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 .
@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.