arXiv subjects

Sourav Chakrabarty

Publications and source records attributed to Sourav Chakrabarty.

3 recordsLinked to original sources

arXiv2026

Two-stage Ensemble Clustering of Functional Data Using Random Projections

We propose a computationally simple framework for clustering functional data based on Gaussian-process-generated random projections. In this approach, each curve is first projected onto a large collection of independent Gaussian process realizations. The resulting high-dimensional representations are clustered using the Mean Absolute Difference of Distances (MADD), a dissimilarity measure well suited for high-dimensional settings. A population-level analysis of this dissimilarity provides insight into how random projections help capture distributional differences between functional populations. We introduce a second stage of clustering to additionally leverage on data-driven projection directions. Thus, in Stage I, an initial clustering is obtained using a set of prespecified projection families. In Stage II, this partition is refined by constructing Gaussian random projections based on an estimated covariance operator that uses the first stage of cluster labels. Finally, a normalized cost function is used to select the optimal clustering among candidate solutions. The proposed clustering algorithm is broadly applicable to diverse functional data regimes including irregular and partially observed data. Through extensive simulations and real-data applications, we show that the proposed method achieves a high degree of accuracy and outperforms many of the state-of-the-art methods across a wide range of functional data settings.

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arXiv2025

Consistent detection and estimation of multiple structural changes in functional data: unsupervised and supervised approaches

We develop algorithms for detecting multiple changepoints in functional data when the number of changepoints is unknown (unsupervised case), when it is specified apriori (supervised case), and when certain bounds are available (semi-supervised case). These algorithms utilize the maximum mean discrepancy (MMD) measure between distributions on Hilbert spaces. We develop an oracle analysis of the changepoint detection problem which reveals an interesting relationship between the true changepoint locations and the local maxima of the oracle MMD curve. The proposed algorithms are shown to detect general distributional changes by exploiting this connection. In the unsupervised case, we test the significance of a potential changepoint and establish its consistency under the single changepoint setting. We investigate the strong consistency of the changepoint estimators in both single and multiple changepoint settings. In both supervised and semi-supervised scenarios, we include a step to merge consecutive groups that are similar to appropriately utilize the prior information about the number of changepoints. In the supervised scenario, the algorithm satisfies an order-preserving property: the estimated changepoints are contained in the true set of changepoints in the underspecified case, while they contain the true set under overspecification. We evaluate the performance of the algorithms on a variety of datasets demonstrating the superiority of the proposed algorithms compared to some of the existing methods.

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arXiv2025

Near-perfect Clustering Based on Recursive Binary Splitting Using Max-MMD

We develop novel clustering algorithms for functional data when the number of clusters $K$ is unknown and also when it is prefixed. These algorithms are developed based on the Maximum Mean Discrepancy (MMD) measure between two sets of observations. The algorithms recursively use a binary splitting strategy to partition the dataset into two subgroups such that they are maximally separated in terms of an appropriate weighted MMD measure. When $K$ is unknown, the proposed clustering algorithm has an additional step to check whether a group of observations obtained by the binary splitting technique consists of observations from a single population. We also obtain a bonafide estimator of $K$ using this algorithm. When $K$ is prefixed, a modification of the previous algorithm is proposed which consists of an additional step of merging subgroups which are similar in terms of the weighted MMD distance. The theoretical properties of the proposed algorithms are investigated in an oracle scenario that requires the knowledge of the empirical distributions of the observations from different populations involved. In this setting, we prove that the algorithm proposed when $K$ is unknown achieves perfect clustering while the algorithm proposed when $K$ is prefixed has the perfect order preserving (POP) property. Extensive real and simulated data analyses using a variety of models having location difference as well as scale difference show near-perfect clustering performance of both the algorithms which improve upon the state-of-the-art clustering methods for functional data.

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