Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures

• URL: http://arxiv.org/abs/2304.11901v2
• Date: Wed, 26 Apr 2023 08:29:49 GMT
• Title: Unsupervised Machine Learning to Classify the Confinement of Waves in Periodic Superstructures
• Authors: Marek Kozo\v{n}, Rutger Schrijver, Matthias Schlottbom, Jaap J.W. van der Vegt, and Willem L. Vos
• Abstract summary: We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We employ unsupervised machine learning to enhance the accuracy of our recently presented scaling method for wave confinement analysis [1]. We employ the standard k-means++ algorithm as well as our own model-based algorithm. We investigate cluster validity indices as a means to find the correct number of confinement dimensionalities to be used as an input to the clustering algorithms. Subsequently, we analyze the performance of the two clustering algorithms when compared to the direct application of the scaling method without clustering. We find that the clustering approach provides more physically meaningful results, but may struggle with identifying the correct set of confinement dimensionalities. We conclude that the most accurate outcome is obtained by first applying the direct scaling to find the correct set of confinement dimensionalities and subsequently employing clustering to refine the results. Moreover, our model-based algorithm outperforms the standard k-means++ clustering.

Related papers

• Self-Supervised Graph Embedding Clustering [70.36328717683297]
  K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. We propose a unified framework that integrates manifold learning with K-means, resulting in the self-supervised graph embedding framework.
  arXiv  Detail & Related papers  (2024-09-24T08:59:51Z)
• Fuzzy K-Means Clustering without Cluster Centroids [21.256564324236333]
  Fuzzy K-Means clustering is a critical technique in unsupervised data analysis. This paper proposes a novel Fuzzy textitK-Means clustering algorithm that entirely eliminates the reliance on cluster centroids.
  arXiv  Detail & Related papers  (2024-04-07T12:25:03Z)
• From Large to Small Datasets: Size Generalization for Clustering Algorithm Selection [12.993073967843292]
  We study a problem in a semi-supervised setting, with an unknown ground-truth clustering. We introduce a notion of size generalization for clustering algorithm accuracy. We use a subsample of as little as 5% of the data to identify which algorithm is best on the full dataset.
  arXiv  Detail & Related papers  (2024-02-22T06:53:35Z)
• Rethinking k-means from manifold learning perspective [122.38667613245151]
  We present a new clustering algorithm which directly detects clusters of data without mean estimation. Specifically, we construct distance matrix between data points by Butterworth filter. To well exploit the complementary information embedded in different views, we leverage the tensor Schatten p-norm regularization.
  arXiv  Detail & Related papers  (2023-05-12T03:01:41Z)
• An enhanced method of initial cluster center selection for K-means algorithm [0.0]
  We propose a novel approach to improve initial cluster selection for K-means algorithm. The Convex Hull algorithm facilitates the computing of the first two centroids and the remaining ones are selected according to the distance from previously selected centers. We obtained only 7.33%, 7.90%, and 0% clustering error in Iris, Letter, and Ruspini data respectively.
  arXiv  Detail & Related papers  (2022-10-18T00:58:50Z)
• K-ARMA Models for Clustering Time Series Data [4.345882429229813]
  We present an approach to clustering time series data using a model-based generalization of the K-Means algorithm. We show how the clustering algorithm can be made robust to outliers using a least-absolute deviations criteria. We perform experiments on real data which show that our method is competitive with other existing methods for similar time series clustering tasks.
  arXiv  Detail & Related papers  (2022-06-30T18:16:11Z)
• Gradient Based Clustering [72.15857783681658]
  We propose a general approach for distance based clustering, using the gradient of the cost function that measures clustering quality. The approach is an iterative two step procedure (alternating between cluster assignment and cluster center updates) and is applicable to a wide range of functions.
  arXiv  Detail & Related papers  (2022-02-01T19:31:15Z)
• A sampling-based approach for efficient clustering in large datasets [0.8952229340927184]
  We propose a simple and efficient clustering method for high-dimensional data with a large number of clusters. Our contribution is substantially more efficient than k-means as it does not require an all to all comparison of data points and clusters.
  arXiv  Detail & Related papers  (2021-12-29T19:15:20Z)
• Estimating leverage scores via rank revealing methods and randomization [50.591267188664666]
  We study algorithms for estimating the statistical leverage scores of rectangular dense or sparse matrices of arbitrary rank. Our approach is based on combining rank revealing methods with compositions of dense and sparse randomized dimensionality reduction transforms.
  arXiv  Detail & Related papers  (2021-05-23T19:21:55Z)
• Scalable Hierarchical Agglomerative Clustering [65.66407726145619]
  Existing scalable hierarchical clustering methods sacrifice quality for speed. We present a scalable, agglomerative method for hierarchical clustering that does not sacrifice quality and scales to billions of data points.
  arXiv  Detail & Related papers  (2020-10-22T15:58:35Z)
• Differentially Private Clustering: Tight Approximation Ratios [57.89473217052714]
  We give efficient differentially private algorithms for basic clustering problems. Our results imply an improved algorithm for the Sample and Aggregate privacy framework. One of the tools used in our 1-Cluster algorithm can be employed to get a faster quantum algorithm for ClosestPair in a moderate number of dimensions.
  arXiv  Detail & Related papers  (2020-08-18T16:22:06Z)

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.