Modern technology has generated high dimensional multivariate data in various biomedical fields including continuous monitoring of physical activity with wearable accelerometry. To address high-dimensionality, dimension reduction techniques such as principal component analysis (PCA) are often applied to explore and analyze these data. Finding components based on the covariance matrix (second order statistics) is only adequate to characterize multivariate Gaussian distribution. However, accelerometry data often exhibits significant deviation from Gaussian distribution with high skewness and kurtosis. To address this problem, we propose a novel method that considers higher order tensorian statistics. Motivated by univariate properties, the approach constructs third and fourth order standardized moment tensors to capture higher order information, and then decomposes them via symmetric tensor decompositions. Thus, it provides enriched information that accounts for the non-Gaussianity. We applied it to accelerometry data of 3390 participants of 2003-2006 National Health and Nutrition Examination Survey and explored the predictability of estimated diurnal patterns on 5-year mortality.