In recent years, the preliminary diagnosis of Attention Deficit Hyperactivity
Disorder (ADHD) using electroencephalography (EEG) has garnered attention from
researchers. EEG, known for its expediency and efficiency, plays a pivotal role
in the diagnosis and treatment of ADHD. However, the non-stationarity of EEG
signals and inter-subject variability pose challenges to the diagnostic and
classification processes. Topological Data Analysis (TDA) offers a novel
perspective for ADHD classification, diverging from traditional time-frequency
domain features. Yet, conventional TDA models are restricted to single-channel
time series and are susceptible to noise, leading to the loss of topological
features in persistence diagrams.This paper presents an enhanced TDA approach
applicable to multi-channel EEG in ADHD. Initially, optimal input parameters
for multi-channel EEG are determined. Subsequently, each channel's EEG
undergoes phase space reconstruction (PSR) followed by the utilization of
k-Power Distance to Measure (k-PDTM) for approximating ideal point clouds.
Then, multi-dimensional time series are re-embedded, and TDA is applied to
obtain topological feature information. Gaussian function-based Multivariate
Kernel Density Estimation (MKDE) is employed in the merger persistence diagram
to filter out desired topological feature mappings. Finally, persistence image
(PI) method is utilized to extract topological features, and the influence of
various weighting functions on the results is discussed.The effectiveness of
our method is evaluated using the IEEE ADHD dataset. Results demonstrate that
the accuracy, sensitivity, and specificity reach 85.60%, 83.61%, and 88.33%,
respectively. Compared to traditional TDA methods, our method was effectively
improved and outperforms typical nonlinear descriptors. These findings indicate
that our method exhibits higher precision and robustness.

近年来，利用脑电图（EEG）进行注意力缺陷多动障碍（ADHD）预诊断吸引了研究人员的关注。本文提出一种改进的拓扑数据分析方法，用于多通道 EEG 信号在 ADHD 中的应用。结果表明，该方法具有更高的精确度和鲁棒性。