令和3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
2021 Shikoku-Section Joint Convention Record of the Institutes of Electrical and Related Engineers

1-30
Chaotic Data Classification by Using 1D, 3D and 4D Images
with Residual Network
Aika OHNO,

Yoko UWATE, and Yoshifumi NISHIO(Tokushima University)

1. Introduction
Chaotic characteristics can be observed in various kindsof time series data such as biological signals and stock pricefluctuations. Chaotic theory is also applied for other fields
including analysis of pulse wave and communication system.
Chaos shift keying is one of the example of application ofchaotic theory for communication system. In this method,chaos signals that have different parameters are sent, andreceivers need to recognize the differences of chaos parameters in the signals. Therefore, it is important to recognize
chaotic features and classify depends on the differences ofchaotic statements. As to the analysis of pulse wave, proper
recognition of the differences of chaos parameters enable toestimate their bodies and feeling conditions with better accuracies.
In this study, we classify three classes of chaos time series data that have different parameters by using neuralnetworks, and we compare the differences of the input data
shape among 1D, 3D and 4D images.

we use, and it is pretrained by ImageNet dataset. To makethe figure simple, the repetitions of batch normalization andactivation between convolution layers are omitted. Dotted lines indicate the process to increase dimensions with astride of 2.

Figure 2: The structure of ResNet50.

2. Method
By using Takens’ embedding theorem, time series datax(t) can be embedded into n-dimensional vector v(t).
v(t) = (x(t), x(t + τ ), x(t + 2τ ), ..., x(t + (n − 1)τ ))Lorenz equations are used as chaotic time series data,
and these equations are shown the following Eq. (2).

 dx
 dt = σ(y − x)

(1)

dy

1-dimension (1D) time series data is converted into 3dimensions (3D) and 4-dimensions (4D) attractors, and it
is shown in Fig. 1. In this study, x dimension of Lorenz
data is embedded with time lag τ = 10. Image size is 512
× 128 for 1D data, and 256 × 256 for both of 3D and 4D
data.

= x(ρ − z) − y=xy − βzdtdt dz(2)σ= 10 and ρ= 28 are used, and the dataset belongs tothree classes β=7/3, 8/3, 15/6. Train data and test data
are divided randomly. Train data has 1800 data and test
data has 1200 data in total of 3 classes. The data havedifferent initial values. The length of each time series data
is 500 time steps.

3. Simulation Results
Table 1 shows the simulation result. Batch size is 16, andthe number of epoch is 250.

Table 1: Simulation result1D3D4D

Figure 1: Reconstructed 3D attractor from time series
data.
Residual Network (ResNet) is commonly used for theclassification of image data. ResNet is the network that enable to have deep layered networks without vanishing gradient problem. Figure 2 shows the structure of ResNet50 that

Train accuracy
0.8156
0.95280.8539Test accuracy
0.70000.90630.8025

3D data shows the best accuracy result, and 1D datashows the worst accuracy.

4. Conclusion
In this study, we classified 3 classes of Lorenz data byusing 1D, 3D and 4D attractors image data from time series
data by applying Takens’ embedding theorem. For future
work, we would like to apply it different kinds of chaos timeseries data, and also we would like to study for efficientchaos feature extracting.

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