令和5年度 電気・電子・情報関係学会 四国支部連合大会 講演論文集＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿
2023 Shikoku-Section Joint Convention Record of the Institutes of Electrical and Related Engineers

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Effect of Delay Time for Chaotic Attractors
on Classification Accuracy Using Neural Networks
Masaki Fujita

Hiromu Hamanaka Yoko Uwate( Tokushima University )Yoshifumi Nishio

1. Introduction
Previous studies of chaotic data classification have known
that using attractor images improves classification accuracy[1]. We focused on the delay time that is an importantparameter in attractor generation. In this study, reconstruct chaotic data as attractors and classify them by image recognition. In addition, we generated attractors withdifferent delay times and investigated how they affect classification accuracy. As a result, we confirm that classification
accuracy changed greatly depending on the delay times.

2. Proposed Methods
The neural network used in this study is shown in Fig.
1. Residual Network 50 (ResNet50) consisting of 50 intermediate layers that incorporates residual learning is used.
ResNet50 is used as a method for image classification of
chaotic attractors in previous studies. ResNet50 is a Deep
Neural Network that overcomes the conventional problemsof gradient loss and degradation by incorporating residuallearning. In this study, ResNet50 is used to classify attractors.

Figure 2: Attractors for each delay times.

Table 1: Test accuracy for each delay times.

τ =1
τ = 10τ = 20τ = 30τ = 40τ = 50All training settings for each attractor image are same
except for delay times. The settings in this study are training data = 1800 images, test data = 1200 images, batch
size = 16, epoch = 300. As a result, increasing the delay
time improved classification accuracy.

Figure 1: ResNet50.
In this study, image classification was performed on attractors embedded with different delay times. Takens’ theorem in Equation (1) was used for embedding. It is known
that the reconstruction is valid if the relationship between
the dimension m of the attractor to be reconstructed andthe original dimension d is m > 2d + 1 according to Takens’ embedding theorem. In this study, we investigated theeffect of delay time τ (>0) on classification accuracy.
v(t) = (x(t), x(t + τ ), x(t + 2τ ), ......, x(t + (n − 1)τ ))test accuracy(%)
46.4
69.1
83.4
84.7
83.3
82.4

4. Conclusion
In this study, attractors were generated with different delay times by Takens’ embedding theorem and investigatedthe classification accuracy of attractor images.As a result,increasing the delay time greatly improved classification accuracy. We consider that increase in attractor features contributed to the improvement in classification accuracy.

(1)

3. Results

5. Reference

We performed image classification of chaotic data withattractors embedded in Takens’ theorem with different delay times. Fig. 2 shows the attractors generated for each of
the different delay times. Table 1 shows the classification
accuracy with each attractor generated in different delaytimes.

[1]Hiromu Hamanaka, Yoko Uwate, Yoshifumi Nishio,”Chaotic Data Classification Methods for Residual Neural Network” Proceedings of International Symposium onNonlinear Theory and its Applications (NOLTA’23), Sep.
2023.(accepted)

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