Tensorial Principal Component Analysis in Detecting Temporal Trajectories of Purchase Patterns in Loyalty Card Data: Retrospective Cohort Study.

BACKGROUND: Loyalty card data automatically collected by retailers provide an excellent source for evaluating health-related purchase behavior of customers. The data comprise information on every grocery purchase, including expenditures on product groups and the time of purchase for each customer. Such data where customers have an expenditure value for every product group for each time can be formulated as 3D tensorial data. OBJECTIVE: This study aimed to use the modern tensorial principal component analysis (PCA) method to uncover the characteristics of health-related purchase patterns from loyalty card data. Another aim was to identify card holders with distinct purchase patterns. We also considered the interpretation, advantages, and challenges of tensorial PCA compared with standard PCA. METHODS: Loyalty card program members from the largest retailer in Finland were invited to participate in this study. Our LoCard data consist of the purchases of 7251 card holders who consented to the use of their data from the year 2016. The purchases were reclassified into 55 product groups and aggregated across 52 weeks. The data were then analyzed using tensorial PCA, allowing us to effectively reduce the time and product group-wise dimensions simultaneously. The augmentation method was used for selecting the suitable number of principal components for the analysis. RESULTS: Using tensorial PCA, we were able to systematically search for typical food purchasing patterns across time and product groups as well as detect different purchasing behaviors across groups of card holders. For example, we identified customers who purchased large amounts of meat products and separated them further into groups based on time profiles, that is, customers whose purchases of meat remained stable, increased, or decreased throughout the year or varied between seasons of the year. CONCLUSIONS: Using tensorial PCA, we can effectively examine customers' purchasing behavior in more detail than with traditional methods because it can handle time and product group dimensions simultaneously. When interpreting the results, both time and product dimensions must be considered. In further analyses, these time and product groups can be directly associated with additional consumer characteristics such as socioeconomic and demographic predictors of dietary patterns. In addition, they can be linked to external factors that impact grocery purchases such as inflation and unexpected pandemics. This enables us to identify what types of people have specific purchasing patterns, which can help in the development of ways in which consumers can be steered toward making healthier food choices.

Effects of physical activity intervention on 24-h movement behaviors: a compositional data analysis.

We utilized compositional data analysis (CoDA) to study changes in the composition of the 24-h movement behaviors during an activity tracker based physical activity intervention. A total of 231 recently retired Finnish retirees were randomized into intervention and control groups. The intervention participants were requested to use a commercial activity tracker bracelet with daily activity goal and inactivity alerts for 12 months. The controls received no intervention. The 24-h movement behaviors, i.e., sleep, sedentary time (SED), light physical activity (LPA), and moderate-to-vigorous physical activity (MVPA) were estimated from wrist-worn ActiGraph data using the GGIR R-package. Three balance coordinates describing the composition of movement behaviors were applied: ratio of active vs. passive behaviors, LPA vs. MVPA, and sleep vs. SED. A linear mixed model was used to study changes between the baseline and 6-month time point. Overall, the changes in the 24-h movement behaviors were small and did not differ between the groups. Only the ratio of LPA to MVPA tended to change differently between the groups (group*time interaction p = 0.08) as the intervention group increased LPA similarly to controls but decreased their MVPA. In conclusion, the use of a commercial activity tracker may not be enough to induce changes in the 24-h movement behaviors among retirees.

Fast tensorial JADE.

We propose a novel method for tensorial-independent component analysis. Our approach is based on TJADE and k-JADE, two recently proposed generalizations of the classical JADE algorithm. Our novel method achieves the consistency and the limiting distribution of TJADE under mild assumptions and at the same time offers notable improvement in computational speed. Detailed mathematical proofs of the statistical properties of our method are given and, as a special case, a conjecture on the properties of k-JADE is resolved. Simulations and timing comparisons demonstrate remarkable gain in speed. Moreover, the desired efficiency is obtained approximately for finite samples. The method is applied successfully to large-scale video data, for which neither TJADE nor k-JADE is feasible. Finally, an experimental procedure is proposed to select the values of a set of tuning parameters. Supplementary material including the R-code for running the examples and the proofs of the theoretical results is available online.

Tensorial blind source separation for improved analysis of multi-omic data.

There is an increased need for integrative analyses of multi-omic data. We present and benchmark a novel tensorial independent component analysis (tICA) algorithm against current state-of-the-art methods. We find that tICA outperforms competing methods in identifying biological sources of data variation at a reduced computational cost. On epigenetic data, tICA can identify methylation quantitative trait loci at high sensitivity. In the cancer context, tICA identifies gene modules whose expression variation across tumours is driven by copy-number or DNA methylation changes, but whose deregulation relative to normal tissue is independent of such alterations, a result we validate by direct analysis of individual data types.