This chapter examines methodologies for dimensional analysis and linear decomposition of multivariate data sets, and discusses their implicit hypotheses and interpretations for muscle coordination of movement. It presents tutorials to compare how two common methods—principal components analysis (PCA) and non-negative matrix factorization (NMF)—decompose electromyographic signals into underlying components. To facilitate the integration of such mathematical techniques with physiological hypothesis testing, the chapter focuses on developing an intuitive understanding to the two techniques. It provides a simple two-dimensional tutorial, focusing on how orthogonality constraints in PCA and non-negativity constraints in NMF impact the resulting data decomposition and physiological relevance. Examples are presented using real data sets from human balance control and locomotion. The chapter examines the structure of the resulting components, their robustness across tasks, and their implications for various muscle synergy hypotheses. The chapter addresses practical issues and caveats in organizing datasets, the selection of the appropriate number of components, and considerations and pitfalls of experimental design and analysis, as well as offering suggestions and cautions for interpreting results. Based on these comparisons and on the work in the visual system over the last decade, evidence is presented for the increased neurophysiological relevance of the factors derived from NMF compared to PCA.
Keywords: dimensional analysis; linear decomposition; multivariate data sets; muscle coordination; movement; principle components analysis; non-negative matrix factorization; data decomposition
Chapter. 13691 words. Illustrated.
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