Showing papers on "Metric (mathematics) published in 2015"

Person re-identification by Local Maximal Occurrence representation and metric learning

Abstract: Person re-identification is an important technique towards automatic search of a person's presence in a surveillance video. Two fundamental problems are critical for person re-identification, feature representation and metric learning. An effective feature representation should be robust to illumination and viewpoint changes, and a discriminant metric should be learned to match various person images. In this paper, we propose an effective feature representation called Local Maximal Occurrence (LOMO), and a subspace and metric learning method called Cross-view Quadratic Discriminant Analysis (XQDA). The LOMO feature analyzes the horizontal occurrence of local features, and maximizes the occurrence to make a stable representation against viewpoint changes. Besides, to handle illumination variations, we apply the Retinex transform and a scale invariant texture operator. To learn a discriminant metric, we propose to learn a discriminant low dimensional subspace by cross-view quadratic discriminant analysis, and simultaneously, a QDA metric is learned on the derived subspace. We also present a practical computation method for XQDA, as well as its regularization. Experiments on four challenging person re-identification databases, VIPeR, QMUL GRID, CUHK Campus, and CUHK03, show that the proposed method improves the state-of-the-art rank-1 identification rates by 2.2%, 4.88%, 28.91%, and 31.55% on the four databases, respectively.

From Word Embeddings To Document Distances

Abstract: We present the Word Mover's Distance (WMD), a novel distance function between text documents. Our work is based on recent results in word embeddings that learn semantically meaningful representations for words from local cooccurrences in sentences. The WMD distance measures the dissimilarity between two text documents as the minimum amount of distance that the embedded words of one document need to "travel" to reach the embedded words of another document. We show that this distance metric can be cast as an instance of the Earth Mover's Distance, a well studied transportation problem for which several highly efficient solvers have been developed. Our metric has no hyperparameters and is straight-forward to implement. Further, we demonstrate on eight real world document classification data sets, in comparison with seven state-of-the-art baselines, that the WMD metric leads to unprecedented low k-nearest neighbor document classification error rates.

Deep metric learning using Triplet network

Abstract: Deep learning has proven itself as a successful set of models for learning useful semantic representations of data. These, however, are mostly implicitly learned as part of a classification task. In this paper we propose the triplet network model, which aims to learn useful representations by distance comparisons. A similar model was defined by Wang et al. (2014), tailor made for learning a ranking for image information retrieval. Here we demonstrate using various datasets that our model learns a better representation than that of its immediate competitor, the Siamese network. We also discuss future possible usage as a framework for unsupervised learning.

An improved deep learning architecture for person re-identification

Abstract: In this work, we propose a method for simultaneously learning features and a corresponding similarity metric for person re-identification. We present a deep convolutional architecture with layers specially designed to address the problem of re-identification. Given a pair of images as input, our network outputs a similarity value indicating whether the two input images depict the same person. Novel elements of our architecture include a layer that computes cross-input neighborhood differences, which capture local relationships between the two input images based on mid-level features from each input image. A high-level summary of the outputs of this layer is computed by a layer of patch summary features, which are then spatially integrated in subsequent layers. Our method significantly outperforms the state of the art on both a large data set (CUHK03) and a medium-sized data set (CUHK01), and is resistant to over-fitting. We also demonstrate that by initially training on an unrelated large data set before fine-tuning on a small target data set, our network can achieve results comparable to the state of the art even on a small data set (VIPeR).

MatchNet: Unifying feature and metric learning for patch-based matching

Abstract: Motivated by recent successes on learning feature representations and on learning feature comparison functions, we propose a unified approach to combining both for training a patch matching system. Our system, dubbed Match-Net, consists of a deep convolutional network that extracts features from patches and a network of three fully connected layers that computes a similarity between the extracted features. To ensure experimental repeatability, we train MatchNet on standard datasets and employ an input sampler to augment the training set with synthetic exemplar pairs that reduce overfitting. Once trained, we achieve better computational efficiency during matching by disassembling MatchNet and separately applying the feature computation and similarity networks in two sequential stages. We perform a comprehensive set of experiments on standard datasets to carefully study the contributions of each aspect of MatchNet, with direct comparisons to established methods. Our results confirm that our unified approach improves accuracy over previous state-of-the-art results on patch matching datasets, while reducing the storage requirement for descriptors. We make pre-trained MatchNet publicly available.

An Underwater Color Image Quality Evaluation Metric

Abstract: Quality evaluation of underwater images is a key goal of underwater video image retrieval and intelligent processing. To date, no metric has been proposed for underwater color image quality evaluation (UCIQE). The special absorption and scattering characteristics of the water medium do not allow direct application of natural color image quality metrics especially to different underwater environments. In this paper, subjective testing for underwater image quality has been organized. The statistical distribution of the underwater image pixels in the CIELab color space related to subjective evaluation indicates the sharpness and colorful factors correlate well with subjective image quality perception. Based on these, a new UCIQE metric, which is a linear combination of chroma, saturation, and contrast, is proposed to quantify the non-uniform color cast, blurring, and low-contrast that characterize underwater engineering and monitoring images. Experiments are conducted to illustrate the performance of the proposed UCIQE metric and its capability to measure the underwater image enhancement results. They show that the proposed metric has comparable performance to the leading natural color image quality metrics and the underwater grayscale image quality metrics available in the literature, and can predict with higher accuracy the relative amount of degradation with similar image content in underwater environments. Importantly, UCIQE is a simple and fast solution for real-time underwater video processing. The effectiveness of the presented measure is also demonstrated by subjective evaluation. The results show better correlation between the UCIQE and the subjective mean opinion score.

Using free energy principle for blind image quality assessment

Abstract: In this paper we propose a new no-reference (NR) image quality assessment (IQA) metric using the recently revealed free-energy-based brain theory and classical human visual system (HVS)-inspired features. The features used can be divided into three groups. The first involves the features inspired by the free energy principle and the structural degradation model. Furthermore, the free energy theory also reveals that the HVS always tries to infer the meaningful part from the visual stimuli. In terms of this finding, we first predict an image that the HVS perceives from a distorted image based on the free energy theory, then the second group of features is composed of some HVS-inspired features (such as structural information and gradient magnitude) computed using the distorted and predicted images. The third group of features quantifies the possible losses of “naturalness” in the distorted image by fitting the generalized Gaussian distribution to mean subtracted contrast normalized coefficients. After feature extraction, our algorithm utilizes the support vector machine based regression module to derive the overall quality score. Experiments on LIVE, TID2008, CSIQ, IVC, and Toyama databases confirm the effectiveness of our introduced NR IQA metric compared to the state-of-the-art.

Efficient PSD Constrained Asymmetric Metric Learning for Person Re-Identification

Abstract: Person re-identification is becoming a hot research topic due to its value in both machine learning research and video surveillance applications. For this challenging problem, distance metric learning is shown to be effective in matching person images. However, existing approaches either require a heavy computation due to the positive semidefinite (PSD) constraint, or ignore the PSD constraint and learn a free distance function that makes the learned metric potentially noisy. We argue that the PSD constraint provides a useful regularization to smooth the solution of the metric, and hence the learned metric is more robust than without the PSD constraint. Another problem with metric learning algorithms is that the number of positive sample pairs is very limited, and the learning process is largely dominated by the large amount of negative sample pairs. To address the above issues, we derive a logistic metric learning approach with the PSD constraint and an asymmetric sample weighting strategy. Besides, we successfully apply the accelerated proximal gradient approach to find a global minimum solution of the proposed formulation, with a convergence rate of O(1/t^2) where t is the number of iterations. The proposed algorithm termed MLAPG is shown to be computationally efficient and able to perform low rank selection. We applied the proposed method for person re-identification, achieving state-of-the-art performance on four challenging databases (VIPeR, QMUL GRID, CUHK Campus, and CUHK03), compared to existing metric learning methods as well as published results.

K‐Stability and Kähler‐Einstein Metrics

Abstract: We prove that if a Fano manifold M is K-stable, then it admits a Kahler-Einstein metric. It affirms a longstanding conjecture for Fano manifolds. © 2015 Wiley Periodicals, Inc.

Autoencoding beyond pixels using a learned similarity metric

Abstract: We present an autoencoder that leverages learned representations to better measure similarities in data space. By combining a variational autoencoder with a generative adversarial network we can use learned feature representations in the GAN discriminator as basis for the VAE reconstruction objective. Thereby, we replace element-wise errors with feature-wise errors to better capture the data distribution while offering invariance towards e.g. translation. We apply our method to images of faces and show that it outperforms VAEs with element-wise similarity measures in terms of visual fidelity. Moreover, we show that the method learns an embedding in which high-level abstract visual features (e.g. wearing glasses) can be modified using simple arithmetic.

Superpixel segmentation using Linear Spectral Clustering

Abstract: We present in this paper a superpixel segmentation algorithm called Linear Spectral Clustering (LSC), which produces compact and uniform superpixels with low computational costs. Basically, a normalized cuts formulation of the superpixel segmentation is adopted based on a similarity metric that measures the color similarity and space proximity between image pixels. However, instead of using the traditional eigen-based algorithm, we approximate the similarity metric using a kernel function leading to an explicitly mapping of pixel values and coordinates into a high dimensional feature space. We revisit the conclusion that by appropriately weighting each point in this feature space, the objective functions of weighted K-means and normalized cuts share the same optimum point. As such, it is possible to optimize the cost function of normalized cuts by iteratively applying simple K-means clustering in the proposed feature space. LSC is of linear computational complexity and high memory efficiency and is able to preserve global properties of images. Experimental results show that LSC performs equally well or better than state of the art superpixel segmentation algorithms in terms of several commonly used evaluation metrics in image segmentation.

Personalized ranking metric embedding for next new POI recommendation

Abstract: The rapidly growing of Location-based Social Networks (LBSNs) provides a vast amount of check-in data, which enables many services, e.g., point-of-interest (POI) recommendation. In this paper, we study the next new POI recommendation problem in which new POIs with respect to users' current location are to be recommended. The challenge lies in the difficulty in precisely learning users' sequential information and personalizing the recommendation model. To this end, we resort to the Metric Embedding method for the recommendation, which avoids drawbacks of the Matrix Factorization technique. We propose a personalized ranking metric embedding method (PRME) to model personalized check-in sequences. We further develop a PRME-G model, which integrates sequential information, individual preference, and geographical influence, to improve the recommendation performance. Experiments on two real-world LBSN datasets demonstrate that our new algorithm outperforms the state-of-the-art next POI recommendation methods.

Sobolev Spaces on Metric Measure Spaces: An Approach Based on Upper Gradients

Abstract: Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of metric measure spaces supporting a Poincare inequality. This coherent treatment from first principles is an ideal introduction to the subject for graduate students and a useful reference for experts. It presents the foundations of the theory of such first-order Sobolev spaces, then explores geometric implications of the critical Poincare inequality, and indicates numerous examples of spaces satisfying this axiom. A distinguishing feature of the book is its focus on vector-valued Sobolev spaces. The final chapters include proofs of several landmark theorems, including Cheeger's stability theorem for Poincare inequalities under Gromov–Hausdorff convergence, and the Keith–Zhong self-improvement theorem for Poincare inequalities.

Learning with a Wasserstein Loss

Abstract: Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe an efficient learning algorithm based on this regularization, as well as a novel extension of the Wasserstein distance from probability measures to unnormalized measures. We also describe a statistical learning bound for the loss. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data tag prediction problem, using the Yahoo Flickr Creative Commons dataset, outperforming a baseline that doesn't use the metric.

No-Reference Image Sharpness Assessment in Autoregressive Parameter Space

Abstract: In this paper, we propose a new no-reference (NR)/ blind sharpness metric in the autoregressive (AR) parameter space. Our model is established via the analysis of AR model parameters, first calculating the energy- and contrast-differences in the locally estimated AR coefficients in a pointwise way, and then quantifying the image sharpness with percentile pooling to predict the overall score. In addition to the luminance domain, we further consider the inevitable effect of color information on visual perception to sharpness and thereby extend the above model to the widely used YIQ color space. Validation of our technique is conducted on the subsets with blurring artifacts from four large-scale image databases (LIVE, TID2008, CSIQ, and TID2013). Experimental results confirm the superiority and efficiency of our method over existing NR algorithms, the state-of-the-art blind sharpness/blurriness estimators, and classical full-reference quality evaluators. Furthermore, the proposed metric can be also extended to stereoscopic images based on binocular rivalry, and attains remarkably high performance on LIVE3D-I and LIVE3D-II databases.

Learning with a Wasserstein loss

Abstract: Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe an efficient learning algorithm based on this regularization, as well as a novel extension of the Wasserstein distance from probability measures to unnormalized measures. We also describe a statistical learning bound for the loss. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data tag prediction problem, using the Yahoo Flickr Creative Commons dataset, outperforming a baseline that doesn't use the metric.

On the Differential Structure of Metric Measure Spaces and Applications

Abstract: Introduction Preliminaries Differentials and gradients Laplacian Comparison estimates Appendix A. On the duality between cotangent and tangent spaces Appendix B. Remarks about the definition of the Sobolev classes References

Riemannian Ricci curvature lower bounds in metric measure spaces with -finite measure

Abstract: In prior work (4) of the first two authors with Savare, a new Riemannian notion of lower bound for Ricci curvature in the class of metric measure spaces (X,d,m) was introduced, and the corresponding class of spaces denoted by RCD(K,∞). This notion relates the CD(K,N) theory of Sturm and Lott-Villani, in the case N = ∞, to the Bakry-Emery approach. In (4) the RCD(K,∞) property is defined in three equivalent ways and several properties of RCD(K,∞) spaces, including the regularization properties of the heat flow, the connections with the theory of Dirichlet forms and the stability under tensor products, are provided. In (4) only finite reference measures m have been considered. The goal of this paper is twofold: on one side we extend these results to general σ-finite spaces, on the other we remove a technical assumption appeared in (4) concerning a strengthening of the CD(K,∞) condition. This more general class of spaces includes Euclidean spaces endowed with Lebesgue measure, complete noncompact Riemannian manifolds with bounded geometry and the pointed metric measure limits of manifolds with lower Ricci curvature bounds.

Log-Euclidean Metric Learning on Symmetric Positive Definite Manifold with Application to Image Set Classification

Abstract: The manifold of Symmetric Positive Definite (SPD) matrices has been successfully used for data representation in image set classification. By endowing the SPD manifold with Log-Euclidean Metric, existing methods typically work on vector-forms of SPD matrix logarithms. This however not only inevitably distorts the geometrical structure of the space of SPD matrix logarithms but also brings low efficiency especially when the dimensionality of SPD matrix is high. To overcome this limitation, we propose a novel metric learning approach to work directly on logarithms of SPD matrices. Specifically, our method aims to learn a tangent map that can directly transform the matrix logarithms from the original tangent space to a new tangent space of more discriminability. Under the tangent map framework, the novel metric learning can then be formulated as an optimization problem of seeking a Mahalanobis-like matrix, which can take the advantage of traditional metric learning techniques. Extensive evaluations on several image set classification tasks demonstrate the effectiveness of our proposed metric learning method.

A new image quality metric for image fusion: The sum of the correlations of differences

Abstract: Measuring the quality of fused images is a very important stage for image fusion applications. The fused image must comprise maximum information from each of source images of the same scene taken by different sensors. Therefore, the amount of the information gathered in the fused images reflects the quality of them. This paper proposes a new quality metric by making use of this knowledge. The metric employed to compare the performance of different image fusion algorithms. In the experiments, subjective correspondence of the proposed metric and several well-known metrics are compared. Experimental results show the feasibility of the developed metric.

Gravitational tests of the generalized uncertainty principle

Abstract: We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a generalized uncertainty principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard general relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.

Multi-manifold deep metric learning for image set classification

Abstract: In this paper, we propose a multi-manifold deep metric learning (MMDML) method for image set classification, which aims to recognize an object of interest from a set of image instances captured from varying viewpoints or under varying illuminations. Motivated by the fact that manifold can be effectively used to model the nonlinearity of samples in each image set and deep learning has demonstrated superb capability to model the nonlinearity of samples, we propose a MMDML method to learn multiple sets of nonlinear transformations, one set for each object class, to nonlinearly map multiple sets of image instances into a shared feature subspace, under which the manifold margin of different class is maximized, so that both discriminative and class-specific information can be exploited, simultaneously. Our method achieves the state-of-the-art performance on five widely used datasets.

Interactive interfaces for machine learning model evaluations

Abstract: A first data set corresponding to an evaluation run of a model is generated at a machine learning service for display via an interactive interface. The data set includes a prediction quality metric. A target value of an interpretation threshold associated with the model is determined based on a detection of a particular client's interaction with the interface. An indication of a change to the prediction quality metric that results from the selection of the target value may be initiated.

Deep transfer metric learning

Abstract: Conventional metric learning methods usually assume that the training and test samples are captured in similar scenarios so that their distributions are assumed to be the same. This assumption doesn't hold in many real visual recognition applications, especially when samples are captured across different datasets. In this paper, we propose a new deep transfer metric learning (DTML) method to learn a set of hierarchical nonlinear transformations for cross-domain visual recognition by transferring discriminative knowledge from the labeled source domain to the unlabeled target domain. Specifically, our DTML learns a deep metric network by maximizing the inter-class variations and minimizing the intra-class variations, and minimizing the distribution divergence between the source domain and the target domain at the top layer of the network. To better exploit the discriminative information from the source domain, we further develop a deeply supervised transfer metric learning (DSTML) method by including an additional objective on DTML where the output of both the hidden layers and the top layer are optimized jointly. Experimental results on cross-dataset face verification and person re-identification validate the effectiveness of the proposed methods.

Deep similarity learning for multimodal medical images

Abstract: The present embodiments relate to machine learning for multimodal image data. By way of introduction, the present embodiments described below include apparatuses and methods for learning a similarity metric using deep learning based techniques for multimodal medical images. A novel similarity metric for multi-modal images is provided using the corresponding states of pairs of image patches to generate a classification setting for each pair. The classification settings are used to train a deep neural network via supervised learning. A multi-modal stacked denoising auto encoder (SDAE) is used to pre-train the neural network. A continuous and smooth similarity metric is constructed based on the output of the neural network before activation in the last layer. The trained similarity metric may be used to improve the results of image fusion.

Bijective parameterization with free boundaries

Abstract: We present a fully automatic method for generating guaranteed bijective surface parameterizations from triangulated 3D surfaces partitioned into charts. We do so by using a distortion metric that prevents local folds of triangles in the parameterization and a barrier function that prevents intersection of the chart boundaries. In addition, we show how to modify the line search of an interior point method to directly compute the singularities of the distortion metric and barrier functions to maintain a bijective map. By using an isometric metric that is efficient to compute and a spatial hash to accelerate the evaluation and gradient of the barrier function for the boundary, we achieve fast optimization times. Unlike previous methods, we do not require the boundary be constrained by the user to a non-intersecting shape to guarantee a bijection, and the boundary of the parameterization is free to change shape during the optimization to minimize distortion.

Survey on distance metric learning and dimensionality reduction in data mining

Abstract: Distance metric learning is a fundamental problem in data mining and knowledge discovery. Many representative data mining algorithms, such as $$k$$ k -nearest neighbor classifier, hierarchical clustering and spectral clustering, heavily rely on the underlying distance metric for correctly measuring relations among input data. In recent years, many studies have demonstrated, either theoretically or empirically, that learning a good distance metric can greatly improve the performance of classification, clustering and retrieval tasks. In this survey, we overview existing distance metric learning approaches according to a common framework. Specifically, depending on the available supervision information during the distance metric learning process, we categorize each distance metric learning algorithm as supervised, unsupervised or semi-supervised. We compare those different types of metric learning methods, point out their strength and limitations. Finally, we summarize open challenges in distance metric learning and propose future directions for distance metric learning.

Weakly Supervised Deep Metric Learning for Community-Contributed Image Retrieval

Abstract: Recent years have witnessed the explosive growth of community-contributed images with rich context information, which is beneficial to the task of image retrieval. It can help us to learn a suitable metric to alleviate the semantic gap. In this paper, we propose a new distance metric learning algorithm, namely weakly-supervised deep metric learning (WDML), under the deep learning framework. It utilizes a progressive learning manner to discover knowledge by jointly exploiting the heterogeneous data structures from visual contents and user-provided tags of social images. The semantic structure in the textual space is expected to be well preserved while the problem of the noisy, incomplete or subjective tags is addressed by leveraging the visual structure in the original visual space. Besides, a sparse model with the ${\ell _{2,1}}$ mixed norm is imposed on the transformation matrix of the first layer in the deep architecture to compress the noisy or redundant visual features. The proposed problem is formulated as an optimization problem with a well-defined objective function and a simple yet efficient iterative algorithm is proposed to solve it. Extensive experiments on real-world social image datasets are conducted to verify the effectiveness of the proposed method for image retrieval. Encouraging experimental results are achieved compared with several representative metric learning methods.