Intrinsic dimensionality of human behavioral activity data

Patterns of spatial behavior dictate how we use our infrastructure, encounter other people, or are exposed to services and opportunities. Understanding these patterns through the analysis of data commonly available through commodity smartphones has become an important arena for innovation in both academia and industry. The resulting datasets can quickly become massive, indicating the need for concise understanding of the scope of the data collected. Some data is obviously correlated (for example GPS location and which WiFi routers are seen). Codifying the extent of these correlations could identify potential new models, provide guidance on the amount of data to collect, and even provide actionable features. However, identifying correlations, or even the extent of correlation, is difficult because the form of the correlation must be specified. Fractal-based intrinsic dimensionality directly calculates the minimum number of dimensions required to represent a dataset. We provide an intrinsic dimensionality analysis of four smartphone datasets over seven input dimensions, and empirically demonstrate an intrinsic dimension of approximately two.