Optimal dictionary for least squares representation

03/07/2016
by   Mohammed Rayyan Sheriff, et al.
0

Dictionaries are collections of vectors used for representations of random vectors in Euclidean spaces. Recent research on optimal dictionaries is focused on constructing dictionaries that offer sparse representations, i.e., ℓ_0-optimal representations. Here we consider the problem of finding optimal dictionaries with which representations of samples of a random vector are optimal in an ℓ_2-sense: optimality of representation is defined as attaining the minimal average ℓ_2-norm of the coefficients used to represent the random vector. With the help of recent results on rank-1 decompositions of symmetric positive semidefinite matrices, we provide an explicit description of ℓ_2-optimal dictionaries as well as their algorithmic constructions in polynomial time.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

10/18/2017

A complete characterization of optimal dictionaries for least squares representation

Dictionaries are collections of vectors used for representations of elem...
01/27/2011

A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity

The richness of natural images makes the quest for optimal representatio...
04/23/2018

Towards Learning Sparsely Used Dictionaries with Arbitrary Supports

Dictionary learning is a popular approach for inferring a hidden basis o...
05/25/2011

Multiscale Geometric Methods for Data Sets II: Geometric Multi-Resolution Analysis

Data sets are often modeled as point clouds in R^D, for D large. It is o...
09/04/2019

Optimal translational-rotational invariant dictionaries for images

We provide the construction of a set of square matrices whose translates...
09/07/2009

Sparse image representation by discrete cosine/spline based dictionaries

Mixed dictionaries generated by cosine and B-spline functions are consid...
12/20/2020

Achieving positive rates with predetermined dictionaries

In the first part of the paper we consider binary input channels that ar...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.