A new topological weighted functional regression model to analyse wireless sensor data

Nowadays, modern sensor devices can generate a wide range of data types, including functional data, which can be challenging to analyse due to their complex dependencies. In order to effectively analyse these types of data, it is important to consider both the functional and topological dependencies, as well as any prior information that may be available. This may involve using advanced statistical tech- niques, such as functional data analysis or machine learning methods, to uncover patterns and insights from the data. In this paper, we focus on predicting the signal from such devices considering the topological structure induced by the connectivity sensor network. The approach we propose, is to pre-process the raw discrete func- tional data into smoothed functional data, which can help to reduce noise and make patterns in the data more clear. After that, a geographically weighted functional regression (GWFR) model is generalized to analyse functional data with topolog- ical dependencies induced by the connectivity of the network. Simulation studies with several types of connectivity were conducted to evaluate performances of the method. The method is motivated by an applicative study on the Intel indoor dataset (http://db.csail.mit.edu/labdata/labdata.html) to study the data prediction problem in a wireless sensor network.