155 research outputs found
Fast Approximate Spectral Clustering for Dynamic Networks
Spectral clustering is a widely studied problem, yet its complexity is
prohibitive for dynamic graphs of even modest size. We claim that it is
possible to reuse information of past cluster assignments to expedite
computation. Our approach builds on a recent idea of sidestepping the main
bottleneck of spectral clustering, i.e., computing the graph eigenvectors, by
using fast Chebyshev graph filtering of random signals. We show that the
proposed algorithm achieves clustering assignments with quality approximating
that of spectral clustering and that it can yield significant complexity
benefits when the graph dynamics are appropriately bounded
Variational Quantum Approximate Spectral Clustering for Binary Clustering Problems
In quantum machine learning, algorithms with parameterized quantum circuits
(PQC) based on a hardware-efficient ansatz (HEA) offer the potential for
speed-ups over traditional classical algorithms. While much attention has been
devoted to supervised learning tasks, unsupervised learning using PQC remains
relatively unexplored. One promising approach within quantum machine learning
involves optimizing fewer parameters in PQC than in its classical counterparts,
under the assumption that a sub-optimal solution exists within the Hilbert
space. In this paper, we introduce the Variational Quantum Approximate Spectral
Clustering (VQASC) algorithm - a NISQ-compatible method that requires
optimization of fewer parameters than the system size, N, traditionally
required in classical problems. We present numerical results from both
synthetic and real-world datasets. Furthermore, we propose a descriptor,
complemented by numerical analysis, to identify an appropriate ansatz circuit
tailored for VQASC.Comment: 21 pages, 6 figure
Large Scale Spectral Clustering Using Approximate Commute Time Embedding
Spectral clustering is a novel clustering method which can detect complex
shapes of data clusters. However, it requires the eigen decomposition of the
graph Laplacian matrix, which is proportion to and thus is not
suitable for large scale systems. Recently, many methods have been proposed to
accelerate the computational time of spectral clustering. These approximate
methods usually involve sampling techniques by which a lot information of the
original data may be lost. In this work, we propose a fast and accurate
spectral clustering approach using an approximate commute time embedding, which
is similar to the spectral embedding. The method does not require using any
sampling technique and computing any eigenvector at all. Instead it uses random
projection and a linear time solver to find the approximate embedding. The
experiments in several synthetic and real datasets show that the proposed
approach has better clustering quality and is faster than the state-of-the-art
approximate spectral clustering methods
Fast Spectral Clustering Using Autoencoders and Landmarks
In this paper, we introduce an algorithm for performing spectral clustering
efficiently. Spectral clustering is a powerful clustering algorithm that
suffers from high computational complexity, due to eigen decomposition. In this
work, we first build the adjacency matrix of the corresponding graph of the
dataset. To build this matrix, we only consider a limited number of points,
called landmarks, and compute the similarity of all data points with the
landmarks. Then, we present a definition of the Laplacian matrix of the graph
that enable us to perform eigen decomposition efficiently, using a deep
autoencoder. The overall complexity of the algorithm for eigen decomposition is
, where is the number of data points and is the number of
landmarks. At last, we evaluate the performance of the algorithm in different
experiments.Comment: 8 Pages- Accepted in 14th International Conference on Image Analysis
and Recognitio
Performance Analysis of Spectral Clustering on Compressed, Incomplete and Inaccurate Measurements
Spectral clustering is one of the most widely used techniques for extracting
the underlying global structure of a data set. Compressed sensing and matrix
completion have emerged as prevailing methods for efficiently recovering sparse
and partially observed signals respectively. We combine the distance preserving
measurements of compressed sensing and matrix completion with the power of
robust spectral clustering. Our analysis provides rigorous bounds on how small
errors in the affinity matrix can affect the spectral coordinates and
clusterability. This work generalizes the current perturbation results of
two-class spectral clustering to incorporate multi-class clustering with k
eigenvectors. We thoroughly track how small perturbation from using compressed
sensing and matrix completion affect the affinity matrix and in succession the
spectral coordinates. These perturbation results for multi-class clustering
require an eigengap between the kth and (k+1)th eigenvalues of the affinity
matrix, which naturally occurs in data with k well-defined clusters. Our
theoretical guarantees are complemented with numerical results along with a
number of examples of the unsupervised organization and clustering of image
data
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