2020 RISP International Workshop on Nonlinear Circuits,Communications and Signal Processing (NCSP 2020)
Honolulu, Hawaii, USA, February 28 - March 2, 2020

Effective Data Augmentation Methodwith Sequence Numbers from Chaos Phenomenon
for Convolution Neural Network Learning
Yuji Yamauchi, Yuichi Miyata, Yoko Uwate and Yoshifumi Nishio
Dept. of Electrical and Electronic Engineering, Tokushima University
2-1 Minami-Josanjima, Tokushima 770-8506, Japan
Email: {yamauchi, y.miyata, uwate, nishio}@ee.tokushima-u.ac.jp

Abstracttification part for classifying into the prediction result by thecombination of detected features. The output value in the outConvolution Neural Network (CNN) exhibits excellent per- put layer is the probability that the category is predicted. The
formance in image recognition, and is widely used as a base term robust as used herein means that the image position
network for solving various tasks such as segmentation and is not affected. This model exhibits excellent performancevarious object detection. However, there are still many fields mainly in image recognition, and is also widely used as awhere it is difficult to collect enough data to learn CNN. An base network for solving various tasks such as segmentation
effective technique for learning with such a small amount of and various object detection.
data is data augmentation.
In this study, image classification is performed for fields
where it is difficult to collect sufficient data. At this time,
we propose to perform image processing is performed using
a sequence obtained from chaos phenomenon to augment thedata. The proposed method is evaluated by comparing thelearning accuracy of the model trained with the augmented
data after image processing using random numbers and thetest accuracy of image classification based on the model.
Figure 1: LeNet in CNN with typical structure.
1. Introduction
A neural network that can acquire the features of an imagegroup by learning a large amount of labeled learning data,and can cope with unknown data. Among them Convolutional Neural Network (CNN) is consisted of convolution
layers that extracts features such as edge and a poolinglayers that provides robustness to the extracted features toa convention neural network in Fig. 1 [1]. The Convolution
layer can maintain spatial information. The output obtainedby processing the feature points with the filter from the original image becomes one of the units of the next layer. Thepooling layer is usually applied after the Convolution layer.
To transform the input data into a more manageable form, theinformation is compressed and down-sampled. There are effects such as being robust against minute position changes,
suppressing over-learning to some extent, and reducing thecalculation cost. The units in each layer of the fully connected layer are connected to all units in the next layer. It isoften used before the output layer, and this part is an iden-Machine learning has greatly developed various fields suchas natural language analysis [2], sound recognition, reinforcement learning, and so on by the recent development of CNN.
For instance, application such as detecting and labeling a feature included in an image, or converting human voice into
text can be cited. In the fashion industry, the Electronic
Commerce (EC) market has expanded due to computer learn
trends from a large amount of data accumulated every day,and analyzing product images from each person’s purchasehistory to find products that suit those people. However, EC
in a state where it is impossible to add value to vintage clothing, such as materials and manufacturing techniques that are
rare now, and values that arise from the state changes overtime. For this reason, vintage secondhand clothing cannot
enter the EC market so much, and there is little amount oflearning data is needed for CNN to learn. When learning sucha small amount of data, there are three methods of using highquality data, augmentation, and transfer learning. Therefore,
in this study, we focus on the augmentation of data and aim515

to improve the learning accuracy and image classification testaccuracy by the new augmentation method of a small amountdata of image data.
2. Date augmentation
Date augmentation is a technique that increases the amountof data by converting the original data. Conversion of images
include increasing noise and adjusting contrast and brightness, and so on. For example, when you rotate a plant image,
you can recognize that it is an image of a plant with the same
name. In other words, it is not necessary to change the label for the image. In addition, there are actually photographsfrom various angles, which helps to increase robustness. The
quality of images is not constant, such as shooting from various angles or shadows of other objects, so an approach that
improves robustness is important [3].
3. Logistic map
Determinism is that “giving an initial value inevitably gives
future behavior”. By combining non-linearity and deterministic rules, a phenomenon in which future behavior cannot beassumed even with a very small initial value error is a chaos
phenomenon.
The logistic map [4] is one of the simplest systems thatgenerate chaos, and shown by the following one-variable
quadratic difference equation. x represents a variable, andα represents a branch parameter.
xn+1 = αxn (1 − xn ).

Figure 2: Bifurcation diagram of logistic map.
• Intermittent chaos (α=3.83)
The time domain in which behaves irregularly and thetime domain in which periodic behavior of 3 period occur are alternately generated in Fig. 3(a).
• Pure chaos (α=4.00)
The logistic map has all natural number k periodic orbits, but all of them are unstable periodic orbits, andthe orbits keep going around the interval [0,1] withoutasymptoticing to the periodic orbits.
The sequence of pure chaos arranged in chronological order is determined according deterministic regularrules, unlike completely random numbers in Fig. 3(b).

(1)

Where n is the number of steps (n=0,1,2...). It means thedevelopment of discrete time and returns a real value between
0 and 1 by giving an initial value.
The change of the value of xn depends on what value isgiven to the parameter α. The value of α is taken between
2 and 4. When the parameter α is between 2 and 3, xn converges to a fixed point. When parameter α exceeds 3, theconvergence destination of xn is not a fixed point but a periodic solution of period 2. If parameter a is further increased,
the period of the periodic solution at the convergence destination doubles to 4, 8, and 16, and finally a chaotic time change
appears in Fig. 2.

(a) Intermittent chaos (α=3.83)(b) Pure chaos (α=4.00)
Figure 3: Time series of intermittent and pure chaos.

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4. Proposed method
In this study, the images are rotated when augmenting thedata [5]. We use a sequence derived from the chaotic phenomenon and random number. The numbers in the sequence
are from 0 to 1. These numbers are turned into angles. The
image is rotated using the obtained angle in Fig.4.
The training data is a vintage t-shirt images, even among
vintage clothing. As original data, 200 images of 70s, 80s
and 90s vintage t-shirts are collected. This original data wasaugmented by 600 each using random numbers or the value
obtained from chaos on the method that is the images are rotated, and a total data of 2400 images were obtained in Table 1.

In this study, we use a Spatial Pyramid Pooling (SPP) as apooling layer. Max pooling is done in SPP which is the operation to select the largest one for a small area. In particular,
SPP can obtain a fixed-length output regardless of the input
image size. Furthermore, the test accuracy of iamge classification by using CNN of various structures can be improvedby using SPP in the pooling layer. The convolution layer andPooling layer function to detect features.
As with the Convolution layer, the output unit value of thefully connected layer is calculated by adding a bias to theinner product of each input unit value and the connection
weight. In addition, dropout is applied to all bonding layers.
At some update time, some nodes in the layer are disabled and
CNN learning is performed. This improves generalization
performance and avoids over-learning by forcing decrease in
the degree of freedom of the network being learned [6].

(a) Original date(b) A data after processing
Figure 4: Image processing method.
Table 1: Learning data set.
The number of data
200 images each
Original data
(600 images in total)
600 images each + original data
Random(2400 images in total)
600 images each + original data
Intermittent chaos(2400 images in total)
600 images each + original data
Pure chaos(2400 images in total)
Data set nameFigure 5: CNN structure used in this paper.

In this study the CNN structure is used in Fig. 5. The structure has two convolution layers, two pooling layers, and twolayer fully connected layers. Processing in the convolution
layer is performed by calculating an inner product for eachfilter, adding a bias, and applying an activation function.
The softmax function is used as the activation function. Softmax functions are commonly used in classification problems.
Figure 6: Softmax function.
It is a real number from 0 to 1 depending on the size of each
input value, and the sum of output values is always 1. Thismeans that the output of a softmax function can be treated as
CNN learns each data set. We prepare 75 images of 70s,
a “probability”. The expression of the softmax function is ex- 80s, and 90s vintage t-shirts as the test data different frompressed Eq. (2) in Fig. 6.
the original data. The test data is input to each CNN, andthe T-shirt of the input image is classified into 70s, 80s, andexp(ak )yk = ∑n(2) 90s. We compare and evaluate the learning accuracy and test
i=1 exp(ai )accuracy of image classification by CNN trained on each datasets.

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5. Simulation result

6. Conclusion

Figure 7 shows the learning accuracy and step on CNN.
All the augmented datasets show better results than the original data set. The learning accuracy when learning the data
augmented using the sequence obtained from the pure chaosreach 100% learning accuracy faster about 20 steps than thelearning accuracy when learning the data augmented using
random numbers.

In this study, we used data from an area where it is difficult
to collect enough data for CNN learning.. The data is augmented by image processing using sequences derived fromchaotic phenomena. In addition, image classification was performed by letting CNN learn the augmented data. The proposed method was evaluated by comparing the learning accuracy of the CNN trained with the data augmented by image
processing using random numbers and the accuracy of image
classification by using the CNN.
For the both learning accuracy and test accuracy, the data
augmented used the sequence obtained from the pure chaos
showed better results than the the augmented data using random numbers. Therefore, it is effective to combine a sequence obtained from chaos for data expansion. We consider
that the important thing here is pure chaos is a non-periodicity
that is not completely random and not periodic, further has acharacteristic that is never takes the same value.
References[1] Yann LeCun, Leon Botton, Yoshua Bengio and PatrickHaffner, “Gradient-Based Leaning Applied to Document Recognition,” PROC. OF THE IEEE, 1998.

Figure 7: The accuracy of image classification.

Table 2 shows the test accuracy of image classification
when CNN learns each data set. The CNN that learns theaugmented data using the sequence obtained from pure chaosshows the highest test accuracy.

[2] Collobert, Ronan, Weston and Jason, “A Unified Architecture for Natural Language Processing: Deep Neural Networks with Multitask Learning,” Proceedings ofthe 25th International Conference on Machine Learning.
ICML ’08,2008.
[3] Luke Taylor and Geoff Nitschke, “Improving Deep
Learning using Generic Data Augmentation,” Submitted on 20 Aug 2017.
[4] Robert M. May, “Simple mathematical models withvery complicated dynamics,” Nature, vol.261, 459-467
1976.

Table 2: Test accuracy.
Test accuracy (%)
Original data
48.8637
Random52.2727
Intermittent chaos (α=3.83)
51.1364
Pure chaos (α=4)
56.8182[5] Yu-Dong Zhang, Zhengchao Dong, Xianqing Chen,
Wenjuan Jia, Sidan Du, Khan Muhammad and ShuiHua Wang, “Image based fruit category classification
by 13-layer deep convolutional neural network and dataaugmentation,” Multimed Tools Appl 2019.

However, for the both learning rate and test accuracy, themethod using intermittent chaos show a lower result than thatusing random numbers.
We consider that the differences between the propertiesof pure chaos and random is related. Pure chaos is a nonperiodicity that is not completely random like random numbers and that is not periodic, further has a characteristic thatis never takes the same value.

518[6] Nitish Srivastava, Geoffrey Hinton, Alex Krizhevsky,
Ilya Sutskever and Ruslan Salakhutdinov, “Dropout: ASimple Way to Prevent Neural Networks from Overfitting,” The Journal of Machine Learning Research, Volume 15 Issue 1, January 2014.