Definition In learning systems with kernels, the shape and size of a kernel plays a critical role for accuracy and generalization. Most kernels have a distance metric parameter, which determines the size and shape of the kernel in the sense of a Mahalanobis distance. Advanced kernel learning tune every kernel’s distance metric individually, instead of turning one global distance metric for all ...

we consider the concept of ω-distance on a complete partially ordered g-metric space and prove some common fixed point theorems.

Learning a distance metric from training samples is often a crucial step in machine learning and pattern recognition. Locality, compactness and consistency are considered as the key principles in distance metric learning. However, the existing metric learning methods just consider one or two of them. In this paper, we develop a multi-granularity distance learning technique. First, a new index, ...

The need for appropriate ways to measure the distance or similarity between data is ubiquitous in machine learning, pattern recognition and data mining, but handcrafting such good metrics for specific problems is generally difficult. This has led to the emergence of metric learning, which aims at automatically learning a metric from data and has attracted a lot of interest in machine learning a...

In this paper, we present a novel two-stage metric learning algorithm. We first map each learning instance to a probability distribution by computing its similarities to a set of fixed anchor points. Then, we define the distance in the input data space as the Fisher information distance on the associated statistical manifold. This induces in the input data space a new family of distance metric ...

In this paper, we consider the notion of distance/similarity metric learning method for classification and similarity search for face recognition purposes. We use the theory of filter banks, and Gabor wavelets for extraction of face features in three datasets: the ORL dataset, Yale face dataset, and ATT face dataset, and we compare the recognition performance with Gabor features to discrete Fou...

This paper proposes a boosting-based solution addressing metric learning problems for high-dimensional data. Distance measures have been used as natural measures of (dis)similarity and served as the foundation of various learning methods. The efficiency of distance-based learning methods heavily depends on the chosen distance metric. With increasing dimensionality and complexity of data, howeve...

Manifold Learning learns a low-dimensional embedding of the latent manifold. In this report, we give the definition of distance metric learning, provide the categorization of manifold learning, and describe the essential connection between manifold learning and distance metric learning, with special emphasis on nonlinear manifold learning, including ISOMAP, Laplacian Eigenamp (LE), and Locally ...