Spherical Topology Self-Organizing Map (SOM) Neural Networks for Visualization of

Complex Data

Huajie Wu u4932885 Supervisor: Professor Tom Gedeon

Proposed by Kohonen in 1982

Regular Arrangement: 1D and 2D

But 1D and 2D have a “border effect”.

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Therefore, many spherical SOMs are proposed H-SOM(proposed by Hirokazu in 2006), S-SOM (proposed by Sangole and Leontitsis in 2006).

H-SOM arrange the neurons along a helix, but calculating neighbors is quite complicated. My project CSSOM, mainly based on S-SOM.

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The arrangement & neighborhood structure: Predefined grid units The number of vertices can be calculated as:

NN=2+10*4n

The representations of distortions and colors: Two significantly different colors Two clumps between the

boundaries of the colors

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S-SOM has limitations. Arrangement and representation of a sequence of events. Concentric spherical SOM solved those problems. CSSOM Structure: ‘a’ in sphere1 is the winning neuron

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Plot the spheres in form of a chain (Plot ‘Chain’ Glyph) Analyze a specified sphere and adjacent. Good for analyzing the spheres as a whole.

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Plot an arbitrary continuous equal-size spheres (Plot ‘Equal’ Glyph)

Solved the problem in displaying “Plot ‘Chain’ Glyph” schema.

Provide users optimal visual effects.

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The difference between parallel training and sequence training

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Spheres Times S1 S2 S3

1 P2 P2 P2 2 P3 P3 P3

3 P1 P1 P1 4 P5 P5 P5

5 P4 P4 P4

… … … …

Spheres Times S1 S2 S3

1 P1 P2 P3 2 P2 P3 P4

3 P3 P4 P5 4 P4 P5 P1

5 P5 P1 P2

… … … …

Quantization Error and Topological Error:

QE evaluate how well the neural network map fits the input patterns. Average distance between vectors and BMU.

TE is used to measure the topology preservation. Proportion of all data vectors for 1st and 2nd BMU are not adjacent.

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The quality of SOMs

Focus on comparing between SSOM and CSSOMs. “ECSH” dataset is used. 3,641 patterns. Read paragraphs in Easy, Calm, Stressful, Hard order. It reflects 60Hz recordings and spans one minute. The representations of SOMs

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SOMs structure The number of spheres Units/per layer Total units

S-SOM 1 2,562 2,562 CSSOM(4S) 4 642 2,568 CSSOM(16S) 15 162 2,592 CSSOM(61S) 61 42 2,562 CSSOM(214S) 214 12 2,568

Continued…

1498

376

684

1595

1267

0200400600800

10001200140016001800

Average number of neighborhoods per unit

SSOM

CSSOM(4S)

CSSOM(15S)

CSSOM(61S)

CSSOM(214S)

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7 4 2 1 0

5101520253035

The number of units with different neighborhoods

the number of unitswith differentneighbors

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Figure 1. Figure 2.

Table 1: QE and TE of SSOM and CSSOM using dataset “ECSH”

ERROR SSOM CSSOM(4S) CSSOM(16S) CSSOM(61S) CSSOM(214S)

QE 193.77 381.71 188.25 587.73 426.14 TE 0.101 0.328 0.179 0.092 0.105

Parallel training and sequence training

“ECSH” dataset is used. The results are not expected.

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Table 1: QE and TE of Parallel Training and Sequence Training using dataset “ECSH”

ERRORS Parallel Training Sequence Training

QE 188.25 1511.52

TE 0.179 0.496

Comparisons with parallel training and sequence training in visualization

Figure 1:Visual glyph for “Parallel Training”

Figure 2:Visual glyph for “Sequence Training” 13

Fulfilled the objectives

Implemented working CSSOM Evaluation code to test Sequence training needs more work e.g. For each epoch, the first pattern selected randomly for training, but patterns’ order (time series) still kept sequential.

Other future work More diverse dataset R and epochs are adjustable automatically, depending on the dataset’s characteristics…

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