利用深度学习的模糊复发图分析早期帕金森病键盘敲击序列

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本文探讨了"基于深度学习的对早期帕金森病的短时间序列进行分类"这一主题，主要聚焦在利用先进技术来识别帕金森病早期症状的研究。帕金森病（Parkinson's Disease, PD）是一种常见的神经系统退行性疾病，其早期症状往往难以察觉。随着传感器和可穿戴设备的发展，科学家们正在寻找新的非侵入性方法来监测患者的运动症状，以便早期诊断。传统上，研究人员依赖于长时间的计算机键盘按键序列数据来区分健康控制组与帕金森病患者。然而，这种长时间的数据收集可能会给参与者带来不适，特别是对于需要执行物理任务来获取数据的病人。为了解决这个问题，本文提出了一种创新的方法，即使用模糊再现图（Fuzzy Recurrence Plots）处理非常短的时间序列数据。模糊再现图是一种数学工具，它通过可视化数据点之间的相似性和重复模式来分析动态系统的复杂行为。通过将这些短时间序列作为输入，论文介绍了一种结合了长短时记忆（Long Short-Term Memory, LSTM）神经网络的深度学习模型。LSTM是一种特殊的递归神经网络，特别适合处理序列数据，因为它能够捕捉长期依赖性，这对于理解和预测帕金森病的短期运动模式至关重要。使用短时间序列和模糊再现图的优势在于，一方面可以减少参与者的不适，另一方面，由于数据处理的灵活性，这种方法可以显著增加特征维度，使模型能够更好地捕捉到疾病特征的细微变化。此外，通过确定性动力系统性质的体现，这种技术可能揭示出帕金森病早期运动障碍的隐藏模式，从而提高诊断的准确性和效率。总结来说，这篇研究旨在通过深度学习和模糊再现图技术，开发一种新型、舒适的帕金森病早期检测方法，为临床实践提供一个潜在的、无侵入性的工具，以期更早地识别和干预该病的发展。未来的研究将进一步优化模型性能，以期在医疗领域得到广泛应用。

, x

)

state pair as follows [32]

R(i, k) = H[d(x

, x

)] (1)

R(i, k)

(i, k)

d(x

, x

)

H(·)

where is an element of the recurrence matrix ,

is a distance function of and , and is the

Heaviside function expressed as

H[d(x

, x

)] =

{

1, d(x

, x

) ≤ ϵ

0, d(x

, x

) > ϵ.

(2)

[0, 1]

An FRP constructs the recurrence of the phase-space vectors

as a grayscale image that takes values in without

requiring the similarity threshold parameter needed for the

RP analysis. The formulation of an FRP is described as

follows [19].

V = {v}

X × V

µ ∈ [0,1]

, v

) ∈

i = 1,. . . , N

j = 1,. . . , c

Let be the set of fuzzy clusters of the phase-space

vectors. A binary relation from to is a fuzzy subset of

characterized by a fuzzy membership function

. This fuzzy membership grade is the degree of

relation of each pair , , , that

has the following properties [33]:

µ(x

, x

) = 1, ∀x ∈ X

1) Reflexivity: ,

µ(x

, v

) = µ(v

, x

), ∀x ∈ X,∀v ∈ V

2) Symmetry: , and

µ(x

, x

) = ∨

[µ(x

, v

) ∧ µ(v

, x

)], ∀x ∈ X

∨

∧

3) Transitivity: ,

which is called the max-min composition, where the symbols

and stand for max and min, respectively.

By specifying several clusters for the data, the fuzzy -

means algorithm [34] is applied to identify the fuzzy clusters

of the phase-space vectors and determine the similarity

between the states and the fuzzy cluster centers. Based on this

direct similarity measure, the inference of the similarity

between the pairs of the states can be carried out using the

max-min composition of a fuzzy relation.

µ(x

, v

)

i j

1 < c < N

The fuzzy membership of assigned to a cluster center

of , or denoted as , is computed using the fuzzy

-means (FCM) algorithm [34] that attempts to partition

elements of into a set of fuzzy clusters, , by

minimizing the following objective function :

F =

∑

i=1

∑

k=1

(µ

i j

)

∥x

− v

∥

(3)

w ∈ [1,∞)

where is the fuzzy weighting exponent, and is

subject to

∑

j=1

i j

= 1, i = 1,. . . , N. (4)

The minimization of the objective function of the FCM is

numerically carried out by an iterative process of updating the

fuzzy membership grades and cluster centers until the

convergence or maximum number of iterations is reached.

The fuzzy membership grades and cluster centers are updated

i j

∑

q=1

(

∥x

− v

∥

∥x

− v

∥

)

2/(w−1)

. (5)

∑

i=1

(µ

i j

)

∑

i=1

(µ

i j

)

, j = 1,. . . , c. (6)

= x

i, j = 1, .. . , N

Using the values of the fuzzy membership derived from the

FCM and the fuzzy relation to represent the degree of

recurrence among the phase-space vectors of the time series,

an FRP can be visualized as a grayscale image by taking the

complement of the FRP matrix that displays a black pixel if

, , otherwise a pixel with a shade of gray.

IV. LSTM Neural Networks With FRPs

An LSTM neural network [35] is an artificial recurrent

neural network (RNN) used in deep learning. Unlike

conventional feedforward neural networks, an LSTM model

has feedback loops that allow information of previous events

to be carried on in the sequential learning process. Therefore,

LSTM networks are effective in learning and classifying

sequential data such as speech and video analysis [36]–[39].

The internal state of an RNN is used as a memory cell to

map real values of input sequences to those of output

sequences that reflect the dynamic pattern of time series, and

therefore is considered an effective algorithm for learning and

modeling temporal data [40]. However, because an RNN uses

sequential processing over time steps that can easily degrade

the parameters capturing short-term dependencies of

information sequentially passing through all cells before

arriving at the current processing cell. This effect causes the

gradient of the output error with respect to previous inputs to

vanish by the multiplication of many small numbers being less

than zero. This problem is known as vanishing gradients [41].

LSTM networks attempt to overcome the problem of the

vanishing gradients encountered by conventional RNNs by

using gates to keep relevant information and forget irrelevant

information.

The difference between an LSTM neural network and a

conventional RNN is the use of memory blocks for the former

network instead of hidden units for the latter [42]. The input

gate of an LSTM network guides the input activations into the

memory cell and the output gate carry outs the output flow of

cell activations into the rest of the network. The forget gate

allows the flow of information from the memory block to the

cell as an additive input, therefore adaptively forgetting or

resetting the cell memory. Thus, being less sensitive to the

time steps makes LSTM networks better for analysis of

sequential data than conventional RNNs. A common LSTM

model is composed of a memory cell, an input gate, an output

gate, and a forget gate. The cell memorizes values over time

steps and the three gates control the flow of information into

and out of the cell. The weights and biases to the input gate

regulate the amount of new value flowing into the cell, while

the weights and biases to the forget gate and output gate

control the amount of information to remain in the cell and the

extent to which the value in the cell is used to compute the

output activation of the LSTM block, respectively.

The architecture for an LSTM block, in which the fuzzy

1308 IEEE/CAA JOURNAL OF AUTOMATICA SINICA, VOL. 6, NO. 6, NOVEMBER 2019

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