  Topological Data Analysis (TDA) is a recent approach to analyze data sets
from the perspective of their topological structure. Its use for time series
data has been limited. In this work, a system developed for a leading provider
of cloud computing combining both user segmentation and demand forecasting is
presented. It consists of a TDA-based clustering method for time series
inspired by a popular managerial framework for customer segmentation and
extended to the case of clusterwise regression using matrix factorization
methods to forecast demand. Increasing customer loyalty and producing accurate
forecasts remain active topics of discussion both for researchers and managers.
Using a public and a novel proprietary data set of commercial data, this
research shows that the proposed system enables analysts to both cluster their
user base and plan demand at a granular level with significantly higher
accuracy than a state of the art baseline. This work thus seeks to introduce
TDA-based clustering of time series and clusterwise regression with matrix
factorization methods as viable tools for the practitioner.
