Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Manifold Feature Index: A novel index based on high-dimensional data
  simplification   In this paper, we propose a novel stock index model, namely the manifold
feature(MF) index, to reflect the overall price activity of the entire stock
market. Based on the theory of manifold learning, the researched stock dataset
is assumed to be a low-dimensional manifold embedded in a higher-dimensional
Euclidean space. After data preprocessing, its manifold structure and discrete
Laplace-Beltrami operator(LBO) matrix are constructed. We propose a
high-dimensional data feature detection method to detect feature points on the
eigenvectors of LBO, and the stocks corresponding to these feature points are
considered as the constituent stocks of the MF index. Finally, the MF index is
generated by a weighted formula using the price and market capitalization of
these constituents. The stock market studied in this research is the Shanghai
Stock Exchange(SSE). We propose four metrics to compare the MF index series and
the SSE index series (SSE 50, SSE 100, SSE 150, SSE 180 and SSE 380). From the
perspective of data approximation, the results demonstrate that our indexes are
closer to the stock market than the SSE index series. From the perspective of
risk premium, MF indexes have higher stability and lower risk.

23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas