meansfragments

Meansfragments are a concept in multivariate statistics and data analysis referring to fragments of a mean vector derived from a subset of observations and a selected set of variables. They describe local central tendency within subpopulations, complementing global means by highlighting heterogeneity and modular structure in complex data.

Construction and interpretation: For a chosen subset of observations and a chosen subset of variables, compute the mean of each selected variable across the subset. The resulting vector is a meansfragment. Collecting many such fragments across different subpopulations or variable selections yields a landscape of local mean patterns that can be compared, clustered, or visualized to reveal structure not captured by a single average.

Computation and inference: Meansfragments can be generated through stratification, clustering of observations, or sliding-window approaches in high-dimensional settings. Uncertainty can be assessed by bootstrap resampling or permutation tests. Distances between fragments, such as Euclidean distance or cosine similarity, support clustering, visualization, and the discovery of similar local patterns.

Applications: In marketing analytics, meansfragments can reveal how average purchasing behavior varies across regions and product groups. In genomics, they can summarize mean expression across gene sets in different cell types. In sensor networks or social science, fragments may reflect local environmental or behavioral patterns that drive subgroup differences.

Relation to related concepts and limitations: Meansfragments are related to subpopulation means, conditional means, and local statistics. Unlike a single global mean, they emphasize heterogeneity and modular structure. Limitations include sensitivity to the choice of subsets, potential instability in high dimensionality, and the need to account for multiple comparisons when interpreting many fragments.