Related papers: Neural Bregman Divergences for Distance Learning

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…

We introduce a neural implicit framework that exploits the differentiable properties of neural networks and the discrete geometry of point-sampled surfaces to approximate them as the level sets of neural implicit functions. To train a…

Random walk based node embedding algorithms learn vector representations of nodes by optimizing an objective function of node embedding vectors and skip-bigram statistics computed from random walks on the network. They have been applied to…

By analogy to the terminology of curved exponential families in statistics, we define curved Bregman divergences as Bregman divergences restricted to non-affine parameter subspaces and sub-dimensional Bregman divergences when the…

In many applications involving multi-media data, the definition of similarity between items is integral to several key tasks, e.g., nearest-neighbor retrieval, classification, and recommendation. Data in such regimes typically exhibits…

Modern machine learning algorithms have been adopted in a range of signal-processing applications spanning computer vision, natural language processing, and artificial intelligence. Many relevant problems involve subspace-structured…

Deep metric learning (DML) is a popular approach for images retrieval, solving verification (same or not) problems and addressing open set classification. Arguably, the most common DML approach is with triplet loss, despite significant…

Metric learning aims to construct an embedding where two extracted features corresponding to the same identity are likely to be closer than features from different identities. This paper presents a method for learning such a feature space…

Although recovering an Euclidean distance matrix from noisy observations is a common problem in practice, how well this could be done remains largely unknown. To fill in this void, we study a simple distance matrix estimate based upon the…

The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as…

Distance metric learning has attracted a lot of interest for solving machine learning and pattern recognition problems over the last decades. In this work we present a simple approach based on concepts from statistical physics to learn…

Distance measuring is a very important task in digital geometry and digital image processing. Due to our natural approach to geometry we think of the set of points that are equally far from a given point as a Euclidean circle. Using the…

Regression with non-Euclidean responses -- e.g., probability distributions, networks, symmetric positive-definite matrices, and compositions -- has become increasingly important in modern applications. In this paper, we propose deep…

In this paper, we generalize the notions of centroids and barycenters to the broad class of information-theoretic distortion measures called Bregman divergences. Bregman divergences are versatile, and unify quadratic geometric distances…

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal…

In recent years, the crucial importance of metrics in machine learning algorithms has led to an increasing interest for optimizing distance and similarity functions. Most of the state of the art focus on learning Mahalanobis distances…

Deep metric learning algorithms have been utilized to learn discriminative and generalizable models which are effective for classifying unseen classes. In this paper, a novel noise tolerant deep metric learning algorithm is proposed. The…

Neural networks may naturally favor distance-based representations, where smaller activations indicate closer proximity to learned prototypes. This contrasts with intensity-based approaches, which rely on activation magnitudes. To test this…

Recently, a new distance has been introduced for the graphs of two point-to-set operators, one of which is maximally monotone. When both operators are the subdifferential of a proper lower semicontinuous convex function, this distance…

This paper presents a new deep regression model, which we call DeepDistance, for cell detection in images acquired with inverted microscopy. This model considers cell detection as a task of finding most probable locations that suggest cell…