Matlab code for metric multidimensional scaling with Bregman divergences

نویسندگان

  • Jigang Sun
  • Malcolm Crowe
  • Colin Fyfe
چکیده

This toolbox is an implementation of our recently developed dimensionality reduction methods using multidimensional scaling with Bregman divergences, the LeftSammon, RightSammon, LeftExp and RightExp mappings, as well as Step CCA, in Matlab. We use a simple but effective random-walk strategy to select various parameters for the stochastic gradient descent.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Curvilinear component analysis and Bregman divergences

Curvilinear Component Analysis (CCA) is an interesting flavour of multidimensional scaling. In this paper one version of CCA is proved to be related to the mapping found by a specific Bregman divergence and its stress function is redefined based on this insight, and its parameter (the neighbourhood radius) is explained.

متن کامل

Regularized Optimal Transport and the Rot Mover's Distance

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed regularization based on the Boltzmann-Shannon entropy related to the Kullback...

متن کامل

Metrics Defined by Bregman Divergences †

Bregman divergences are generalizations of the well known Kullback Leibler divergence. They are based on convex functions and have recently received great attention. We present a class of “squared root metrics” based on Bregman divergences. They can be regarded as natural generalization of Euclidean distance. We provide necessary and sufficient conditions for a convex function so that the squar...

متن کامل

Efficient Bregman Range Search

We develop an algorithm for efficient range search when the notion of dissimilarity is given by a Bregman divergence. The range search task is to return all points in a potentially large database that are within some specified distance of a query. It arises in many learning algorithms such as locally-weighted regression, kernel density estimation, neighborhood graph-based algorithms, and in tas...

متن کامل

Topological Data Analysis with Bregman Divergences

Given a finite set in a metric space, the topological analysis generalizes hierarchical clustering using a 1-parameter family of homology groups to quantify connectivity in all dimensions. Going beyond Euclidean distance and really beyond metrics, we show that the tools of topological data analysis also apply when we measure distance with Bregman divergences. While these divergences violate two...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012