Automatic cover detection -- the task of finding in an audio database all the covers of one or several query tracks -- has long been seen as a challenging theoretical problem in the MIR community and as an acute practical problem for authors and composers societies. Original algorithms proposed for this task have proven their accuracy on small datasets, but are unable to scale up to modern real-life audio corpora. On the other hand, faster approaches designed to process thousands of pairwise comparisons resulted in lower accuracy, making them unsuitable for practical use. In this work, we propose a neural network architecture that is trained to represent each track as a single embedding vector. The computation burden is therefore left to the embedding extraction -- that can be conducted offline and stored, while the pairwise comparison task reduces to a simple Euclidean distance computation. We further propose to extract each track's embedding out of its dominant melody representation, obtained by another neural network trained for this task. We then show that this architecture improves state-of-the-art accuracy both on small and large datasets, and is able to scale to query databases of thousands of tracks in a few seconds.
The principle is to learn a mapping between the input space and a latent manifold where a simple distance measure (such as Euclidean distance) should approximate the neighborhood relationships in the input space. There is however a trivial solution to the problem, where the function ends up mapping all the examples to the same point. Contrastive Loss was introduced to circumvent this problem, aiming at simultaneously similar pairs together and dissimilar pairs apart @cite_35 .
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Dimensionality reduction involves mapping a set of high dimensional input points onto a low dimensional manifold so that 'similar" points in input space are mapped to nearby points on the manifold. We present a method - called Dimensionality Reduction by Learning an Invariant Mapping (DrLIM) - for learning a globally coherent nonlinear function that maps the data evenly to the output manifold. The learning relies solely on neighborhood relationships and does not require any distancemeasure in the input space. The method can learn mappings that are invariant to certain transformations of the inputs, as is demonstrated with a number of experiments. Comparisons are made to other techniques, in particular LLE. We present a method for training a similarity metric from data. The method can be used for recognition or verification applications where the number of categories is very large and not known during training, and where the number of training samples for a single category is very small. The idea is to learn a function that maps input patterns into a target space such that the L sub 1 norm in the target space approximates the "semantic" distance in the input space. The method is applied to a face verification task. The learning process minimizes a discriminative loss function that drives the similarity metric to be small for pairs of faces from the same person, and large for pairs from different persons. The mapping from raw to the target space is a convolutional network whose architecture is designed for robustness to geometric distortions. The system is tested on the Purdue AR face database which has a very high degree of variability in the pose, lighting, expression, position, and artificial occlusions such as dark glasses and obscuring scarves. Edge-aware operations, such as edge-preserving smoothing and edge-aware interpolation, require assessing the degree of similarity between pairs of pixels, typically defined as a simple monotonic function of the Euclidean distance between pixel values in some feature space. In this work we introduce the idea of replacing these Euclidean distances with diffusion distances, which better account for the global distribution of pixels in their feature space. These distances are approximated using diffusion maps: a set of the dominant eigenvectors of a large affinity matrix, which may be computed efficiently by sampling a small number of matrix columns (the Nystrom method). We demonstrate the benefits of using diffusion distances in a variety of image editing contexts, and explore the use of diffusion maps as a tool for facilitating the creation of complex selection masks. Finally, we present a new analysis that establishes a connection between the spatial interaction range between two pixels, and the number of samples necessary for accurate Nystrom approximations. The squared distance function is one of the standard functions on which an optimization algorithm is commonly run, whether it is used directly or chained with other functions. Illustrative examples include center of mass computation, implementation of k-means algorithm and robot positioning. This function can have a simple expression (as in the Euclidean case), or it might not even have a closed form expression. Nonetheless, when used in an optimization problem formulated on non-Euclidean manifolds, the appropriate (intrinsic) version must be used and depending on the algorithm, its gradient and or Hessian must be computed. For many commonly used manifolds a way to compute the intrinsic distance is available as well as its gradient, the Hessian however is usually a much more involved process, rendering Newton methods unusable on many standard manifolds. This article presents a way of computing the Hessian on connected locally-symmetric spaces on which standard Riemannian operations are known (exponential map, logarithm map and curvature). Although not a requirement for the result, describing the manifold as naturally reductive homogeneous spaces, a special class of manifolds, provides a way of computing these functions. The main example focused in this article is centroid computation of a finite constellation of points on connected locally symmetric manifolds since it is directly formulated as an intrinsic squared distance optimization problem. Simulation results shown here confirm the quadratic convergence rate of a Newton algorithm on commonly used manifolds such as the sphere, special orthogonal group, special Euclidean group, symmetric positive definite matrices, Grassmann manifold and projective space. This paper introduces Pairwise Constrained Component Analysis (PCCA), a new algorithm for learning distance metrics from sparse pairwise similarity dissimilarity constraints in high dimensional input space, problem for which most existing distance metric learning approaches are not adapted. PCCA learns a projection into a low-dimensional space where the distance between pairs of data points respects the desired constraints, exhibiting good generalization properties in presence of high dimensional data. The paper also shows how to efficiently kernelize the approach. PCCA is experimentally validated on two challenging vision tasks, face verification and person re-identification, for which we obtain state-of-the-art results. Isometric surfaces share the same geometric structure, also known as the "first fundamental form." For example, all possible bendings of a given surface that includes all length preserving deformations without tearing or stretching the surface are considered to be isometric. We present a method to construct a bending invariant signature for such surfaces. This invariant representation is an embedding of the geometric structure of the surface in a small dimensional Euclidean space in which geodesic distances are approximated by Euclidean ones. The bending invariant representation is constructed by first measuring the intergeodesic distances between uniformly distributed points on the surface. Next, a multidimensional scaling technique is applied to extract coordinates in a finite dimensional Euclidean space in which geodesic distances are replaced by Euclidean ones. Applying this transform to various surfaces with similar geodesic structures (first fundamental form) maps them into similar signature surfaces. We thereby translate the problem of matching nonrigid objects in various postures into a simpler problem of matching rigid objects. As an example, we show a simple surface classification method that uses our bending invariant signatures. We introduce a novel method for face recognition from image sets. In our setting each test and training example is a set of images of an individual's face, not just a single image, so recognition decisions need to be based on comparisons of image sets. Methods for this have two main aspects: the models used to represent the individual image sets; and the similarity metric used to compare the models. Here, we represent images as points in a linear or affine feature space and characterize each image set by a convex geometric region (the affine or convex hull) spanned by its feature points. Set dissimilarity is measured by geometric distances (distances of closest approach) between convex models. To reduce the influence of outliers we use robust methods to discard input points that are far from the fitted model. The kernel trick allows the approach to be extended to implicit feature mappings, thus handling complex and nonlinear manifolds of face images. Experiments on two public face datasets show that our proposed methods outperform a number of existing state-of-the-art ones. Deep generative models learn a mapping from a low-dimensional latent space to a high-dimensional data space. Under certain regularity conditions, these models parameterize nonlinear manifolds in the data space. In this paper, we investigate the Riemannian geometry of these generated manifolds. First, we develop efficient algorithms for computing geodesic curves, which provide an intrinsic notion of distance between points on the manifold. Second, we develop an algorithm for parallel translation of a tangent vector along a path on the manifold. We show how parallel translation can be used to generate analogies, i.e., to transport a change in one data point into a semantically similar change of another data point. Our experiments on real image data show that the manifolds learned by deep generative models, while nonlinear, are surprisingly close to zero curvature. The practical implication is that linear paths in the latent space closely approximate geodesics on the generated manifold. Structured output prediction aims to learn a predictor to predict a structured output from a input data vector . The structured outputs include vector, tree, sequence, etc. We usually assume that we have a training set of input---output pairs to train the predictor. However, in many real-world applications, it is difficult to obtain the output for a input, and thus for many training input data points, the structured outputs are missing. In this paper, we discuss how to learn from a training set composed of some input---output pairs and some input data points without outputs. This problem is called semi-supervised structured output prediction. We propose a novel method for this problem by constructing a nearest neighbor graph from the input space to present the manifold structure and use it to regularize the structured output space directly. We define a slack structured output for each training data point and propose to predict it by learning a structured output predictor. The learning of both slack structured outputs and the predictor are unified within one single minimization problem. In this problem, we propose to minimize the structured loss between the slack structured outputs of neighboring data points and the prediction error measured by the structured loss. The problem is optimized by an iterative algorithm. Experiment results over three benchmark data sets show its advantage. We address the problem of distance metric learning (DML), defined as learning a distance consistent with a notion of semantic similarity. Traditionally, for this problem supervision is expressed in the form of sets of points that follow an ordinal relationship – an anchor point x is similar to a set of positive points Y , and dissimilar to a set of negative points Z, and a loss defined over these distances is minimized. While the specifics of the optimization differ, in this work we collectively call this type of supervision Triplets and all methods that follow this pattern Triplet-Based methods. These methods are challenging to optimize. A main issue is the need for finding informative triplets, which is usually achieved by a variety of tricks such as increasing the batch size, hard or semi-hard triplet mining, etc. Even with these tricks, the convergence rate of such methods is slow. In this paper we propose to optimize the triplet loss on a different space of triplets, consisting of an anchor data point and similar and dissimilar proxy points which are learned as well. These proxies approximate the original data points, so that a triplet loss over the proxies is a tight upper bound of the original loss. This proxy-based loss is empirically better behaved. As a result, the proxy-loss improves on state-of-art results for three standard zero-shot learning datasets, by up to 15 points, while converging three times as fast as other triplet-based losses. Image-to-image translation aims to learn the mapping between two visual domains. There are two main challenges for many applications: 1) the lack of aligned training pairs and 2) multiple possible outputs from a single input image. In this work, we present an approach based on disentangled representation for producing diverse outputs without paired training images. To achieve diversity, we propose to embed images onto two spaces: a domain-invariant content space capturing shared information across domains and a domain-specific attribute space. Our model takes the encoded content features extracted from a given input and the attribute vectors sampled from the attribute space to produce diverse outputs at test time. To handle unpaired training data, we introduce a novel cross-cycle consistency loss based on disentangled representations. Qualitative results show that our model can generate diverse and realistic images on a wide range of tasks without paired training data. For quantitative comparisons, we measure realism with user study and diversity with a perceptual distance metric. We apply the proposed model to domain adaptation and show competitive performance when compared to the state-of-the-art on the MNIST-M and the LineMod datasets. Recent years have witnessed the growing popularity of hashing in large-scale vision problems. It has been shown that the hashing quality could be boosted by leveraging supervised information into hash function learning. However, the existing supervised methods either lack adequate performance or often incur cumbersome model training. In this paper, we propose a novel kernel-based supervised hashing model which requires a limited amount of supervised information, i.e., similar and dissimilar data pairs, and a feasible training cost in achieving high quality hashing. The idea is to map the data to compact binary codes whose Hamming distances are minimized on similar pairs and simultaneously maximized on dissimilar pairs. Our approach is distinct from prior works by utilizing the equivalence between optimizing the code inner products and the Hamming distances. This enables us to sequentially and efficiently train the hash functions one bit at a time, yielding very short yet discriminative codes. We carry out extensive experiments on two image benchmarks with up to one million samples, demonstrating that our approach significantly outperforms the state-of-the-arts in searching both metric distance neighbors and semantically similar neighbors, with accuracy gains ranging from 13 to 46 . We map categorical variables in a function approximation problem into Euclidean spaces, which are the entity embeddings of the categorical variables. The mapping is learned by a neural network during the standard supervised training process. Entity embedding not only reduces memory usage and speeds up neural networks compared with one-hot encoding, but more importantly by mapping similar values close to each other in the embedding space it reveals the intrinsic properties of the categorical variables. We applied it successfully in a recent Kaggle competition and were able to reach the third position with relative simple features. We further demonstrate in this paper that entity embedding helps the neural network to generalize better when the data is sparse and statistics is unknown. Thus it is especially useful for datasets with lots of high cardinality features, where other methods tend to overfit. We also demonstrate that the embeddings obtained from the trained neural network boost the performance of all tested machine learning methods considerably when used as the input features instead. As entity embedding defines a distance measure for categorical variables it can be used for visualizing categorical data and for data clustering. We describe a latent variable model for supervised dimensionality reduction and distance metric learning. The model discovers linear projections of high dimensional data that shrink the distance between similarly labeled inputs and expand the distance between differently labeled ones. The model's continuous latent variables locate pairs of examples in a latent space of lower dimensionality. The model differs significantly from classical factor analysis in that the posterior distribution over these latent variables is not always multivariate Gaussian. Nevertheless we show that inference is completely tractable and derive an Expectation-Maximization (EM) algorithm for parameter estimation. We also compare the model to other approaches in distance metric learning. The model's main advantage is its simplicity: at each iteration of the EM algorithm, the distance metric is re-estimated by solving an unconstrained least-squares problem. Experiments show that these simple updates are highly effective. Multi-metric learning techniques learn local metric tensors in different parts of a feature space. With such an approach, even simple classifiers can be competitive with the state-of-the-art because the distance measure locally adapts to the structure of the data. The learned distance measure is, however, non-metric, which has prevented multi-metric learning from generalizing to tasks such as dimensionality reduction and regression in a principled way. We prove that, with appropriate changes, multi-metric learning corresponds to learning the structure of a Riemannian manifold. We then show that this structure gives us a principled way to perform dimensionality reduction and regression according to the learned metrics. Algorithmically, we provide the first practical algorithm for computing geodesics according to the learned metrics, as well as algorithms for computing exponential and logarithmic maps on the Riemannian manifold. Together, these tools let many Euclidean algorithms take advantage of multi-metric learning. We illustrate the approach on regression and dimensionality reduction tasks that involve predicting measurements of the human body from shape data. We introduce the Symmetry Factored Embedding (SFE) and the Symmetry Factored Distance (SFD) as new tools to analyze and represent symmetries in a point set. The SFE provides new coordinates in which symmetry is "factored out," and the SFD is the Euclidean distance in that space. These constructions characterize the space of symmetric correspondences between points -- i.e., orbits. A key observation is that a set of points in the same orbit appears as a clique in a correspondence graph induced by pairwise similarities. As a result, the problem of finding approximate and partial symmetries in a point set reduces to the problem of measuring connectedness in the correspondence graph, a well-studied problem for which spectral methods provide a robust solution. We provide methods for computing the SFE and SFD for extrinsic global symmetries and then extend them to consider partial extrinsic and intrinsic cases. During experiments with difficult examples, we find that the proposed methods can characterize symmetries in inputs with noise, missing data, non-rigid deformations, and complex symmetries, without a priori knowledge of the symmetry group. As such, we believe that it provides a useful tool for automatic shape analysis in applications such as segmentation and stationary point detection. The min-sum k -clustering problem is to partition a metric space (P,d) into k clusters C 1,…,C k ⊆P such that @math is minimized. We show the first efficient construction of a coreset for this problem. Our coreset construction is based on a new adaptive sampling algorithm. With our construction of coresets we obtain two main algorithmic results. The first result is a sublinear-time (4+e)-approximation algorithm for the min-sum k-clustering problem in metric spaces. The running time of this algorithm is @math for any constant k and e, and it is o(n 2) for all k=o(log n log log n). Since the full description size of the input is Θ(n 2), this is sublinear in the input size. The fastest previously known o(log n)-factor approximation algorithm for k>2 achieved a running time of Ω(n k ), and no non-trivial o(n 2)-time algorithm was known before. Our second result is the first pass-efficient data streaming algorithm for min-sum k-clustering in the distance oracle model, i.e., an algorithm that uses poly(log n,k) space and makes 2 passes over the input point set, which arrives in form of a data stream in arbitrary order. It computes an implicit representation of a clustering of (P,d) with cost at most a constant factor larger than that of an optimal partition. Using one further pass, we can assign each point to its corresponding cluster. To develop the coresets, we introduce the concept of α -preserving metric embeddings. Such an embedding satisfies properties that the distance between any pair of points does not decrease and the cost of an optimal solution for the considered problem on input (P,d′) is within a constant factor of the optimal solution on input (P,d). In other words, the goal is to find a metric embedding into a (structurally simpler) metric space that approximates the original metric up to a factor of α with respect to a given problem. We believe that this concept is an interesting generalization of coresets. Recently, manifold learning has been widely exploited in pattern recognition, data analysis, and machine learning. This paper presents a novel framework, called Riemannian manifold learning (RML), based on the assumption that the input high-dimensional data lie on an intrinsically low-dimensional Riemannian manifold. The main idea is to formulate the dimensionality reduction problem as a classical problem in Riemannian geometry, that is, how to construct coordinate charts for a given Riemannian manifold? We implement the Riemannian normal coordinate chart, which has been the most widely used in Riemannian geometry, for a set of unorganized data points. First, two input parameters (the neighborhood size k and the intrinsic dimension d) are estimated based on an efficient simplicial reconstruction of the underlying manifold. Then, the normal coordinates are computed to map the input high-dimensional data into a low- dimensional space. Experiments on synthetic data, as well as real-world images, demonstrate that our algorithm can learn intrinsic geometric structures of the data, preserve radial geodesic distances, and yield regular embeddings. Many algorithms rely critically on being given a good metric over their inputs. For instance, data can often be clustered in many "plausible" ways, and if a clustering algorithm such as K-means initially fails to find one that is meaningful to a user, the only recourse may be for the user to manually tweak the metric until sufficiently good clusters are found. For these and other applications requiring good metrics, it is desirable that we provide a more systematic way for users to indicate what they consider "similar." For instance, we may ask them to provide examples. In this paper, we present an algorithm that, given examples of similar (and, if desired, dissimilar) pairs of points in ℝn, learns a distance metric over ℝn that respects these relationships. Our method is based on posing metric learning as a convex optimization problem, which allows us to give efficient, local-optima-free algorithms. We also demonstrate empirically that the learned metrics can be used to significantly improve clustering performance. We investigate neural network training and generalization using the concept of stiffness. We measure how stiff a network is by looking at how a small gradient step on one example affects the loss on another example. In particular, we study how stiffness varies with 1) class membership, 2) distance between data points (in the input space as well as in latent spaces), 3) training iteration, and 4) learning rate. We empirically study the evolution of stiffness on MNIST, FASHION MNIST, CIFAR-10 and CIFAR-100 using fully-connected and convolutional neural networks. Our results demonstrate that stiffness is a useful concept for diagnosing and characterizing generalization. We observe that small learning rates lead to initial learning of more specific features that do not translate well to improvements on inputs from all classes, whereas high learning rates initially benefit all classes at once. We measure stiffness as a function of distance between data points and observe that higher learning rates induce positive correlation between changes in loss further apart, pointing towards a regularization effect of learning rate. When training on CIFAR-100, the stiffness matrix exhibits a coarse-grained behavior suggestive of the model's awareness of super-class membership.