An Empirical Study Of Multi-Factor Stock Selection Model Based On Kernel Function

This paper introduces kernel-based learning algorithms such as kernel principal component analysis,support vector regression,and kernel fisher discriminant analysis,and applies these theories to multi-factor stock selection models.First,the article gives the definition of the kernel function and some of its more important properties.Using the kernel function,the quantity product can be implicitly calculated in the feature space without needing to know the specific mapping.Then this principle is used for supervised learning and unsupervised learning for derivation of algorithm based on kernel function.Principal component analysis a dimensionality reduction algorithm commonly used in unsupervised learning.The main idea is to transform a set of correlated variables into a set of linearly independent variables through orthogonal transformation,and reflect the main information contained in the original multiple variables with a few new variables.Because PCA is a linear algorithm,it cannot extract non-linear structures in the data.Kernel principal component analysis as a non-linear feature extraction method based on kernel functions,maps data to feature space and then solves a linear eigenvalue problem similar to linear PCA to obtain kernel PCA components.Support vector regression uses the principle of structural risk minimization and introduces an?insensitive function as a loss function.For a set of training data,determine a function that allows the function to accurately approximate future values.Nonlinear support vector regression uses implicit mapping of kernel functions to map sample data to high-dimensional feature space through nonlinear mapping,and constructs a linear regression function to achieve nonlinear regression in the original space,then conducts sample training and prediction.When the data is unevenly distributed in the high-dimensional feature space,a single kernel function support vector regression is used to perform the same mapping on all samples,and the effect is not ideal.Multi-core support vector regression combines multiple basic kernel functions in a reasonable and effective combination according to a certain algorithm rule to obtain a more flexible regression model.Kernel function techniques are also applicable to supervised learning scenarios such as fisher discriminant analysis.In the linear case,the purpose of Fisher discriminant method is to find a linear projection so that classes can be well separated from each other,and by maximizing Rayleigh quotient realizes separability.The idea of kernel fisher discriminant analysis is to solve the problem of fisher discriminant function in the kernel feature space,thereby generating a non-linear discriminant function in the input space.Kernel-based learning algorithms are widely used in multi-factor stock selection models.Multi-factor stock selection model explores the factors or indicators related to stock returns to characterize stock returns and select stocks.Multi-factor stock selection model uses multiple linear regression method to predict the rate of return.The problem of factor collinearity will affect the effectiveness and robustness of the strategy.PCA and KPCA can effectively solve the collinearity problem.By selecting appropriate kernel function and kernel parameters,the fitting effect of KPCA-based multi-factor regression stock selection model is better than that of PCA-based multi-factor regression.Support vector regression has good data fitting performance.For the multi-factor stock selection model,it can obtain the ideal factor data fitting effect by selecting the appropriate combination of insensitive parameters ?,penalty factors,and kernel function parameters.The kernel fisher discriminant analysis model is applied to multi-factor stock selection,and the factor nonlinear problem in low-dimensional space is transformed into the linear classification problem in high-dimensional feature space,which effectively improve the classification of multi-factor stock selection model,making the portfolio return rate higher than the benchmark return rate.