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

Area of Science:

• Machine Learning
• Data Mining
• Computational Statistics

Background:

• Feature weighting is crucial for high-dimensional clustering to identify important variables.
• Existing methods often lack feature selection or are computationally complex, deviating from simple heuristics like Lloyd's algorithm.

Purpose of the Study:

• To propose a simple and efficient sparse clustering algorithm for high-dimensional data.
• To introduce a method that integrates feature selection directly into the k-means framework.

Main Methods:

• Developed the Lasso Weighted k-means (LW-k-means) algorithm, incorporating an l1 regularization term for feature selection.
• Designed a block-coordinate descent algorithm for optimization, achieving time-complexity similar to Lloyd's method.
• Established the strong consistency of the LW-k-means procedure.

Main Results:

• LW-k-means demonstrated competitive performance against baseline and state-of-the-art methods on synthetic and real-life datasets.
• The algorithm achieved high clustering accuracy.
• LW-k-means showed significant improvements in computational time compared to other sparse clustering techniques.

Conclusions:

• LW-k-means offers a computationally efficient and accurate approach for high-dimensional clustering with integrated feature selection.
• The theoretical analysis of strong consistency provides a robust foundation for the algorithm's reliability.
• LW-k-means is a promising alternative for analyzing large, high-dimensional datasets where feature importance varies.