Modified Multidimensional Scaling and High Dimensional Clustering
Multidimensional scaling is an important dimension reduction tool in statistics and machine learning. Yet few theoretical results characterizing its statistical performance exist, not to mention any in high dimensions. By considering a unified framework that includes low, moderate and high dimensions, we study multidimensional scaling in the setting of clustering noisy data. Our results suggest that, the classical multidimensional scaling can be modified to further improve the quality of embedded samples, especially when the noise level increases. To this end, we propose {\it modified multidimensional scaling} which applies a nonlinear transformation to the sample eigenvalues. The nonlinear transformation depends on the dimensionality, sample size and moment of noise. We show that modified multidimensional scaling followed by various clustering algorithms can achieve exact recovery, i.e., all the cluster labels can be recovered correctly with probability tending to one. Numerical simulations and two real data applications lend strong support to our proposed methodology.
Code (0)
등록된 구현이 없습니다.
Tasks
ClusteringDimensionality ReductionVocal Bursts Intensity PredictionSimilar Papers 제목 키워드 기반
Exact Cluster Recovery via Classical Multidimensional Scaling
Classical multidimensional scaling is an important dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing th…
ClusteringDimensionality ReductionMultidimensional scaling of two-mode three-way asymmetric dissimilarities: finding archetypal profiles and clustering
Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relati…
Computational EfficiencyConditional Multidimensional Scaling with Incomplete Conditioning Data
Conditional multidimensional scaling seeks for a low-dimensional configuration from pairwise dissimilarities, in the presence of other known features. By taking advantage of available data of the known features, conditio…
Automated regime detection in multidimensional time series data using sliced Wasserstein k-means clustering
Recent work has proposed Wasserstein k-means (Wk-means) clustering as a powerful method to identify regimes in time series data, and one-dimensional asset returns in particular. In this paper, we begin by studying in det…
ClusteringTime SeriesAssessing the impact of dimensionality reduction on clustering performance -- a systematic study
Dimensionality reduction is a critical preprocessing step for clustering high-dimensional data, yet comprehensive evaluation of its impact across diverse methods and data types remains limited. In this study, we systemat…
Dimensionality Reduction