J. D. Tucker | Searcharxiv

arXiv2025

Elastic Shape Analysis of Movement Data

Osteoarthritis (OA) is a highly prevalent degenerative joint disease, and the knee is the most commonly affected joint. Biomechanical factors, particularly forces exerted during walking, are often measured in modern studies of knee joint injury and OA, and understanding the relationship among biomechanics, clinical profiles, and OA has high clinical relevance. Biomechanical forces are typically represented as curves over time, but a standard practice in biomechanics research is to summarize these curves by a small number of discrete values (or landmarks). The objective of this work is to demonstrate the added value of analyzing full movement curves over conventional discrete summaries. We developed a shape-based representation of variation in full biomechanical curve data from the Intensive Diet and Exercise for Arthritis (IDEA) study (Messier et al., 2009, 2013), and demonstrated through nested model comparisons that our approach, compared to conventional discrete summaries, yields stronger associations with OA severity and OA-related clinical traits. Notably, our work is among the first to quantitatively evaluate the added value of analyzing full movement curves over conventional discrete summaries.

stat.AP↗

arXiv2023

Hidden Ancestor Graphs: Models for Detagging Property Graphs

Consider a graph $G$ where each vertex is visibly labelled as a member of a distinct class, but also has a hidden binary state: wild or tame. Edges with end points in the same class are called agreement edges. Premise: an edge connecting vertices in different classes -- a conflict edge -- is allowed only when at least one end point is wild. Interpret wild status as readiness to form connections with any other vertex, regardless of class -- a form of class disaffiliation. The learning goal is to classify each vertex as wild or tame using its neighborhood data. In applications such as communications metadata, bio-informatics, retailing, or bibliography, adjacency in $G$ is typically created by paths of length two in a transactional bipartite graph $B$. Class labelling, imported from a reference data source, is typically assortative, so agreement edges predominate. Conflict edges represent observed behavior (from $B$) inconsistent with prior labelling of $V(G)$. Wild vertices are those whose label is uninformative. The hidden ancestor graph constitutes a natural model for generating agreement edges and conflict edges, depending on a latent tree structure. The model is able to manifest high clustering rates and heavy-tailed degree distributions typical of social and spatial networks. It can be fitted to graph data using a few measurable graph parameters, and supplies a natural statistical classifier for wild versus tame.

math.PR↗