We introduce a sparse multivariate functional principal component analysis method by incorporating ideas from the group sparse maximum variance method to multivariate functional data. Our method can avoid the “curse of dimensionality” from a high-dimensional dataset and enjoy interpretability at the same time. In particular, our unsupervised method can capture important latent factors to explain variability of the dataset, which can induce a clear distinction between important variables in the principal components and unnecessary features based on the sparseness structure. Furthermore, our method can be applied to functional data from a multidimensional domain that hinges on different intervals. In the numerical experiment, we show that our method works well in both low- and high-dimensional multivariate functional data regardless of the number and the type of basis. We further apply our method to stock market data and electroencephalography data in an alcoholism study to demonstrate the theoretical result.

中文翻译：

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稀疏多元泛函主成分分析

我们通过将组稀疏最大方差方法的思想融入多元函数数据，引入了一种稀疏多元函数主成分分析方法。我们的方法可以避免来自高维数据集的“维度诅咒”，同时享受可解释性。特别是，我们的无监督方法可以捕获重要的潜在因素来解释数据集的可变性，这可以基于稀疏结构明确区分主成分中的重要变量和不必要的特征。此外，我们的方法可以应用于来自取决于不同间隔的多维域的功能数据。在数值实验中，我们表明，无论基础的数量和类型如何，我们的方法在低维和高维多元函数数据中都表现良好。我们进一步将我们的方法应用于酒精中毒研究中的股票市场数据和脑电图数据，以证明理论结果。