Detecting Meaningful Clusters From High-Dimensional Data: A Strongly Consistent Sparse Center-Based Clustering Approach

Chakraborty, Saptarshi; Das, Swagatam

doi:10.1109/tpami.2020.3047489

Cited by 27 publications

(7 citation statements)

References 64 publications

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“…Sebastian et al [55] provided an interesting application of k-means clustering in the characterization of snore signals in the context of upperairway collapse. Chakraborty et al [56] proposed the Lass-weighted k-means algorithm specifically useful for a high-dimensional dataset, such as gene-expression data. Another interesting algorithm was developed by Gondeau et al [57], using object-weighting in kmeans clustering.…”

Section: Clustering Strategiesmentioning

confidence: 99%

Bootstrap–CURE: A Novel Clustering Approach for Sensor Data—An Application to 3D Printing Industry

2022

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The agenda of Industry 4.0 highlights smart manufacturing by making machines smart enough to make data-driven decisions. Large-scale 3D printers, being one of the important pillars in Industry 4.0, are equipped with smart sensors to continuously monitor print processes and make automated decisions. One of the biggest challenges in decision autonomy is to consume data quickly along the process and extract knowledge from the printer, suitable for improving the printing process. This paper presents the innovative unsupervised learning approach, bootstrap–CURE, to decode the sensor patterns and operation modes of 3D printers by analyzing multivariate sensor data. An automatic technique to detect the suitable number of clusters using the dendrogram is developed. The proposed methodology is scalable and significantly reduces computational cost as compared to classical CURE. A distinct combination of the 3D printer’s sensors is found, and its impact on the printing process is also discussed. A real application is presented to illustrate the performance and usefulness of the proposal. In addition, a new state of the art for sensor data analysis is presented.

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Section: Clustering Strategiesmentioning

confidence: 99%

Bootstrap–CURE: A Novel Clustering Approach for Sensor Data—An Application to 3D Printing Industry

2022

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“…Then this transformation of the M matrix makes the expected value of m δ i and m δ j equal whenever objects i and j belong to the same cluster. Using the example considered in (6), we now illustrate Θ in the equation (8) below.…”

Section: Full Alignment Of G-vectorsmentioning

confidence: 99%

“…To detect clusters in high dimensional data, one class of clustering techniques (including, [2], [3], [4], [5], [6], [7], [8], [9]) assumes that information regarding meaningful clusters is contained in a small number of features. These algorithms, often referred to as sparse clustering procedures, rely on "relevant" feature extraction that influences resulting cluster partitions.…”

Section: Introductionmentioning

confidence: 99%

A Hyperparameter-Free, Fast and Efficient Framework to Detect Clusters From Limited Samples Based on Ultra High-Dimensional Features

2022

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Clustering is a challenging problem in machine learning in which one attempts to group N objects into K 0 groups based on P features measured on each object. In this article, we examine the case where N P and K 0 is not known. Clustering in such high dimensional, small sample size settings has numerous applications in biology, medicine, the social sciences, clinical trials, and other scientific and experimental fields. Whereas most existing clustering algorithms either require the number of clusters to be known a priori or are sensitive to the choice of tuning parameters, our method does not require the prior specification of K 0 or any tuning parameters. This represents an important advantage for our method because training data are not available in the applications we consider (i.e., in unsupervised learning problems). Without training data, estimating K 0 and other hyperparameters-and thus applying alternative clustering algorithms-can be difficult and lead to inaccurate results. Our method is based on a simple transformation of the Gram matrix and application of the strong law of large numbers to the transformed matrix. If the correlation between features decays as the number of features grows, we show that the transformed feature vectors concentrate tightly around their respective cluster expectations in a low-dimensional space. This result simplifies the detection and visualization of the unknown cluster configuration. We illustrate the algorithm by applying it to 32 benchmarked microarray datasets, each containing thousands of genomic features measured on a relatively small number of tissue samples. Compared to 21 other commonly used clustering methods, we find that the proposed algorithm is faster and twice as accurate in determining the "best" cluster configuration.

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“…Lloyd's algorithm (Lloyd, 1982) is a popular coordinate descent algorithm to optimize (17). Despite its wide-spread application, k-means is notoriously unsuitable for highdimensional datasets, where only a handful of features are relevant in revealing the cluster structure of the dataset (Chakraborty and Das, 2020). To tackle this problem, researchers have often resorted to the concept of feature weighting (De Amorim, 2016).…”

Section: Application To Clusteringmentioning

confidence: 99%

t-Entropy: A New Measure of Uncertainty with Some Applications

Chakraborty¹,

Paul²,

Das³

2021

Preprint

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The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning. This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically show that the proposed t-entropy satisfies the prominent axiomatic properties of an entropy measure. We demonstrate an application of the proposed entropy measure for multi-level thresholding of images. We also propose the entropic-loss as a measure of the divergence between two probability distributions, which leads to robust estimators in the context of parametric statistical inference. The consistency and asymptotic breakdown point of the proposed estimator are mathematically analyzed. Finally, we also show an application of the t-entropy to feature weighted data clustering.

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Detecting Meaningful Clusters From High-Dimensional Data: A Strongly Consistent Sparse Center-Based Clustering Approach

Cited by 27 publications

References 64 publications

Bootstrap–CURE: A Novel Clustering Approach for Sensor Data—An Application to 3D Printing Industry

Bootstrap–CURE: A Novel Clustering Approach for Sensor Data—An Application to 3D Printing Industry

A Hyperparameter-Free, Fast and Efficient Framework to Detect Clusters From Limited Samples Based on Ultra High-Dimensional Features

t-Entropy: A New Measure of Uncertainty with Some Applications

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