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Statistical depth in abstract metric spaces
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion of...
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Densities of codes of various linearity degrees in translation-invariant metric spaces
We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including (sub)linear...
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Robustness in Metric Spaces over Continuous Quantales and the Hausdorff-Smyth Monad
Generalized metric spaces are obtained by weakening the requirements (e.g., symmetry) on the distance function and by allowing it to take values in...
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Class Representatives Selection in Non-metric Spaces for Nearest Prototype Classification
The nearest prototype classification is a less computationally intensive replacement for the...
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Codes with respect to weighted poset block metric
We study a new family of metrics, weighted poset block metric, which generalizes the weighted coordinates poset metric introduced by Panek and...
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Fast, exact, and parallel-friendly outlier detection algorithms with proximity graph in metric spaces
In many fields, e.g., data mining and machine learning, distance-based outlier detection (DOD) is widely employed to remove noises and find abnormal...
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Metric Learning on Complex Projective Spaces
Shape analysis of landmarks is a fundamental problem in computer vision and multimedia. We propose a family of metrics called Fubini-Study distances...
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Deep Metric Learning
It was mentioned in Chap. 11 that metric learning can be divided into spectral, probabilistic, and deep...
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Pivot selection algorithms in metric spaces: a survey and experimental study
Similarity search in metric spaces is used widely in areas such as multimedia retrieval, data mining, data integration, to name but a few. To...
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Transferable Deep Metric Learning for Clustering
Clustering in high dimension spaces is a difficult task; the usual distance metrics may no longer be appropriate under the curse of dimensionality....
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A family of pairwise multi-marginal optimal transports that define a generalized metric
The Optimal transport (OT) problem is rapidly finding its way into machine learning. Favoring its use are its metric properties. Many problems admit...
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Computability of Subsets of Metric Spaces
We present a survey on computability of subsets of Euclidean space and, more generally, computability concepts on metric spaces and their subsets. In...
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Boundary-restricted metric learning
Metric learning aims to learn a distance metric to properly measure the similarities between pairwise examples. Most existing learning algorithms are...
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Improved Metric Space for Shape Correspondence
Shape correspondence is a fundamental task of finding a map among the elements of a pair of shapes. Particularly, non-rigid shapes add to the...
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Enhancing image retrieval through entropy-based deep metric learning
The increasing demand for effective retrieval from image datasets has been driven by the rapid growth of digital images. Image retrieval is a method...
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Three Methods to Put a Riemannian Metric on Shape Space
In many applications, one is interested in the shape of an object, like the contour of a bone or the trajectory of joints of a tennis player,...
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Signal Spaces
Hilbert spaces of square-integrable functions or square-summable sequences provide a mathematically rigorous framework for many engineering...
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Relational multi-scale metric learning for few-shot knowledge graph completion
Few-shot knowledge graph completion (FKGC) refers to the task of inferring missing facts in a knowledge graph by utilizing a limited number of...
