Effect of dimensionality reduction on stock selection with cluster analysis in different market situations Abstract   Dimensionality reduction is inevitable in stock selection with cluster analysis. Considering relations among dimensionality reduction, noise trading, and market situations, we empirically investigate the effect of dimensionalityreduction methodsxe2x80x93principal component analysis, stacked autoencoder, and stacked restricted Boltzmann machinexe2x80x93on stock selection with cluster analysis in different market situations. Based on the index fluctuation, the market is divided into sideways and trend situations. For the CSI 100 and Nikkei 225 constituent stocks, experimental results show that: (1) in sideways situations, dimensionality reduction hardly improves the performance of stock selection with cluster analysis; (2) the advantage of dimensionality reduction is mainly reflected in trend situations, but whether it is in an up or down trend depends on the market analyzed. More importantly, according to the above findings and assuming that the dimensionalityreduction effect will continue, we propose a rotation strategy with and without dimensionality reduction. The results of experiments show that the proposed rotation strategy outperforms the stock market indices as well as the stockselection strategies based on dimensionality reduction and cluster analysis. These findings offer practical insights into how dimensionality reduction can be efficiently used for stock selection.

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.