Comparing Principal and Independent Modes of Variation in 3D Human Torso Shape Using PCA and ICA

We analyse 3D human torso data using Principal Components Analysis (PCA) and Independent Components Analysis (ICA) and compare their respective principal and independent modes of variation. Both PCA and ICA have been used to analyse variations in observed data for different applications. PCA offers a means of capturing the significant variations present in a data sample while ICA is useful in identifying “blind sources” or contributing factors that produce the observed variation. We use both methods to analyse a set of female 3D human torso data and study how the two sets of modes describe the shape, size and other variations in the data. Thirty PCA modes describing 90% of the total variation in the sample were used, together with the corresponding 30 ICA modes calculated therefrom using FastICA. Sample mode weight coefficients from both sets are evaluated and correlated with age, weight and a set of twelve key torso measurements to determine how individual PCA and ICA modes correlate with body measurements such as those used in the clothing industry and in human anthropometry. When the two sets of modes are visualised, the individual ICA modes are seen to identify more specific variations in the overall size, shape and posture variation in the sample than the individual PCA modes. When compared with age, weight and the key torso measurements, the measurements were found to have strong correlations with a small number of the most significant PCA modes whilst the correlations with each of the ICA modes were weaker, spread over a much larger number of modes, and could be used to group the measurements into clusters suggestive of different types of torso variation. This is consistent with the fact that each ICA mode encapsulates a significant range of shape variation whilst only the first few, most significant PCA modes do so. We conclude therefore that ICA offers a means of identifying specific variations in 3D human torso shape that better describe how torso shape varies. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. c ©2006 The University of Liverpool