DMS Statistics and Data Science Seminar

Speaker: Marzia A. Cremona (Dept. Operations and Decision Systems; Université Laval; Québec, Canada)

Title: Local clustering and motif discovery of functional data

Abstract: Recent evolution in data acquisition technologies enabled the generation of high-dimensional, complex data in several research areas – in the sciences and engineering, among other disciplines. Increasingly sophisticated statistical and computational methods are needed in order to analyze these data. Functional data analysis (FDA) can be broadly employed to analyze functional data, i.e., data that vary over a continuum and can be naturally viewed as smooth curves or surfaces, exploiting information in their shapes.

In this talk, I will present probabilistic 𝐾-mean with local alignment (probKMA, [1]), an unsupervised learning method to locally cluster a set of misaligned curves and to address the problem of discovering functional motifs, i.e. typical “shapes” or “patterns” that may recur several times along and across a set of curves, capturing important local characteristics of these curves. After demonstrating the performance of the method on simulated data and showing how it generalizes other clustering methods for functional data, I will present three applications to the analysis of functional data from different fields. First, I will apply probKMA to discover functional motifs in “Omics” signals related to mutagenesis and genome dynamics. Second, I will employ probKMA as a probabilistic clustering method to group COVID-19 death curves of the different Italian regions during the first wave of the pandemic. Finally, I will present a generalization of probKMA and its application to the discovery and characterization of functional motifs in stock market prices [2].

[1] Cremona, Chiaromonte (2023) Probabilistic K-means with local alignment for clustering and motif discovery in functional data. Journal of Computational and Graphical Statistics 32(3): 1119-1130.

[2] Cremona, Doroshenko, Severino (2023) Functional motif discovery in stock market prices. SSRN 4642040.