Measuring Abnormality in High Dimensional Spaces with Applications in Biomechanical Gait Analysis

Accurately measuring a subject's abnormality using high dimensional data can empower better outcomes research. Utilizing applications in instrumented gait analysis, this article demonstrates how using data that is inherently non-independent to measure overall abnormality may bias results. A methodology is then introduced to address this bias and accurately measure abnormality in high dimensional spaces. While this methodology is in line with previous literature, it differs in two major ways. Advantageously, it can be applied to datasets in which the number of observations is less than the number of features/variables, and it can be abstracted to practically any number of domains or dimensions. Initial results of these methods show that they can detect known, real-world differences in abnormality between subject groups where established measures could not. This methodology is made freely available via the abnormality R package on CRAN.