1 A latent information function to extend domain attributes to improve the accuracy of small-data-set forecasting Reporter ： Zhao-Wei Luo Che-Jung Chang,Der-Chiang Li,Wen-Li Dai,Chien-Chih Chen Neurocomputing Volume 129,10 April 2014, Pages

Outline Introduction Methodology Experimental studies Conclusions Personal remark 2

Introduction(1/3) How to control a manufacturing system effectively and efficiently is thus very important for manufacturing firms, especially in the early stages of such systems. Few observations are usually available in the early stages of manufacturing systems, so it is difficult to find robust results using prediction methods that depend on large data sets. The generation of virtual samples is usually not directly applied to time series data; because the developing trends of such data are closely related to the order of observations. 3

Introduction(2/3) 4 Fig.1 provides a simple illustration of this issue. If we create virtual samples and get the trend line, shown as the dotted line in the figure, we can see that there is a significant accumulative difference between the dotted line of virtual samples and the solid line of real data.

Introduction(3/3) This study thus proposes a Latent Information (LI) function to analyze data characteristics and extract information to assist knowledge acquisition with small data sets. The experimental results show that the LI function is an appropriate technique for small-sample learning, because it can improve forecasting accuracy. 5

Methodology(1/5) Authors utilize four indexes from statistics to describe the data feature in this work, and these are the central tendency (CT), dispersion, skewness and kurtosis. Authors set the kurtosis at 1 (the most widely used value), since changes in the kurtosis value would not affect the LI value of each datum. The central tendency is a single value that summarizes a set of data. It lies in the position where the data is most likely located to reflect the whole trend of the series. 6

Methodology(2/5) 7 Fig.2 shows that the incoming datum, x n, provides the direction of movement of the CT in phase n, i.e., the newest CT, CT new, will move to a new position between the prior CT, CT old, andx n. CT new is thus a linear combination of CT old and x n. (1)

Methodology(3/5) The dispersion is used to evaluate the variation of data. A small dispersion value indicates that the data are clustered together closely. This study selects the simplest measure of dispersion in statistics, range (R), to evaluate the variation in a small data set. 8 (2)

Methodology(4/5) The skewness can show the distribution of the whole data. Authors utilize the central location (CL) as the benchmark to measure the degree of skewness of a data set, and the CL is the average of the largest datum and smallest datum in the data set.. Authors thus define + X as the set consisting of all data with values larger than CL in X, and − X as the set consisting of all data with values less than CL in X. By using + X and − X, calculate the increasing tendency (IT) and the decreasing tendency (DT), and together these ratios present the future of the data distribution. 9

Methodology(5/5) 10 (3) (4) (5) (2) (1)

11 (6)

Experimental studies(1/9) 12

Experimental studies(2/9) Authors use four training samples to train the BPN, and each paired sample includes one input attribute and one output attribute, as{(x 1,x 2 ),(x 2,x 3 ),(x 3,x 4 ),(x 4,x 5 )}. 13

Experimental studies(3/9) In the first case of the SCCTS data set, training set contains five observations,{ , , , , }. Input x 5 = to output the predicted value as x 6 = Originally x 6 =

Experimental studies(4/9) This study employs the LI values to extend the training set to improve the learning performance of the BPN. There are four learning samples, as {(x 1,LI 1,x 2 ),(x 2,LI 2,x 3 ),(x 3,LI 3,x 4 ),(x 4,LI 4,x 5 )}. 15

Experimental studies(5/9) Authors employ the LI function to extend the information and obtain the LI value for each datum, as LI={0.3144, , , , }. (x 5,LI 5 )=( ,0.3626) is input into the model to obtain the predicted value of x 6 =

Experimental studies(6/9) 17

Experimental studies(7/9) Authors use four measurements to evaluate the forecasting results, namely the mean squared error (MSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), and standard deviation of forecasting errors (SD). 18

Experimental studies(8/9) 19

Experimental studies(9/9) 20

Conclusions 21 The LI function is considered a useful forecasting approach for application in today's complex and highly competitive business environment. For future research,one suggestion is based on the impact of training size with regard to small-data-set learning, and thus developing a rule to determine the appropriate numbers of training data for a specific case is an issue that deserves further attention. Another goal for further research is to optimize the parameter settings for the LI function.

Personal remark 22 Cyclic have less effect. LI done on optimization, try to narrow the scope to do. (5)

Thanks for your attention 23