Smoothness of Schatten Norms and Sliding-Window Matrix Streams

03/15/2021
by   Robert Krauthgamer, et al.
0

Large matrices are often accessed as a row-order stream. We consider the setting where rows are time-sensitive (i.e. they expire), which can be described by the sliding-window row-order model, and provide the first (1+ϵ)-approximation of Schatten p-norms in this setting. Our main technical contribution is a proof that Schatten p-norms in row-order streams are smooth, and thus fit the smooth-histograms technique of Braverman and Ostrovsky (FOCS 2007) for sliding-window streams.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
05/10/2018

Numerical Linear Algebra in the Sliding Window Model

We initiate the study of numerical linear algebra in the sliding window ...
research
11/07/2017

SWOOP: Top-k Similarity Joins over Set Streams

We provide efficient support for applications that aim to continuously f...
research
05/10/2020

Approaching Optimal Duplicate Detection in a Sliding Window

Duplicate detection is the problem of identifying whether a given item h...
research
08/06/2022

Implementing Window Functions in a Column-Store with Late Materialization (Extended Version)

A window function is a generalization of the aggregation operation. Unli...
research
10/26/2018

Sub-O(log n) Out-of-Order Sliding-Window Aggregation

Sliding-window aggregation summarizes the most recent information in a d...
research
07/11/2019

Schatten Norms in Matrix Streams: Hello Sparsity, Goodbye Dimension

The spectrum of a matrix contains important structural information about...
research
09/18/2018

MNIST Dataset Classification Utilizing k-NN Classifier with Modified Sliding Window Metric

This paper evaluates the performance of the K-nearest neighbor classific...

Please sign up or login with your details

Forgot password? Click here to reset