Related papers: Weighting vectors for machine learning: numerical …
Extending the `metric spaces' of Lawvere, we study `real metrics', with values in the extended real line. Formally, this ordered set is a symmetric monoidal closed category, and our structures are enriched categories on the latter.…
We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM} and developed the idea further in \cite{AS}. In this paper we study locally $M$-metrizable spaces and the products of $M$-metrizable spaces. Finally we…
Deep learning methods achieve great success recently on many computer vision problems, with image classification and object detection as the prominent examples. In spite of these practical successes, optimization of deep networks remains an…
Vectors of data are at the heart of machine learning and data mining. Recently, vector quantization methods have shown great promise in reducing both the time and space costs of operating on vectors. We introduce a vector quantization…
Quantum coherence and entanglement are fundamental resources in quantum technologies, yet their efficient estimation for unknown states by employing minimal resources in experimental settings remains challenging, particularly in…
Advances in statistical learning theory present the opportunity to develop statistical models of quantum many-body systems exhibiting remarkable predictive power. The potential of such ``theory-thin'' approaches is illustrated with the…
Metric learning aims to learn a highly discriminative model encouraging the embeddings of similar classes to be close in the chosen metrics and pushed apart for dissimilar ones. The common recipe is to use an encoder to extract embeddings…
Support vector machines (SVMs) are special kernel based methods and belong to the most successful learning methods since more than a decade. SVMs can informally be described as a kind of regularized M-estimators for functions and have…
Distance-based outlier detection is widely adopted in many fields, e.g., data mining and machine learning, because it is unsupervised, can be employed in a generic metric space, and does not have any assumptions of data distributions. Data…
Support vector machines (SVMs) have been successful in solving many computer vision tasks including image and video category recognition especially for small and mid-scale training problems. The principle of these non-parametric models is…
We introduce a new nearest-prototype classifier, the prototype vector machine (PVM). It arises from a combinatorial optimization problem which we cast as a variant of the set cover problem. We propose two algorithms for approximating its…
High dimension low sample size statistical analysis is important in a wide range of applications. In such situations, the highly appealing discrimination method, support vector machine, can be improved to alleviate data piling at the…
Similarity metrics are a core component of many information retrieval and machine learning systems. In this work we propose a method capable of learning a similarity metric from data equipped with a binary relation. By considering only the…
The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is…
Classifying points in high dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address classifying points in the $d$-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of…
Galaxy morphology, a key tracer of the evolution of a galaxy's physical structure, has motivated extensive research on machine learning techniques for efficient and accurate galaxy classification. The emergence of quantum computers has…
The support vector machine (SVM) algorithm is well known to the computer learning community for its very good practical results. The goal of the present paper is to study this algorithm from a statistical perspective, using tools of…
Machine learning has played an important role in information retrieval (IR) in recent times. In search engines, for example, query keywords are accepted and documents are returned in order of relevance to the given query; this can be cast…
Support Vector Machines (SVMs) are powerful learners that have led to state-of-the-art results in various computer vision problems. SVMs suffer from various drawbacks in terms of selecting the right kernel, which depends on the image…
We consider a situation where the state of a system is represented by a real-valued vector. Under normal circumstances, the vector is zero, while an event manifests as non-zero entries in this vector, possibly few. Our interest is in the…