Incremental Spectral Sparsification for Large-Scale Graph-Based Semi-Supervised Learning

01/21/2016
by   Daniele Calandriello, et al.
0

While the harmonic function solution performs well in many semi-supervised learning (SSL) tasks, it is known to scale poorly with the number of samples. Recent successful and scalable methods, such as the eigenfunction method focus on efficiently approximating the whole spectrum of the graph Laplacian constructed from the data. This is in contrast to various subsampling and quantization methods proposed in the past, which may fail in preserving the graph spectra. However, the impact of the approximation of the spectrum on the final generalization error is either unknown, or requires strong assumptions on the data. In this paper, we introduce Sparse-HFS, an efficient edge-sparsification algorithm for SSL. By constructing an edge-sparse and spectrally similar graph, we are able to leverage the approximation guarantees of spectral sparsification methods to bound the generalization error of Sparse-HFS. As a result, we obtain a theoretically-grounded approximation scheme for graph-based SSL that also empirically matches the performance of known large-scale methods.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/12/2023

Efficiently Learning the Graph for Semi-supervised Learning

Computational efficiency is a major bottleneck in using classic graph-ba...
research
09/27/2020

Analysis of label noise in graph-based semi-supervised learning

In machine learning, one must acquire labels to help supervise a model t...
research
12/04/2019

Large-Scale Semi-Supervised Learning via Graph Structure Learning over High-Dense Points

We focus on developing a novel scalable graph-based semi-supervised lear...
research
09/13/2016

Mapping the Similarities of Spectra: Global and Locally-biased Approaches to SDSS Galaxy Data

We apply a novel spectral graph technique, that of locally-biased semi-s...
research
07/31/2023

Semi-Supervised Laplacian Learning on Stiefel Manifolds

Motivated by the need to address the degeneracy of canonical Laplace lea...
research
10/16/2017

Large Scale Graph Learning from Smooth Signals

Graphs are a prevalent tool in data science, as they model the inherent ...
research
02/26/2021

Graph-based Semi-supervised Learning: A Comprehensive Review

Semi-supervised learning (SSL) has tremendous value in practice due to i...

Please sign up or login with your details

Forgot password? Click here to reset