Related papers: Metric Learning on Manifolds

Deep networks are successfully used as classification models yielding state-of-the-art results when trained on a large number of labeled samples. These models, however, are usually much less suited for semi-supervised problems because of…

In this paper, we propose a point cloud classification method based on graph neural network and manifold learning. Different from the conventional point cloud analysis methods, this paper uses manifold learning algorithms to embed point…

Understanding how explicit theoretical features are encoded in opaque neural systems is a central challenge now common to neuroscience and AI. We introduce Metric Learning Encoding Models (MLEMs) to address this challenge most directly as a…

We introduce an algorithm for computing geodesics on sampled manifolds that relies on simulation of quantum dynamics on a graph embedding of the sampled data. Our approach exploits classic results in semiclassical analysis and the…

In recent years it has become popular to study machine learning problems in a setting of ordinal distance information rather than numerical distance measurements. By ordinal distance information we refer to binary answers to distance…

Classical vector analysis is the predominant formalism used by engineers of computational electromagnetism, despite the fact that manifold as a theoretical concept has existed for a century. This paper discusses the benefits of manifolds…

Modern sample points in many applications no longer comprise real vectors in a real vector space but sample points of much more complex structures, which may be represented as points in a space with a certain underlying geometric structure,…

With the emergence of deep learning, metric learning has gained significant popularity in numerous machine learning tasks dealing with complex and large-scale datasets, such as information retrieval, object recognition and recommendation…

Non-Euclidean data is frequently encountered across different fields, yet there is limited literature that addresses the fundamental challenge of training neural networks with manifold representations as outputs. We introduce the trick…

Knowledge transfer from large teacher models to smaller student models has recently been studied for metric learning, focusing on fine-grained classification. In this work, focusing on instance-level image retrieval, we study an asymmetric…

Embedding complex objects as vectors in low dimensional spaces is a longstanding problem in machine learning. We propose in this work an extension of that approach, which consists in embedding objects as elliptical probability…

Learning representations on Grassmann manifolds is popular in quite a few visual recognition tasks. In order to enable deep learning on Grassmann manifolds, this paper proposes a deep network architecture by generalizing the Euclidean…

Consider an i.i.d. sample from an unknown density function supported on an unknown manifold embedded in a high dimensional Euclidean space. We tackle the problem of learning a distance between points, able to capture both the geometry of…

Euclidean distance matrices (EDM) are matrices of squared distances between points. The definition is deceivingly simple: thanks to their many useful properties they have found applications in psychometrics, crystallography, machine…

Graph comparison plays a major role in many network applications. We often need a similarity metric for comparing networks according to their structural properties. Various network features - such as degree distribution and clustering…

Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learning is typically applied with the assist of side-information provided by experts,…

Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…

We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…

We study the problem of supervised learning a metric space under discriminative constraints. Given a universe $X$ and sets ${\cal S}, {\cal D}\subset {X \choose 2}$ of similar and dissimilar pairs, we seek to find a mapping $f:X\to Y$, into…

Complex-valued data is ubiquitous in signal and image processing applications, and complex-valued representations in deep learning have appealing theoretical properties. While these aspects have long been recognized, complex-valued deep…