论文标题
歧管特征指数：基于高维数据简化的新索引
Manifold Feature Index: A novel index based on high-dimensional data simplification
论文作者
论文摘要
在本文中，我们提出了一种新颖的股票指数模型，即歧管功能（MF）指数，以反映整个股票市场的整体价格活动。基于多种学习理论，认为研究的库存数据集被认为是嵌入在较高维的欧几里得空间中的低维流形。在数据预处理后，构建了其歧管结构和离散的Laplace-Beltrami操作员（LBO）矩阵。我们提出了一种高维数据特征检测方法，用于检测LBO特征向量的特征点，与这些特征点相对应的股票被视为MF索引的组成股。最后，使用这些成分的价格和市值通过加权公式生成MF指数。这项研究中研究的股票市场是上海证券交易所（SSE）。我们建议四个指标比较MF索引系列和SSE索引系列（SSE 50，SSE 100，SSE 150，SSE 180和SSE 380）。从数据近似的角度来看，结果表明，我们的指数比SSE指数系列更接近股票市场。从风险溢价的角度来看，MF指数具有更高的稳定性和较低的风险。
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.
