. Instead of computing distances in the image space, we compute distances between image features extracted by deep neural networks. This metric better reflects perceptually similarity of images and thus leads to better results. We show three applications: autoencoder training, a modification of a variational autoencoder, and inversion of deep convolutional networks. In all cases, the generated images look sharp and resemble natural images. Person recognition aims at recognizing the same identity across time and space with complicated scenes and similar appearance. In this paper, we propose a novel method to address this task by training a network to obtain robust and representative features. The intuition is that we directly compare and optimize the cosine distance between two features - enlarging inter-class distinction as well as alleviating inner-class variance. We propose a congenerous cosine loss by minimizing the cosine distance between samples and their cluster centroid in a cooperative way. Such a design reduces the complexity and could be implemented via softmax with normalized inputs. Our method also differs from previous work in person recognition that we do not conduct a second training on the test subset. The identity of a person is determined by measuring the similarity from several body regions in the reference set. Experimental results show that the proposed approach achieves better classification accuracy against previous state-of-the-arts. With the proliferation of images on the Web, fast search of visually similar images has attracted significant attention. State-of-the-art techniques often embed high-dimensional visual features into low-dimensional Hamming space, where search can be performed in real-time based on Hamming distance of compact binary codes. Unlike traditional metrics (e.g., Euclidean) of raw image features that produce continuous distance, the Hamming distances are discrete integer values. In practice, there are often a large number of images sharing equal Hamming distances to a query, resulting in a critical issue for image search where ranking is very important. In this paper, we propose a novel approach that facilitates query-adaptive ranking for the images with equal Hamming distance. We achieve this goal by firstly offline learning bit weights of the binary codes for a diverse set of predefined semantic concept classes. The weight learning process is formulated as a quadratic programming problem that minimizes intra-class distance while preserving interclass relationship in the original raw image feature space. Query-adaptive weights are then rapidly computed by evaluating the proximity between a query and the concept categories. With the adaptive bit weights, the returned images can be ordered by weighted Hamming distance at a finer-grained binary code level rather than at the original integer Hamming distance level. Experimental results on a Flickr image dataset show clear improvements from our query-adaptive ranking approach. In this paper, we aim at super-resolving a low-resolution texture under the assumption that a high-resolution patch of the texture is available. To do so, we propose a variational method that combines two approaches that are texture synthesis and image reconstruction. The resulting objective function holds a nonconvex energy that involves a quadratic distance to the low-resolution image, a histogram-based distance to the high-resolution patch, and a nonlocal regularization that links the missing pixels with the patch pixels. As for the histogram-based measure, we use a sum of Wasserstein distances between the histograms of some linear transformations of the textures. The resulting optimization problem is efficiently solved with a primal-dual proximal method. Experiments show that our method leads to a significant improvement, both visually and numerically, with respect to the state-of-the-art algorithms for solving similar problems. We propose a class of loss functions, which we call deep perceptual similarity metrics (DeePSiM), allowing to generate sharp high resolution images from compressed abstract representations. Instead of computing distances in the image space, we compute distances between image features extracted by deep neural networks. This metric reflects perceptual similarity of images much better and, thus, leads to better results. We demonstrate two examples of use cases of the proposed loss: (1) networks that invert the AlexNet convolutional network; (2) a modified version of a variational autoencoder that generates realistic high-resolution random images. In this paper we introduce and experiment with a framework for learning local perceptual distance functions for visual recognition. We learn a distance function for each training image as a combination of elementary distances between patch-based visual features. We apply these combined local distance functions to the tasks of image retrieval and classification of novel images. On the Caltech 101 object recognition benchmark, we achieve 60.3 mean recognition across classes using 15 training images per class, which is better than the best published performance by Zhang, et al Concept similarity has been intensively researched in the natural language processing domain due to its important role in many applications such as language modeling and information retrieval. There are few studies on measuring concept similarity in visual domain, though concept based multimedia information retrieval has attracted a lot of attentions. In this paper, we present a scalable framework for such a purpose, which is different from traditional approaches to exploring correlation among concepts in image video annotation domain. For each concept, a model based on feature distribution is built using sample images collected from the Internet. And similarity between concepts is measured with the similarity between their models. Hereby, a Gaussian mixture model (GMM) is employed to model each concept and two similarity measurements are investigated. Experimental results on 13,974 images of 16 concepts collected through image search engines have demonstrated that the similarity between concepts is very close to human perception. In addition, the entropy of GMM cluster distributions can be a good indication of selecting concepts for image video annotation. Pose variation remains to be a major challenge for real-world face recognition. We approach this problem through a probabilistic elastic matching method. We take a part based representation by extracting local features (e.g., LBP or SIFT) from densely sampled multi-scale image patches. By augmenting each feature with its location, a Gaussian mixture model (GMM) is trained to capture the spatial-appearance distribution of all face images in the training corpus. Each mixture component of the GMM is confined to be a spherical Gaussian to balance the influence of the appearance and the location terms. Each Gaussian component builds correspondence of a pair of features to be matched between two faces face tracks. For face verification, we train an SVM on the vector concatenating the difference vectors of all the feature pairs to decide if a pair of faces face tracks is matched or not. We further propose a joint Bayesian adaptation algorithm to adapt the universally trained GMM to better model the pose variations between the target pair of faces face tracks, which consistently improves face verification accuracy. Our experiments show that our method outperforms the state-of-the-art in the most restricted protocol on Labeled Face in the Wild (LFW) and the YouTube video face database by a significant margin. We propose a new semisupervised learning algorithm, referred to as patch distribution compatible semisupervised dimension reduction, for face and human gait recognition. Each image (a face image or an average human silhouette image) is first represented as a set of local patch features and it is further characterized as the corresponding patch distribution feature, which can be expressed as an image-specific Gaussian mixture model (GMM) adapted from the universal background model. Assuming that the individual components of the image-specific GMMs from all the training images reside on a submanifold, we assign a component-level prediction label matrix to each individual GMM component and introduce a new regularizer based on a set of local submanifold smoothness assumptions in our objective function. We also constrain each component-level prediction label matrix to be consistent with the image-level prediction label matrix , as well as enforce to be close to the given labels for the labeled samples. We further use a linear regression function to provide embeddings for the training data and the unseen test data. Inspired by the recent work flexible manifold embedding, we additionally integrate the regression residue in our objective function to measure the mismatch between and , such that our method can better cope with the data sampled from a nonlinear manifold. Finally, the optimal solutions of the component-level prediction label matrix , the image-level prediction label matrix , the projection matrix , and the bias term b can be simultaneously obtained. Comprehensive experiments on three benchmark face databases CMU PIE, FERET, and AR as well as the USF HumanID gait database clearly demonstrate the effectiveness of our algorithm over other state-of-the-art semisupervised dimension reduction methods. Transfer learning has been proven to be effective for the problems where training data from a source domain and test data from a target domain are drawn from different distributions. To reduce the distribution divergence between the source domain and the target domain, many previous studies have been focused on designing and optimizing objective functions with the Euclidean distance to measure dissimilarity between instances. However, in some real-world applications, the Euclidean distance may be inappropriate to capture the intrinsic similarity or dissimilarity between instances. To deal with this issue, in this paper, we propose a metric transfer learning framework (MTLF) to encode metric learning in transfer learning. In MTLF, instance weights are learned and exploited to bridge the distributions of different domains, while Mahalanobis distance is learned simultaneously to maximize the intra-class distances and minimize the inter-class distances for the target domain. Unlike previous work where instance weights and Mahalanobis distance are trained in a pipelined framework that potentially leads to error propagation across different components, MTLF attempts to learn instance weights and a Mahalanobis distance in a parallel framework to make knowledge transfer across domains more effective. Furthermore, we develop general solutions to both classification and regression problems on top of MTLF, respectively. We conduct extensive experiments on several real-world datasets on object recognition, handwriting recognition, and WiFi location to verify the effectiveness of MTLF compared with a number of state-of-the-art methods. In this paper we propose a novel approach to generate a binary descriptor optimized for each image patch independently. The approach is inspired by the linear discriminant embedding that simultaneously increases inter and decreases intra class distances. A set of discriminative and uncorrelated binary tests is established from all possible tests in an offline training process. The patch adapted descriptors are then efficiently built online from a subset of tests which lead to lower intra class distances thus a more robust descriptor. A patch descriptor consists of two binary strings where one represents the results of the tests and the other indicates the subset of the patch-related robust tests that are used for calculating a masked Hamming distance. Our experiments on three different benchmarks demonstrate improvements in matching performance, and illustrate that per-patch optimization outperforms global optimization.