Parallel Computation of Multi-Slice Clustering of Third-Order Tensors
- URL: http://arxiv.org/abs/2309.17383v1
- Date: Fri, 29 Sep 2023 16:38:51 GMT
- Title: Parallel Computation of Multi-Slice Clustering of Third-Order Tensors
- Authors: Dina Faneva Andriantsiory, Camille Coti, Joseph Ben Geloun, Mustapha
Lebbah
- Abstract summary: We devise parallel algorithms to compute the Multi-Slice Clustering (MSC) for 3rd-order tensors.
We show that our parallel scheme outperforms sequential computing and allows for the scalability of the MSC method.
- Score: 0.08192907805418585
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Machine Learning approaches like clustering methods deal with massive
datasets that present an increasing challenge. We devise parallel algorithms to
compute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method
is based on spectral analysis of the tensor slices and works independently on
each tensor mode. Such features fit well in the parallel paradigm via a
distributed memory system. We show that our parallel scheme outperforms
sequential computing and allows for the scalability of the MSC method.
Related papers
- An Efficient Algorithm for Clustered Multi-Task Compressive Sensing [60.70532293880842]
Clustered multi-task compressive sensing is a hierarchical model that solves multiple compressive sensing tasks.
The existing inference algorithm for this model is computationally expensive and does not scale well in high dimensions.
We propose a new algorithm that substantially accelerates model inference by avoiding the need to explicitly compute these covariance matrices.
arXiv Detail & Related papers (2023-09-30T15:57:14Z) - On the Power of SVD in the Stochastic Block Model [6.661713888517129]
spectral-based dimensionality reduction tools, such as PCA or SVD, improve the performance of clustering algorithms in many applications.
We show that, in the symmetric setting, vanilla-SVD algorithm recovers all clusters correctly.
arXiv Detail & Related papers (2023-09-27T00:04:27Z) - Low-Rank Multitask Learning based on Tensorized SVMs and LSSVMs [65.42104819071444]
Multitask learning (MTL) leverages task-relatedness to enhance performance.
We employ high-order tensors, with each mode corresponding to a task index, to naturally represent tasks referenced by multiple indices.
We propose a general framework of low-rank MTL methods with tensorized support vector machines (SVMs) and least square support vector machines (LSSVMs)
arXiv Detail & Related papers (2023-08-30T14:28:26Z) - Instance-Optimal Cluster Recovery in the Labeled Stochastic Block Model [79.46465138631592]
We devise an efficient algorithm that recovers clusters using the observed labels.
We present Instance-Adaptive Clustering (IAC), the first algorithm whose performance matches these lower bounds both in expectation and with high probability.
arXiv Detail & Related papers (2023-06-18T08:46:06Z) - Multi-View Clustering via Semi-non-negative Tensor Factorization [120.87318230985653]
We develop a novel multi-view clustering based on semi-non-negative tensor factorization (Semi-NTF)
Our model directly considers the between-view relationship and exploits the between-view complementary information.
In addition, we provide an optimization algorithm for the proposed method and prove mathematically that the algorithm always converges to the stationary KKT point.
arXiv Detail & Related papers (2023-03-29T14:54:19Z) - DBSCAN of Multi-Slice Clustering for Third-Order Tensors [0.0]
We propose an extension algorithm called MSC-DBSCAN to extract the different clusters of slices that lie in the different subspaces from the data.
Our algorithm uses the same input as the MSC algorithm and can find the same solution for rank-one tensor data as MSC.
arXiv Detail & Related papers (2023-03-14T10:18:31Z) - Multiway clustering of 3-order tensor via affinity matrix [0.0]
We propose a new method of multiway clustering for 3-order tensors via affinity matrix (MCAM)
Based on a notion of similarity between the tensor slices and the spread of information of each slice, our model builds an affinity/similarity matrix on which we apply advanced clustering methods.
MCAM achieves competitive results compared with other known algorithms on synthetics and real datasets.
arXiv Detail & Related papers (2023-03-14T10:02:52Z) - Tensorized LSSVMs for Multitask Regression [48.844191210894245]
Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement.
New MTL is proposed by leveraging low-rank tensor analysis and Least Squares Support Vectorized Least Squares Support Vectorized tLSSVM-MTL.
arXiv Detail & Related papers (2023-03-04T16:36:03Z) - Multi-Slice Clustering for 3-order Tensor Data [0.12891210250935145]
Several methods of triclustering of three dimensional data require the specification of the cluster size in each dimension.
We propose a new method, namely the multi-slice clustering (MSC) for a 3-order tensor data set.
The effectiveness of our algorithm is shown on both synthetic and real-world data sets.
arXiv Detail & Related papers (2021-09-22T15:49:48Z) - Exact Clustering in Tensor Block Model: Statistical Optimality and
Computational Limit [10.8145995157397]
High-order clustering aims to identify heterogeneous substructure in multiway dataset.
Non- computation and nature of the problem poses significant challenges in both statistics and statistics.
arXiv Detail & Related papers (2020-12-18T00:48:27Z) - Kernel learning approaches for summarising and combining posterior
similarity matrices [68.8204255655161]
We build upon the notion of the posterior similarity matrix (PSM) in order to suggest new approaches for summarising the output of MCMC algorithms for Bayesian clustering models.
A key contribution of our work is the observation that PSMs are positive semi-definite, and hence can be used to define probabilistically-motivated kernel matrices.
arXiv Detail & Related papers (2020-09-27T14:16:14Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.