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In this paper, we propose a novel stock index model, namely the manifoldfeature(MF) index, to reflect the overall price activity of the entire stockmarket. Based on the theory of manifold learning, the researched stock datasetis assumed to be a low-dimensional manifold embedded in a higher-dimensionalEuclidean space. After data preprocessing, its manifold structure and discreteLaplace-Beltrami operator(LBO) matrix are constructed. We propose ahigh-dimensional data feature detection method to detect feature points on theeigenvectors of LBO, and the stocks corresponding to these feature points areconsidered as the constituent stocks of the MF index. Finally, the MF index isgenerated by a weighted formula using the price and market capitalization ofthese constituents. The stock market studied in this research is the ShanghaiStock Exchange(SSE). We propose four metrics to compare the MF index series andthe SSE index series (SSE 50, SSE 100, SSE 150, SSE 180 and SSE 380). From theperspective of data approximation, the results demonstrate that our indexes arecloser to the stock market than the SSE index series. From the perspective ofrisk premium, MF indexes have higher stability and lower risk.

Manifold Feature Index: A novel index based on high-dimensional data simplification