Heizo Tokutaka 1 , Masaaki Ohkita 1 , Makoto Ohki 2 , and Matashige Oyabu 3

1. 10th WSOM2014HochschuleMittweida, University of Applied Sciences, Mittweida, Germany July 2-4 The significance degree calculation among the data components is OK only by once SOM learning -Using the iris, the Tof-SIMS, and genes data- Heizo Tokutaka1, Masaaki Ohkita1, Makoto Ohki2, and Matashige Oyabu3 1SOM Japan Inc., 2Tottori Univ., 3 Kanazawa Institute of Technology 1 (tokutaka@somj.com)

2. Abstract • The significance degree of each component was calculated only by once SOM learning where the Spherical Self-Organizing-Map (SSOM) was used for the demonstration. The method can also be used by the usual planar SOM. In the method, kinds of specimens of the data are inserted in each column as each specimen. The method is first demonstrated using the iris datafor setosa, vergicolor, and virginica, each of 50 stocks. Here, by the previous method, three times learning for three combinations of iris data are necessary. In the proposed method, only once leaning is enough. After the learning, three combinations can be calculated using the learned codebook vector.

3. Table 3 Part of the original iris data with 4 components. The classifications are added • as setosa, versicolor and virginica by 3 columns. Between 1 (setosa) and 2 (versicolor) Table 4 Table 3 continues. Here the border between 2 (versicolor) and 3 (virginica) is shown

4. Table 5 After normalization of the iris data in tables 3, 4,Here, the classification of 1_set and 2_ver (yellow columns) are assigned in the table.Normalization data of onlysetosa 1 and versicolor 2, with 100 stocksare used.New Table 6 Same data of Table 5 are used. However, here, the classification is only one yellow column. After normalization Previous

5. After SSOM learning Fig.1 (a)The U-matrix display at Griff value (0). (b)The boundary in coloring display of 1_set, 2_ver, and 3_gnc region. The red mark in (b) on the spherical surface is the one of iris classification 1(setosa) where the minimum value (0.981816) is shown. Also, 2_11 in classification 2 and 3_20, in classification 3, shows the minimum value where label code books have minimum value of 0.991068 in 2_11 and 0.987421 in 3_20. They are on the other side of the sphere

6. Table 7 (a) Arrange the table in the descending order of a B column of 1_set in the code book vector of 642 node learning. Then, searche the minimum value of 1_16. Above it, compute the average and the result in the 130th line. (b) Next, carry the same procedure of (a) in C column of 2_ver And search the minimum code book label of 2_11. (c) In the same way, arrange and search the minimum value as 3_20 to the D column, in the descending order of 3_gnc. Then, computes the average values at 146th line, and 152th line, respectively. Arrange Descending Order From B(a) of 1_set To D(c) of 3_gnc ofAll 642 nodes Search minimum Label And calculate average

7. Select each 3 average values from (a) – (c) in the previous page Table 8Copy the 130th line in (a), 146th line in (b) and 152th line in (c), in the previous Table 7 and multiply them by 100 times and display them in this table again • Cf: For essence, you can get similar results by averaging the componentsof each 50 iris data of set, ver, and gnc. However, by this method you can include 642 nodes for SSOM learning. Then, by dividing 3, actually, you can get averaging about 200 nodes not 50 data.

8. Averagingnodes results Fig.3 The figure of 1_16_setin table 8 Fig.4 The figure of 2_11_ver Fig.4 The figure of 3_20_gnc

9. Table 9The differences of 2ver-1set, 3gnc-1set and 2ver-3gnc are calculated using the averaged values with each line, based on table 8. Subtraction of 3 combinations of each line in the previous page

10. Whole 3 labeling 2 labeling Fig. 6 (a) The significance degree among versicolor:setosa calculated by the propsed method using Tables 3 and 4 (b) using Table 5

11. 2 labeling 1 labeling As usual (old) Fig. 7 (a) The significance degree among versicolor:setosa in the proposed method using Table 5 and (b) using Table 6. The both results agree very well

12. Each Comparison of 3 cases Fig. 8 By 3 methods of (a) using Tables 3 and 4, (b) Table 5, and (c) Table 6 in each figure, the significance degree are calculated and compared among 2ver-1set of vericolor: setosa, 3gnc-1set of versinica :setosa, and 3gnc-2ver of virginica : versicolor. The significance degree among gnc-ver of virginica : versicolor doesn't agree only a little as shown in the figure

13. The gene number is 831 in the crosswise-direction. The, each classification has five lines as the weight. Four kinds of 2-3, 1, 4, and 5 are made as label classifications, 5lines as the weight of 4 kinds of 2-3, 1, 4, and 5 as label classificationsof Genes data

14. health The SSOMlearning result 1 cluster (health), (b) 2-3 cluster, (c) 4cluster, and (d) 5cluster (breast cancer) Breast cancer the significance degree of 5-1 1 5 5-1

15. Significance degree .(a) to 1-150thgene, (b) to 301-450th gene Signficancedegree. (a) to 601-750th gene, (b) to 751-831th gene.

16. Significancedegree on the 5 side of the breast cancer Significance degree of the side of 1 health

17. The check is between 4-1 at two kinds of label classification in 1 and 4. Here, also the weight is 5 lines. 2kinds of 2 columns with 5lines weights The check is between 4-1 at two kinds of label classification in 1 column. 2kinds of 1 column

18. The significance degree of the 1-150 genes between 4-1 at two kinds of label classification 1-150 Significance Comparison of 3 methods

19. 601-831

20. Conclusion • Iris-data • Tof-SIMS data (not indicated) • 831 gene data • All significance degrees are calculated by 3 methods and agreed with reasonable coincidence • Therefore, it is OK to get the significance degree by only once SOM leaning