The Application Of KPCA In The Analysis Of Enerterprise Economic Benefits

The economic benefit of enterprise is the final aggregative indicator which measures all the business activities and the fundamental starting point of the enterprise economic activities and it's as well. The enterprise has to lower the manual consuming for development, and gains the most benefits with the least investment. Only in this way, can the enterprise compete with other companies and develop. The paper is based on the KPCA (kernel principal component analysis) to analyze the enterprise economic benefits, in order to deduce the relation of each economic indicator, estimate the condition of enterprise economic benefits and provide the bases for the financial analysis.The papers introduces the traditional analytical method of the analysis of the enterprise economic benefits firstly, namely comparative analysis method, ratio analysis method, factor analysis approach, balancing analysis method, trend analysis approach and mathematical programming method. However, these traditional approaches are not unified; they can't express the relation of each economic indicator definitely, they are inaccurate and have the bigger errors, which can not react the weakness of the contribution rate of the enterprise's each economic indicator. Then it discusses the basic theory of kernel function, and elaborates the approach of KPCA. The basic theory of KPCA is that it has a reflection, which can map the sampled data to the feature space, and the dimensionality of space is really high, by computing the scalar product in the feature space, we can get the feature without needing to know how the concrete reflection has worked. It's easy to compute and operate. By defining the kernel matrix, we can deem PCA as the problem of matrix eigenvalues. Using the approach of PCA and KPCA to analyze the economic conditions of some enterprises in Shandong Province and comparing the two results, we can know that KPCA has a good effect of dimension reduction. Finally the paper introduces the selection of kernel function, based on the data, selecting different kernel functions and different nuclear parameters, thus comparing the characteristics of kernel functions, and finding out the kernel functions which are appropriate for the data. Put the mixed kernel functions into use of the analysis of the enterprise economic benefits, thereby it can make the contribution rate of the fist principal component more obvious.