Massachusetts Institute of Technology Lecturer : Piotr Indyk
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چکیده
The goal is to acquire signals in R that are well approximated by sparse signals with k nonzero components, where k << n. The measurement process can be represented by an m× n matrix A, where m is roughly proportional to k rather than n. The recovery algorithm uses the sketch and a description of the measurement matrix to construct a signal approximation x̂ that has only O(k) nonzero components. The recovery algorithms have the following properties
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Massachusetts Institute of Technology Lecturer : Piotr Indyk
Let x be a vector variable taking values from Zm. We consider a setting where the value of x changes over time through updates of its coordinate values. Every update can be specified in form of a pair (i, a), 1 ≤ i ≤ m and a is an integer, which has a meaning of increasing the value of xi by a. A sequence of such pairs is called a stream in our context. The value of x before the first update is...
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In previous lectures, we have seen streaming algorithms that operate a number of different data types, including numerical, metric, and geometric. Today we will investigate streaming algorithms on graphs. Our model for graph data will be as follows. Given a graph G = (V,E) with |V | = n, we will assume that V is known, and that the edges in E are revealed in arbitrary order (deletions are not s...
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Description of the series-need to check with Bob Prior what it is iv 2005 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.
متن کاملof Technology Lecturer : Piotr Indyk
The goal is to acquire signals in R that are well approximated by sparse signals with k nonzero components, where k << n. The measurement process can be represented by an m× n matrix A, where m is roughly proportional to k rather than n. The recovery algorithm uses the sketch and a description of the measurement matrix to construct a signal approximation x̂ that has only O(k) nonzero components....
متن کاملof Technology Lecturer : Piotr Indyk 6 . 895 : Sketching , Streaming and Sub - linear Space Algorithms
consider the case where x is has exactly k + 1 nonzero entries. Then, Errk(x) = Err 2 k(x) = x (k+1), where x(k+1) represents the smallest of the k + 1 nonzero entries in x. Thus, the formula above implies that for such x, the LP finds an x∗ that is better than the best k-sparse approximation, so clearly x∗ cannot be k-sparse. In practice, it is often not important that x∗ be k-sparse. For exam...
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تاریخ انتشار 2007