Publications

We propose a novel factor model in the graph frequency domain for multivariate data lying on the vertices of a graph, called a multivariate graph signal. By utilizing graph filters, our model extends the frequency-domain approach of the dynamic factor model from time series to graphs, enabling a graph-aware and multiscale interpretation of factors across graph frequencies. This approach reduces the dimensionality of graph signals and improves the understanding of their structure. It also allows the use of the extracted factors for subsequent analyses, such as clustering. We describe the estimation of factors and their loadings and investigate the consistency of the factor estimator. In addition, we propose two consistent estimators for determining the number of factors. The finite sample performance of the proposed method is demonstrated through simulation studies under different graph structures, including a comparison with classical factor analysis and an exploration of how the graph structure affects the results. Furthermore, we demonstrate the effectiveness of the proposed method by applying it to G20 economic data, water quality data from the Geum River, and passenger data from the Seoul Metropolitan subway.

With the advancements in technology and monitoring tools, we often encounter multivariate graph signals, which can be seen as the realizations of multivariate graph processes, and revealing the relationship between their constituent quantities is one of the important problems. To address this issue, we propose a cross-spectral analysis tool for bivariate graph signals. The main goal of this study is to extend the scope of spectral analysis of graph signals to the multivariate case. In this study, we define joint weak stationarity and introduce cross-spectral density and coherence for multivariate graph processes. We propose estimators for the cross-spectral density and investigate the theoretical properties of the proposed estimators. Furthermore, we demonstrate the effectiveness of these tools through numerical experiments, including simulation studies and a real data application. Finally, as an interesting extension, we discuss a robust spectral analysis of graph signals.

We propose a quantile based fitting method for analyzing graph signals. Unlike traditional approaches for data fitting such as smoothing splines and quantile smoothing splines working on Euclidean space, the proposed method is designed for graph domain, considering the inherent graph structure. In contrast to prevalent graph signal denoising methods that rely on optimization problem with L2-norm fidelity, our approach provides denoised signals that are robust to the existence of outliers, and identifies varying structural relationships within graph signals. We validate the efficacy of our method through comprehensive simulation studies and real data analysis.

In this paper, we present several semiparametric approaches for the inference of univariate and multivariate extremes to resolve the tasks from the Data Challenge at the 13th Conference on Extreme Value Analysis. We implement generalized additive models to capture the flexible relationship for point and interval estimations of the conditional quantiles. We also adopt Lp-quantile to estimate the marginal quantiles of extreme levels. To predict probabilities of multivariate extreme events, we implement conditional methods by Heffernan and Tawn (2004) and Keef et al. (2013). When estimating the excess probability of 50-dimensional data, we cluster variables with high correlation after simple data exploration and combine the results obtained from each cluster. We further validate predicted models based on cross-validation and select the best estimates to achieve high accuracy.

Optical emission spectroscopy (OES) data is essential for virtual metrology, enabling accurate predictions of wafer performance in plasma etching processes. This approach not only leads to resource savings but also supports better decision-making. To exploit the consecutive nature of OES data, we propose a prediction method based on a functional approach using multivariate functional partial least squares regression, coupled with dimension reduction and a novel outlier detection technique via functional independent component analysis. The proposed approach improves prediction performance by capturing the continuous nature of OES data and effectively extracting the components that describe the data structure. Numerical experiments, including simulation studies and real-world applications of OES data, demonstrate the effectiveness of the proposed method, especially in the presence of outliers.

We proposed a novel method for forecasting network time series that occur in graphs or networks. Our approach is based on a spectral graph wavelet transform (SGWT) that provides the localized behavior of graph signals around each node. The proposed method improves forecasting performance over other existing methods. In particular, the advantages of the proposed method stand out when signals observed on a graph are inhomogeneous or non-stationary.

We developed a PCA method to reflect the unique characteristics of river networks. The strengths of our approach are that it can (i) reduce dimensionality for streamflow data while effectively removing correlation among them and (ii) identify the group structure of data.