ABSTRACT
When doing comprehensive evaluation, it is often necessary to process and analyze high-dimensional data. The basis of most of traditional research is that the data is generally normally distributed. However, in fact, certain data is not distributed normally. Therefore, more robust and practical methods are needed. Projection pursuit is a new statistical approach suitable for analyzing and processing observed high-dimensional data, especially the nonlinear high-dimensional data that is not normally distributed. Accelerating genetic algorithm can downsize the data set and speed up processing. With these two methods, it is possible to obtain more reasonable and objective comprehensive evaluation results. In this study, listed Chinese companies in automobile manufacturing industry were taken as the examples and a projection pursuit model was established. The empirical results demonstrated that the projection pursuit model based on genetic algorithm was applicable to processing of high-dimensional data. This could help improve the evaluation methods and optimize the evaluation results.
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DOI: 10.3923/itj.2014.1837.1842
URL: https://scialert.net/abstract/?doi=itj.2014.1837.1842
INTRODUCTION
In reality, the following problem often exists: when assess a thing, its strengths and weaknesses are always affected by many factors; to access each of them, multiple indexes are needed but shall not be simply accumulated. A comprehensive assessment problem is how to give a comprehensive comment by taking overall consideration on influences of all factors on the basis of giving a separate comment to each factor. Comprehensive assessment method is a kind of statistical analysis technique synthesizing items which may not be accumulated directly and with different natures to summarize the conclusion according to the statistical research purpose, based on the statistical data and with certain measures and methods, thereby to reveal the nature and development law of the thing (Niu and Zheng, 2006).
Projection pursuit is a new method used to solve the high-dimensional problem, the starting point of which is to reduce the dimensions and then conduct research. The method of projection pursuit was first proposed in the late 1960s. In order to discover the clustering structure of data (Kruskal, 1969), first employed projection pursuit method to project the multi-dimensional data into the low-dimensional space (Kruskal, 1969). Through numerical calculation, he maximized an index that reflected the degree of data clustering to find the optimal projection which revealed characteristic of data structure. Switzer (1970) classified fossils by projection of high-dimensional data and numerical calculation (Switzer, 1970). After that, a series of research breakthroughs on projection pursuit were achieved and caught the attention of scholars in theoretical and application research fields. To solve problems with the projection pursuit method, it is critical to construct efficient algorithms that can be used to find optimal projection direction. Kruskal (1969) proposed to use computers to enhance functions of human eyes through projection pursuit. Friedman and Tukey (1974) constructed a projection pursuit algorithm suitable for analysis of multivariate data based on Kruscals ideas. Since then, finding optimal projection with projection pursuit algorithm was mainly based on the above mentioned ideas. Optimal projection could be found using various optimal calculation methods, such as gradient descent method, Gauss- Newton method and so on.
When the object of study is complex, multivariate data has complex topology. In this case, local optimum, prematurity or early convergence often occur when using the above mentioned algorithms and it is difficult to find the optimal result. In this study, according to the characteristic of multi-dimensional data reflected by objective function, the author employed improved genetic algorithm to search the optimal result directly in the optimal area, thereby identifying a projection direction. In this way, it was possible to avoid doing a lot of calculation which traditional genetic algorithm often required.
METHODOLOGY OF PROJECTION PURSUIT BASED ON IMPROVED GENETIC ALGORITHM
Building projection pursuit model: The inadequacy of traditional data analysis method is that when the structure or feature disagrees with the assumption, the mode will have poor fitting and prediction accuracy, especially for high-dimensional non-normal and nonlinear data. PP model is a new method to process multi-dimensional data since the 1960s with basic thought of projecting multi-dimensional data to one to three dimensions subspace to search the projection reflecting structure or feature of multi-dimensional data, thereby to research and analyze high-dimensional data. Classification or predication with data after projection may effectively avoid the influence of assessment personnels knowledge, experience and other subjective factors on the assessment results.
• | Normalization processing: Avoidance of inordinate influence on the results was considered. Unusual exceptional financial events could potentially skew the validity of the assessment. Extraordinary data can mitigated by eliminating the magnitude of each respective index assessment. To accomplish this, each index shall firstly be diminished by the following method: let the sample set of each index be {X*(i,j)|i = 1, 2, , n; j = 1, 2, , p},where, X*(i,j) is the jth index value of the ith sample. n and p, therefore, are the number of samples and the quantity of the indices, respectively. |
• | For positive indexes the bigger the better: |
(1) |
• | For negative indexes the smaller the better: |
(2) |
• | For moderate indexes: |
(3) |
where, q is the most suitable value of moderate index.
where, Xmax(j) and Xmin(j) are, respectively the peak value and the valley value of the jth index and x(i, j) is the normalized sequence of indexs characteristic value.
• | Building projection index function Q(a): Projection pursuit method is to synthesize P-dimension data {X(i, j)| j = 1, 2, , p} into one-dimension projection value z(i) in projection direction: |
(4) |
Then, make classification according to one-dimension scatter diagram of {z(i)|i = 1, 2, , n}. In Eq. 4, a is the unit length vector quantity. When synthesize projection index value, scatter characteristic of projection value z(i) shall be: partial projection shall be as intensive as possible and better condensing into several point clusters, while the projection point clusters shall be as scattering as possible as a whole. Building the following index function:
(5) |
where, Sz is the standard deviation of projection value z(i), Dz is the local density of the same, namely:
(6) |
(7) |
where, E(z) is the mean value of sequence {z(i)|i = 1, 2, , n}; R is the window radius of local density; r(i, j) represents the distance between samples (r(i, j) = |z(i)-z(j)|); u(t) is a unit step function, when t = 0, the value is 1 and when t<0, its function value is 0.
• | Optimize projection index function: When building a PP model it is critical to find the optimal projection direction that best reflects the scale and scope of the model. Based on the above analysis, the projection direction exposes certain feature structures of the multi-dimensional data to its greatest extent. The optimal projection direction might, therefore, be estimated by solving the maximization problem of the projection index function. At present, genetic algorithm is a commonly used solving method |
• | Maximizing objective function: |
(8) |
• | Contra in condition: |
(9) |
• | Comprehensive assessment: Insertion of the optimal projection direction, a*, calculation stated above into the method Eq. 4, projects the characteristic quantities reflected in the comprehensive data. Each assessment index can then be more reflective when comprehensive assessment analysis is conducted on the samples according to the discrepancy level of Zi |
Improved genetic algorithm of projection pursuit model: Genetic algorithm is an optimization procedure imitating natural evolution and hybridization of living beings in the nature proposed by Professor John Holland from Michigan University, USA in 1962. As a highly parallel, random and self-adaptive universal global searching algorithm, it can deal with the optimization problem with strong nonlinearity (Holland, 1962). However, due to the slow search speed of traditional genetic algorithm, long training time is needed for obtaining accurate solution; besides, to avoid premature convergence in actual application, an improved method which may both reserve excellent individual and maintain population diversity is needed. In this study, accelerating genetic algorithm is adopted, which effectively avoid the huge calculated quantity and slow speed of traditional genetic algorithm, with the following specific coding:
Major simulation program of Projection pursuit + accelerating genetic algorithm optimization |
DISCUSSION OF INDEXES
Core competitiveness are the collective learning in an organization. Specific examples cited include coordination of diverse production skills and multiple streams of technologies. This coordination experience which is formed in the business process establishes unique skill capabilities of the enterprise. This expertise may not be imitated by competitors and can bring extraordinary profit (Xu, 2005). Enterprise core competitiveness contains multiple levels of capabilities and involves many factors; in this study, from the view point of finance and taking listed Chinese automobile companies as examples, comprehensive assessment is conducted with the projection pursuit model based on improved genetic algorithm.
Assessment indexes selection: The above Harvard Business Review authors implied and asserted that core competiveness that is unique to a particular enterprise may enable the enterprise to maintain the competence of competitive advantage for a very long time. A focused study of the core competitiveness of 14 Chinese automobile companies was, therefore, undertaken. The sample of 14 was a random representation of the car manufacturing industry listed in the Shanghai and Shenzhen Stock Exchanges. The study was conducted from the view point of financial health. This study selected the 14 companies profitability, debt paying ability, operation capacity and development capacity as the indexed variables. This data was used to build the assessment index model of Chinese Automobile Enterprises Financial Prospects (Table 1).
Table 1: | Assessment index system for core competitiveness of automobile manufacturing enterprise in financial perspective |
• | Profitability: Profitability is enterprises capability in gaining profit, which is often represented by the profit amount and level of the enterprise in certain period. Referring to related literatures and combining characteristics of automobile enterprises, this study selects four indexes of net profit margin on sales, return on assets, earnings per share and weighted mean net assets income rate to assess profitability of the enterprise. These four indexes are all positive, hence bigger index value will represent stronger profitability of the enterprise |
• | Debt paying ability: Debt paying ability means the enterprises capability in repaying long-term and short-term liabilities with its assets. This study selects three indexes of liquidity ratio, quick ratio and asset-liability ratio, respectively from long-term debt paying ability and short-term debt paying ability to fully reflect the enterprises bearing capacity and assurance level in repaying matured debts. Moderate liabilities may bring tax reduction and minimally impact other financial characteristics of the enterprise, however, excessive liabilities may drive the enterprise into capital insolvency. Therefore, for these three moderate indices, it is generally considered that liquidity ratios and quick ratios be maintained at 2:1 and 1:1, respectively. In doing so, the enterprises short-term debt paying ability will be favorable. Asset-liability ratio is a comprehensive index for assessing liabilities level of the company. In this study, its optimal value is set as 58% according to average asset-liability ratio of automobile industry in Analysis Report on automobile industry of China in 2011 |
• | Operation capacity: Operation capacity means the enterprises business operation capacity, namely the ability in making profit with various assets. In this study, turnover ratio of account receivable, inventory turnover ratio and total assets turnover ratio are selected to comprehensively assess operation capacity of automobile manufacturing enterprises. Bigger values of these three indexes represent higher assets liquidity of the enterprise and faster profit taking of the assets; therefore, they are all positive indexes |
• | Development capacity: Development capacity means the enterprises potential ability in scaling up and strength growing. When assess enterprises core competitiveness, besides assessing current condition, more importance will be attached to long-term sustainable development capacity of the enterprise. This study selects four indexes of basic growth rate of earnings per share, sustainable growth rate, rate of net profit growth and rate of total assets growth to access long-term development capacity of automobile manufacturing enterprises. Bigger values of these four indexes indicate huger development potential continuously accumulated in production and operation activities by the enterprise; therefore, these four indexes are all positive |
Sample data: Only data of the same industry is comparable. Therefore, this study selects data of 13 representative automobile manufacturing enterprises listed in Shanghai and Shenzhen Stock Exchange Markets as samples to analyze and assess the core competitiveness from the view point of finance.
Table 2: | Financial index data of sample companies in 2011 |
Data source: GSMAR database |
The 13 listed automobile manufacturing enterprises are: Jiangling Motors Ltd., Ankai Coach Ltd., FAW Ltd., Xiali Ltd., Sinotruk Ltd., Zhongtong Bus Ltd., Dongfeng Automobile Ltd., Yutong Bus Ltd., Shanghai Automotive Industry Corporation (SAIC), Foton Ltd., CAMC Ltd., Jianghuai Automobile Corporation (JAC), DIMA Ltd. and King Long Auto, Ltd. (Table 2).
ANALYSIS OF THE RESULTS
Analysis on overall index: The following result can be got from the above PP model.
a* = (0.6407, 0.9055, 0.9390, 1, 0.2527, 0.2347, 0.1005, 0.2477, 0.1717, 0.1409, 0.1548, 0.8020, 0.5602, 0.4725). According to above model calculation, the rates of contribution of financial indexes to core competitiveness of listed automobile manufacturing companies are ranked as: Weighted mean net assets income rate, Earnings per share, Return on assets, Sustainable growth rate, Profit margin on sales, rate of net profit growth, rate of total assets growth, Liquidity ratio, Turnover ratio of account receivable, quick ratio, Inventory turnover ratio, Basic growth rate of earnings per share, assets turnover and asset-liability ratio. Insert the optimal projection direction a* obtained to Eq. 4. The result that Zi = (3.5524, 1.3607, 0.1297, 0.9293, 0.8982, 0.7854, 4.4331, 3.3202, 0.9062, 2.3047, 0.9622, 0.9569, 1.3051) can be obtained. Therefore, the core competitiveness of the sample listed automobile manufacturing companies are ranked as: Yutong Bus, Jiangling Motors, SAIC, CAMC, Ankai Coach, King Long Auto, JAC, DIMA, Sinotruk, Foton, Zhongtong Bus, Dongfeng Automobile and FAW Xiali.
Analysis on primary indexes:
• | Assessment on debt paying ability: Adopting the same calculation procedure with the overall index, the following can be obtained a* = (0.6765, 0.5401, 0.7828, 0.7031) Zi = (2.3972, 0.3944, 0, 0.6012, 0.2582, 0.2792, 2.4318, 1.8460, 0.5599, 1.5027, 0.4357, 0.3592, 0.5712) |
The debt paying abilities of the sample listed automobile manufacturing companies are ranked as follows: Yutong Bus, Jiangling Motors, SAIC, CAMC, Sinotruk, King Long Auto, Foton, JAC, Ankai Coach, DIMA, Dongfeng Automobile, Zhongtong Bus and FAW Xiali.
• | Assessment on debt paying ability: Through calculating by above procedure, the following can be obtained a* = (0.3887, 0.5294, 0.3786), Zi = (0.8814, 0.0053, 0.1087, 0.2402, 0.1119, 0.0952, 0.1467, 0.2220, 0.2593, 0.0938, 0.0088, 0.6388, 0.1108). Debt paying abilities of the sample listed automobile manufacturing companies are ranked as follows: Jiangling Motors, DIMA, Foton, Sinotruk, SAIC, Yutong Bus, Zhongtong Bus, King Long Auto, FAW Xiali, Dongfeng Automobile, CAMC, JAC and Ankai Coach |
• | Assessment on operation capacity: Through calculating by above procedure, the following can be obtained a* = (0.9712, 0.4332, 0.2996), Zi = (0.2694, 0.0735, 1.1427, 0.0113, 0.0121, 0.1265, 0.0130.0.2274, 0.0586, 0.0026, 0.5286, 0.0039, 0.0035). The operation capacities of the sample listed automobile manufacturing companies are ranked as follows: FAW Xiali, JAC, Jiangling Motors, SAIC, Dongfeng Automobile, Ankai Coach, Foton, Yutong Bus, Zhongtong Bus, Sinotruk, DIMA, King Long Auto and CAMC |
• | Assessment on development capacity: Through calculating by above procedure, the following can be obtained a* = (0.9746, 0.2948, 0.3627, 0.2130), Zi = (0.0121, 0.0037, 0.0195, 0.0966, 0.0977, 0.9818, 0.1149, 0.1039, 0.1633, 0.1118, 0.2532, 0.8913, 0.2187). The development capacities of the sample listed automobile manufacturing companies are ranked as follows: Dongfeng Automobile, DIMA, JAC, King Long Auto, Foton, Yutong Bus, CAMC, SAIC, Zhongtong Bus, Sinotruk, FAW Xiali, Jiangling Motors and Ankai Coach |
CONCLUSION
In this study, projection pursuit model based on improved genetic algorithm is adopted to assess core competitiveness of Chinese automobile manufacturing enterprises. According to the examples, compared with traditional assessment methods, projection pursuit model based on improved genetic algorithm possesses greater advantages in comprehensive assessment. By projecting multi-dimensional data to low dimensional space, dimensionality reduction may be achieved, thereby to avoid subjectivities in artificial weighting; especially for high-dimensional and non-normal data processing, it is quite visualized and operable with empirical results having strong guiding significances in perfecting and improving assessment object. As for examples in this study, according to empirical study on data of listed automobile manufacturing companies in China, the profitability and development capacity have significant influence on core competitiveness.
REFERENCES
- Kruskal, J.B., 1969. Toward a Practical Method which Helps Uncover the Structure of a Set of Multivariate Observations by Finding the Linear Transformation which Optimizes a New Index of Condensation. In: Statistical Computation, Milton, R.C. and J.A. Nelder (Eds.). Academic Press, New York, USA., pp: 427-440.
- Friedman, J.H. and J.W. Tukey, 1974. A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comput., 23: 881-890.
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