The main theme of this paper is to develop a novel eigenvalue optimization framework for learning a Mahalanobis metric. Within this context, we introduce a novel metric learning approach called DML-eig which is shown to be equivalent to a well-known eigenvalue optimization problem called minimizing the maximal eigenvalue of a symmetric matrix (Overton, 1988; Lewis and Overton, 1996). Moreover, ...

We compare techniques for embedding a data set into Euclidean space under different notions of proximity constraints.

Vectored data frequently occur in a variety of fields, which are easy to handle since they can be mathematically abstracted as points residing in a Euclidean space. An appropriate distance metric in the data space is quite demanding for a great number of applications. In this paper, we pose robust and tractable metric learning under pairwise constraints that are expressed as similarity judgemen...

1 Distance metrics and similarity measures 2 1.1 Distance metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Vector norm and metric . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 The `p norm and `p metric . . . . . . . . . . . . . . . . . . . . . 4 1.4 Distance metric learning . . . . . . . . . . . . . . . . . . . . . . . 7 1.5 The mean as a similarity measure . . . . . . ...

Many real-world networks are described by both connectivity information and features for every node. To better model and understand these networks, we present structure preserving metric learning (SPML), an algorithm for learning a Mahalanobis distance metric from a network such that the learned distances are tied to the inherent connectivity structure of the network. Like the graph embedding a...

We present Deep Stochastic Neighbor Compression (DSNC), a framework to compress training data for instance-based methods (such as k-nearest neighbors). We accomplish this by inferring a smaller set of pseudo-inputs in a new feature space learned by a deep neural network. Our framework can equivalently be seen as jointly learning a nonlinear distance metric (induced by the deep feature space) an...

There has been much recent attention to the problem of learning an appropriate distance metric, using class labels or other side information. Some proposed algorithms are iterative and computationally expensive. In this paper, we show how to solve one of these methods with a closed-form solution, rather than using semidefinite programming. We provide a new problem setup in which the algorithm p...

The diameter of a cluster is the maximum intracluster distance between pairs of instances within the same cluster, and the split of a cluster is the minimum distance between instances within the cluster and instances outside the cluster. Given a few labeled instances, this paper includes two aspects. First, we present a simple and fast clustering algorithm with the following property: if the ra...

2 Distance metrics and similarity measures 2 2.1 Distance metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Vector norm and metric . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 The `p norm and `p metric . . . . . . . . . . . . . . . . . . . . . 3 2.4 Distance metric learning . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 The mean as a similarity measure . . . . . . ...

in this paper, we prove the existence of fixed point for chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. the main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.