WO2009082042A1

WO2009082042A1 - Nonlinear time series prediction method for weighted average defuzzification based on newfm

Info

Publication number: WO2009082042A1
Application number: PCT/KR2007/006739
Authority: WO
Inventors: Soo Han Chai; Joon Shik Lim; Sang Hong Lee; Hyoung Jong Jang
Original assignee: Industry University Cooperation Foundation Of Kyungwon University
Priority date: 2007-12-21
Filing date: 2007-12-21
Publication date: 2009-07-02

Abstract

The present invention relates, in general, to a nonlinear time series prediction method using weighted average defuzzification based on a Neural Network with Weighted Fuzzy Membership functions (NEWFM), and more particularly, to a nonlinear time series prediction method using weighted average defuzzification based on a NEWFM, which measures the classification strengths of respective classes, classified according to NEWFM, determines the classification strengths which indicate membership degrees for respective classes, and predicts a nonlinear time series through the weighted average defuzzification of the classification strengths, so that the nonlinear time series can be applied to the determination and forecasting of an economic phase using a Composite index (CI), thus enabling the nonlinear time series to be used for determining the direction of the economic phase as well as the classification of the economic phase.

Description

NONLINEAR TIME SERIES PREDICTION METHOD FOR WEIGHTED AVERAGE DEFUZZIFICATION BASED ON NEWFM

Technical Field

The present invention relates, in general, to a nonlinear time series prediction method using weighted average defuzzification based on a Neural Network with Weighted Fuzzy Membership functions (NEWFM), and more particularly, to a nonlinear time series prediction method using weighted average defuzzification based on a NEWFM, which measures the classification strengths of respective classes, classified according to NEWFM, determines the classification strengths which indicate membership degrees for respective classes, and predicts a nonlinear time series through the weighted average defuzzification of the classification strengths, so that the nonlinear time series can be applied to the determination and forecasting of an economic phase using a Composite index (Cl), thus enabling the nonlinear time series to be used for determining the direction of the economic phase as well as the classification of the economic phase.

Background Art

Various Fuzzy Neural Networks (FNN) have been proposed, which are an adaptive decision support tool combining a neural network with fuzzy set theory for the purpose of performing pattern classification, diagnosis, and forecasting.

Examples of the prior art are disclosed in "Voting in Fuzzy Rule-Based Systems for Pattern Classification Problems" by H. Ishibuchi and T. Nakashima, in Fuzzy Sets and

Systems, Vol.103, pp.223-238, 1999, Foundation of Neural Networks, Fuzzy Systems and

Knowledge Engineering by N. Kasabov, MIT Press, Cambridge, MA, 1996., "Finding Fuzzy Rules by Neural Network with Weighted Fuzzy Membership Function" by Joon Shik Lim in International Journal of Fuzzy Logic and Intelligent Systems, Vol. 4, No.2, pp.211- 217, September, 2004., etc.

Further, FNNs with various structures have been proposed together with algorithms for learning, adaptation, and rule extraction. A fuzzy rule extraction technique in 'IF-THEN' form is advantageous in decision making, and represents a general pattern in classification or forecasting using a simple form of knowledge such as an IF-THEN fuzzy rule. A self-organizing system-based fuzzy neural network has been also developed for knowledge extraction from a given series of learning data These are disclosed in "A Neuro-Fuzzy Approach for Diagnosis of Antibody Deficiency Syndrome" by Joon. S. Lim, D. Wang, Y.-S. Kim, and S. Gupta in Neurocomputing 69, Issues 7-9, pp. 969-974, March 2006., and "Feature Selection for Specific Antibody Deficiency Syndrome by Neural Network with Weighted Fuzzy Membership Functions," by Joon S. Lim, T-W Ryu, H-J Kim, and S. Gupta, in FSKD 2005 (LNCS 3614), pp. 811-820, Springer-Verlag, Aug. 2006.

However, the techniques of the above-described prior art can not be applied to determine the direction of an economic situation or to classify an economic situation, because it does not apply the weighted average defuzzification to predict a nonlinear time series for forecasting the economic situation using an economic composite index.

Disclosure of the Invention

Accordingly, the present invention has been conceived to resolve the above problems. An object of the present invention is to predict a nonlinear time series through weighted average defuzzification and to apply the nonlinear time series in determining and forecasting an economic situation using a Composite Index (CI), thus determining the direction of the economic situation in addition to classifying the economic situation.

Brief Description of the Drawings

FIG. 1 is a flowchart showing a nonlinear time series prediction method using weighted average defuzzifi cation based on a NEWFM according to the present invention; FIG. 2 is a diagram showing the structure of a NEWFM according to the present invention;

FIG. 3 is a diagram showing an example of the calculation of weighted fuzzy membership functions according to the present invention;

FIG. 4 is a diagram showing an example of the bounded sum of weighted fuzzy membership functions;

FIGS. 5A to 5G are diagrams showing examples of the bounded sum of weighted fuzzy membership functions generated by 7 leading indexes according to the present invention;

FIG. 6 is a diagram showing the modified structure of NEWFM to predict a nonlinear time series according to the present invention; and

FIG. 7 is a diagram showing GDP and a NEWFM-based nonlinear time series using leading indexes according to the present invention.

Best Mode for Carrying Out the Invention

In order to accomplish the above object, the present invention provides a nonlinear time series prediction method using weighted average defuzzification based on a Neural

Network with Weighted Fuzzy Membership Functions (NEWFM), comprising the steps of: installing a NEWFM algorithm in a server, and generating fuzzy rules for business forecasting using the installed NEWFM algorithm; installing a non-overlap area distribution measurement algorithm in the server, and applying the generated fuzzy rules to the installed non-overlap area distribution measurement algorithm; generating a minimum number of fuzzy rule functions in the server as the fuzzy rules are applied to the non-overlap area distribution measurement algorithm; and installing a modified NEWFM algorithm for predicting a nonlinear time series in the server, and applying the generated fuzzy rule functions to the modified NEWFM algorithm, thus predicting a time series which is a series of classes representing expansion or contraction phases of the economy.

According to an embodiment of the present invention, the method may further comprise the step of, after the step of predicting the time series, uploading the predicted time series on a website operated by the server and allowing a plurality of clients to read the time series.

According to an embodiment of the present invention, the step of installing the non- overlap area distribution measurement algorithm in the server and applying the generated fuzzy rules to the installed non-overlap area distribution measurement algorithm, is performed to eliminate input features with a low importance level from n Bounded Sums of Weighted Fuzzy Membership Functions (BSWFMs) by using the non-overlap area distribution measurement algorithm, thus minimizing the number of BSWFMs.

According to an embodiment of the present invention, the clients are economic entities including a policy maker, a financial institution, and a business enterprise, who are prospective customers for business forecasting.

Hereinafter, embodiments of the present invention will be described in detail with reference to the attached drawings. First, for the better understanding of the present invention, the Neural Network with Weighted Fuzzy Membership Functions (NEWFM) is described. The NEWFM is a supervised fuzzy neural network which classifies using the bounded sum of Weighted Fuzzy Membership Functions (WFMs) trained by inputs. The bounded sum of WFMs is obtained by combining the bounded sums of three fuzzy membership functions of large, medium, and small fuzzy membership functions with weights, into a single fuzzy membership function.

FIG. 1 is a flowchart showing a nonlinear time series prediction method using weighted average defuzzification based on NEWFM according to an embodiment of the present invention. The nonlinear time series prediction method using weighted average defuzzification based on NEWFM includes the following steps. The method includes the step SlO of installing a NEWFM algorithm in a server and generating fuzzy rules for business forecasting using the installed NEWFM algorithm, the step S20 of installing a non-overlap area distribution measurement algorithm in the server and applying the generated fuzzy rules to the installed non-overlap area distribution measurement algorithm, the step S30 of the server generating a minimum number of fuzzy rule functions as the fuzzy rules are applied to the non-overlap area distribution measurement algorithm, and the step S40 of installing a modified NEWFM algorithm for predicting a nonlinear time series in the server, and applying the generated fuzzy rule functions to the modified NEWFM algorithm, thus predicting a time series which is a series of classes representing expansion or contraction phases of the economy Preferably, the method may further include, after steps S 10 to S40, the step S50 of uploading the predicted time series on a website operated by the server and allowing a plurality of clients to read the time series.

In the following, Steps SlO to S50 are described further, in detail. Step SlO of installing the NEWFM algorithm in the server and generating fuzzy rules for business forecasting using the installed NEWFM algorithm, is performed to generate fuzzy rules. As shown in FIG. 2, the NEWFM for generating the fuzzy rules is composed of three layers, consisting of an input node group, a hyperbox node group, and a class node group.

The input node group is composed of n input nodes and each of the input nodes is inputted with a single feature input. The hyperbox node group is composed of m hyperbox nodes, and the 1-th hyperbox node B₁ is connected to only a single class node and has n fuzzy sets. The class node group of C₁, C₂,... C_p includes p class nodes, and each class node is connected to one or more hyperbox nodes of Bi, B₂, ..., B_m.

The i-th fuzzy set of B₁ is denoted by B\ , and has three weighted fuzzy

membership functions of large, medium, and small functions. The h-th input pattern to the input nodes is recorded as I_h = {A_h = (a_l , a₂ , - - -,a_n), class} . Here, 'class' is a class value, and A_h includes n feature inputs.

A weight for the connection between the hyperbox node B₁ and the class node C is given by W_n = 0 as an initial value when the connection is not formed yet, but is given by W_n = 1 when the connection is formed. In order to initially connect the hyperbox node B₁ to the class node C₁ , B₁ having the maximum value among the output values Output(B, ) of respective hyperboxes given by the input I_h = {A_h - (a₁ , a₂ ,- - - ,a_n ), class} , and C₁ given by i=class are selected. After the initial connection, B₁ is trained only when B₁ having the maximum value for input I_h is connected to C₁ , and the function Output(B_t ) is given by the following Equation 1. [Equation 1]

Output) = -∑∑BXJI_J&W,. n ι=l 7=1

In FIG. 3, V₁ , V₂ , and v₃ are the central positions of the large, medium and

small fuzzy membership functions denoted by B\ , and are horizontally adjusted during learning. v₀ and V₄ are fixed to certain values. Input α₍ falls within the range from V_011n to v_max ofFIG. 3. μ_} (.) denotes the weighted fuzzy membership function of B\ , and j (=1, 2 and

3) denotes the indices of the large, medium, and small weighted fuzzy membership functions. The shapes of respective weighted fuzzy membership functions μ_} (.) are

triangles represented by three points (v_M ,0 ),(v_/+1 ,0), and (V_j ,W_j ), where W_} is a

membership function weight (OS W₁ <1, and the initial value thereof satisfies 0.45<

W <0.55), indicating the strength of the membership function.

AdJuSt(B₁ ) is a function for adjusting the values of B\ (l≤i≤n) in B₁ using

the input A_h = (a_l ,a₂,- - -,a_n) during learning of B₁ . v_; and W₁ (j =1, 2, and 3) of

B\ , which receives input a_t , are adjusted by the value of α, in the direction for converging

to the value a_t as shown in FIG. 3.

The hyperbox node B₁ , having undergone the learning, can be used as a fuzzy

rule in IF-THEN form for classifying input patterns. B\ is composed of three Weighted

Fuzzy Membership Functions (WFMs), //, (.) , where j = 1 , 2 , and 3. The μ_b' (.)

ranging from v₀ to V₄ in FIG. 4 is the Bounded Sum of WFMs (BSWFM), and is defined by the following Equation 2, in which the fuzzy characteristics of three WFMs are

combined. The learned BSWFM, μ_b' (.) , is used as the fuzzy rule for an i-th input.

[Equation 2] μ_b ^ι (x) = ∑ B; (μ_} (x)) In step S20 the non-overlap area distribution measurement algorithm is installed in the server and the generated fuzzy rules are applied to the installed non-overlap area distribution measurement algorithm. The non-overlap area distribution measurement algorithm is disclosed in "Fuzzy Identification of Systems and Its Applications to Modeling and Control" by T. Takagi and M. Sugeno in IEEE Trans., Syst. Man, Cyberα, Vol. 15, pp.l 16-132, 1985. Here, the fuzzy rules generated at step SlO are applied to the non- overlap area distribution measurement algorithm.

In step S30 the server generates a minimum number of fuzzy rule functions as the fuzzy rules are applied to the non-overlap area distribution measurement algorithm such that, after step S20, input features having a low importance level are eliminated from n BSWFMs, which are generated through the n feature inputs at step SlO, by using the non-overlap area distribution measurement method, so that the number of BSWFMs is minimized.

That is, when fuzzy rules for business forecasting are generated using 10 leading Composite Index (CI) components and the NEWFM, a minimum number of fuzzy rules are extracted using the above-described non-overlap area distribution measurement method.

As an example, learning was conducted with 180 time series for the period from January, 1991 to December, 2005. As leading indices, 10 leading indexes such as employment and production in the manufacturing industry were selected as feature inputs, and GDP increase rate was classified into two classes with an upper and a lower threshold.

[Table 1] final 7 leading indices using non-overlap area distribution measurement

Table 1 indicates the ranks of respective feature inputs obtained as a result of applying the non-overlap area distribution measurement method to the generated fuzzy membership functions. The rank is an indicator for indicating efficiency in prediction or classification. When a learning process is performed again without deteriorating prediction performance while decreasing the number of feature inputs by the rank, a minimum number of fuzzy membership functions are extracted. FIGS. 5 A to 5G show the Bounded Sums of Weighted Fuzzy Membership Functions (BSWFMs) of 7 leading indices finally extracted through the non-overlap area distribution measurement method, and these are used as the fuzzy rules.

In step S40 the fuzzy rule functions generated at step S30 are inputted into the server in which the modified NEWFM algorithm for predicting the nonlinear time series of expanded classes is installed in order to predict the time series, which is a series of classes representing expansion or contraction phases of the economy.. Accordingly, when the hyperbox node B₁ is connected to the class node C₁ through learning of the modified NEWFM, and then the input A_h = (α, , a₂ , ^{■ ■} • , a_n ) is received, the class node C₁ having the maximum value among the output values of B₁ , that is values of Output(B, ) , is determined, and this becomes the classification strength of C₁ . As this classification strength increases, the membership degree of a given class becomes stronger. So, the prediction of a nonlinear time series, in addition to classification, is possible using the classification strength of each C₁ .

As shown in FIG. 6, when an output node O, being an output node for weighted average defuzzification, is added to the structure of the NEWFM, in which the number of class nodes is limited to two, Ci and C₂, the output value of O becomes the predicted nonlinear time series. Business cycles are characterized by periodic changes of aggregate economic activity in a country, that is, an expansion phase and a contraction phase in production, prices, and employment. Various methodologies for explaining business cycles have been proposed. The present invention shows a nonlinear time series using weighted average defuzzification based on NEWFM for forecasting a business cycle using a Composite Index (Cl).

To verify the present invention, Composite Indices (CIs), i.e., leading indices, published monthly by the Korea National Statistical Office (KNSO), were used as business- related indices, and 186 months of data collected over the period from January 1991 to June 2006 were used as the time series. Gross Domestic Product (GDP), representing the aggregate economic activities of the nation, was chosen as the target class index. The monthly correspondence of respective indices was obtained by interpolation. Table 2 shows the summary of input and test data used for NEWFM, and the details thereof. Table 2. Indicators used for NEWFM business forecasting

As shown in FIG. 7, it can be seen that prediction results for the period from January 1991 to June 2006 comply well with the same variation pattern as the tendency of the actual GDP during the same period, and sensitively reflect the expansion phase and contraction phase of the business cycle while maintaining a predetermined time delay.

In step S50 the predicted time series of the expansion and contraction phases of the business cycle as shown in FIG. 7 is uploaded on the website operated by the server to allow a plurality of clients to access and read the time series. The clients preferably include economic entities, such as a policy maker, a financial institution, and a business enterprise, who are prospective customers for business forecasting.

As described above, those skilled in the art will understand that the present invention can be implemented in other forms without changing the technical idea or essential features thereof. Therefore, it should be understood that the above-described calculations are only exemplary embodiments, and are not intended to limit the present invention. The scope of the present invention is defined by the accompanying claims rather than the detailed description, and the meaning and scope of the claims and all changes and modifications derived from the equivalents thereof should be interpreted as being included in the scope of the present invention.

Industrial Applicability

As described above, the present invention is advantageous in that an NEWFM is efficient for classification, and feature inputs having a low importance level can be eliminated using a non-overlap area distribution measurement method, thus minimizing the number of fuzzy rules for classifications; the Bounded Sum of Weighted Fuzzy Membership functions (BSWFM), which are finally extracted, visually shows the characteristics of fuzzy rules, thus facilitating the analysis and interpretation of feature inputs; prediction performance can be maximized through the selection of more reasonable indices; and mobility and convenience, attributable to the automation of business forecasting, can be realized by inputting only economic indices, so that policy making and the establishment and adjustment of business plans can be more promptly performed by economic entities, such as a policy maker, a financial institution, and a business enterprise, who are potential prospective customers for business forecasting.

Claims

1. A nonlinear time series prediction method using weighted average defuzzification based on a Neural Network with Weighted Fuzzy Membership Functions (NEWFM), comprising the steps of: installing a NEWFM algorithm in a server, and generating fuzzy rules for business forecasting using the installed NEWFM algorithm, installing a non-overlap area distribution measurement algorithm in the server, and applying the generated fuzzy rules to the installed non-overlap area distribution measurement algorithm; generating a minimum number of fuzzy rule functions in the server as the fuzzy rules are applied to the non-overlap area distribution measurement algorithm; and installing a modified NEWFM algorithm for predicting a nonlinear time series in the server, and applying the generated fuzzy rule functions to the modified NEWFM algorithm, thus predicting the time series which is a series of classes representing expansion or contraction phases of the economy.

2. The method according to claim 1, further comprising the step of, after the step of predicting the time series, uploading the predicted time series on a website operated by the server and allowing a plurality of clients to read the time series.

3. The method according to claims 1 or 2, wherein the step of installing the non- overlap area distribution measurement algorithm in the server and applying the generated fuzzy rules to the installed non-overlap area distribution measurement algorithm, is performed to eliminate input features with a low importance level from n Bounded Sums of Weighted Fuzzy Membership Functions (BSWFMs) by using the non-overlap area distribution measurement algorithm, thus minimizing the number of BSWFMs.

4. The method according to claim 2, wherein the clients are economic entities including a policy maker, a financial institution, and a business enterprise, who are prospective customers for business forecasting.