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

1-33
Nonlinear Time Series Analysis Using Attractor Dimensionality Reduction
with Neural Network
Ryosuke Shimizu

Furugaki Tomiyuki Yoko Uwate(Tokushima University)

Yoshifumi Nishio

1. Introduction

3. Simulation Result

It is diﬃcult to analyze complicated time series data using Neural Network (NN). Therefore, it is important tosearch for the eﬀective features of the data. In this study,
we reduce the dimensionality of the data and search for features that are suitable for NN classification. We investigate
the eﬀect of dimensionality reduction methods on accuracy.

In this study, electromyogram (EMG) time series data
are used as input. The experiments for collecting data consisted of freely and repeatedly grasping of diﬀerent items
which were essential to conduct the hand movements. In
this study, three motion data are used. Data 1 is Sphericalfor holding spherical tools. Data 2 is Tip for holding smalltools. Data 3 is Palmar for grasping with palm.

2. Proposed Method
In this study, the method of feature transformation forusing 3-dimensional features of time series data is presented.
(Fig. 1).

Table 1: The number of the time series data.
data
train data
test data

Figure 1: Feature translation.
Attractors are constructed by converting 1-dimensional
data (1D-data) into 3-dimensional data using time delay
embedding. x(n) is the amplitude at a certain time. Equation (1) represents this system with the time delay valueτ.
(1)f (x) = [ x(n) x(n + τ ) x(n + 2τ ) ...]

data375
75

Table 2: Test accuracy of the conventional method.

original

test accuracy(%)
64.35

Table 3: Test accuracy of the proposed method.

(a) LLE
step 1. Determine the neighbors of each point.
step 2. Compute set weights that can reconstruct a point.
step 3. Compute lower-dimensional embedding.

(c) t-SNE
step 1. Determine the neighbors of each point.
step 2. Use t-distribution for distance distribution.
step 3. Compute lower-dimensional embedding.

data27575

Table 2 and 3 show the test accuracy of the conventional and the proposed methods using 1D-CNN. By setting
the learning rate to 0.001 and the epoch of the training to20, the training accuracy has reached a maximum value of1.000. Test accuracy is calculated by averaging of 10 times.
The test accuracy of applying PCA is the best, and that ofapplying t-SNE is the worst. LLE is also highly accurate.
It can be said that the features of the data have changed
significantly when converting the original data into the datausing PCA.

In this study, the dimensionality reduction methods
which are (a) Locally Linear Embedding (LLE) , (b) Principle Component Analysis (PCA) and (c) t-SNE are used.
LLE is a method that uses the geodesic distance of multidimensional data. PCA is a method of multivariate analysis
that synthesizes variables called principal components. tSNE expresses proximity as a probability distribution. PCA
is used for dimensionality reduction on linear data. LLE
and t-SNE are used for dimensionality reduction on nonlinear data. The procedures of the methods are shown in thefollowing steps.

(b) PCA
step 1. Compute a correlation matrix from a dataset.
step 2. Get the subspace as eigenvectors by singular value
decomposition.
step 3. Compute lower-dimensional embedding.

data17575

LLE
PCA
t-SNE

test accuracy(%)
72.00
74.62
52.22

4. Conclusion
In this study, the influence of the input features into accuracy is observed each dimensionality reduction. By transforming the data into attractor, it was found that the complex nonlinear data had a certain correlation. It turns outthat t-SNE lost the data connection and erased the feature.
In the future, it is necessary to investigate the reason forthe large change in accuracy depending on the choice ofdimensionality reduction.

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