We consider methods for quantifying the similarity of vertices in networks. We propose a measure of similarity based on the concept that two vertices are similar if their immediate neighbors in the network are themselves similar. This leads to a self-consistent matrix formulation of similarity that can be evaluated iteratively using only a knowledge of the adjacency matrix of the network. We te...

Spectral clustering refers to a class of recent techniques which rely on the eigenstructure of a similarity matrix to partition points into disjoint clusters, with points in the same cluster having high similarity and points in different clusters having low similarity. In this chapter, we introduce the main concepts and algorithms together with recent advances in learning the similarity matrix ...

We investigate task clustering for deep-learning based multi-task and few-shot learning in a many-task setting. We propose a new method to measure task similarities with cross-task transfer performance matrix for the deep learning scenario. Although this matrix provides us critical information regarding similarity between tasks, its asymmetric property and unreliable performance scores can affe...

Retrieval image by shape similarity, given a template shape is particularly challenging, owning to the difficulty to derive a similarity measurement that closely conforms to the common perception of similarity by humans. In this paper, a new method for the representation and comparison of shapes is present which is based on the shape matrix and snake model. It is scaling, rotation, translation ...

considering the nonlinear hyperelastic or viscoelastic nature of soft tissues has an important effect on modeling results. in medicalapplications, accounting nonlinearity begets an ill posed problem, due to absence of external force. myocardium can be consideredas a hyperelastic material, and variational approaches are proposed to estimate stiffness matrix, which take into account the linearand...

Many emerging applications formulate nonpositive semidefinite similarity matrices, and hence cannot fit into the framework of kernel machines. A popular approach to this problem is to transform the spectrum of the similarity matrix so as to generate a positive semidefinite kernel matrix. In this paper, we present an analytical framework to explore four representative transformation methods: den...

Explicitly or implicitly, most of dimensionality reduction methods need to determine which samples are neighbors and the similarity between the neighbors in the original highdimensional space. The projection matrix is then learned on the assumption that the neighborhood information (e.g., the similarity) is known and fixed prior to learning. However, it is difficult to precisely measure the int...

Learning an appropriate (dis)similarity function from the available data is a central problem in machine learning, since the success of many machine learning algorithms critically depends on the choice of a similarity function to compare examples. Despite many approaches to similarity metric learning that have been proposed, there has been little theoretical study on the links between similarit...

We propose a new musical audio search method based on audio signal matching that can cope with key and tempo variations. The method employs the self-similarity matrix of an audio signal to represent a key-invariant structure of musical audio. And, we use dynamic programming (DP) matching of self-similarity matrices to deal with time variations. However, conventional DP-based sequence matching m...