TopologyBased Clusterwise Regression for User Segmentation and Demand Forecasting 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 TDAbased 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 TDAbased clustering of time series and clusterwise regression with matrix factorization methods as viable tools for the practitioner.

Topological Data Analysis in Investment Decisions Abstract   This article explores the applications of Topological Data Analysis (TDA) in the finance field, especially addressing the primordial problem of asset allocation. Firstly, we build a rationale on why TDA can be a better alternative to traditional risk indicators such as standard deviation using real data sets. We apply Takens embedding theorem to reconstruct the time series of returns in a high dimensional space. We adopt the sliding window approach to draw the timedependent point cloud data sets and associate a topological space with them. We then apply the persistent homology to discover the topological patterns that appear in the multidimensional time series. The temporal changes in the persistence landscapes, which are the realvalued functions that encode the persistence of topological patterns, are captured via Lp norm. The time series of the Lp norms shows that it is better at measuring the dynamics of returns than the standard deviation.  Inspired by our findings, we explore an application of TDA in Enhanced Indexing (EI) that aims to build a portfolio of fewer assets than that in the index to outperform the latter. We propose a twostep procedure to accomplish this task. In step one, we utilize the Lp norms of the assets to propose a filtration technique of selecting a few assets from a larger pool of assets. In step two, we propose an optimization model to construct an optimal portfolio from the class of filtered assets for EI. To test the efficiency of this enhanced algorithm, experiments are carried out on ten data sets from financial markets across the globe. Our extensive empirical analysis exhibits that the proposed strategy delivers superior performance on several measures, including excess mean returns from the benchmark index and tail rewardrisk ratios than some of the existing models of EI in the literature. The proposed filtering strategy is also noted to be beneficial for both riskseeking and riskaverse investors.