MuSiCNet: A Gradual Coarse-to-Fine Framework for Irregularly Sampled Multivariate Time Series Analysis

TL;DR

MuSiCNet addresses irregularities in ISMTS by reframing them as relative to sampling rates and learning representations across a coarse-to-fine hierarchy. It introduces CorrNet, an encoder–decoder framework that uses time attention and LSP-DTW-based frequency correlations to fuse intra- and inter-series information at each scale, and couples this with a cross-scale rectification mechanism based on reconstruction alignment and contrastive learning. The method is task-general, delivering competitive or state-of-the-art results in ISMTS classification, interpolation, and forecasting across diverse real-world datasets. By leveraging multi-scale information and robust frequency-domain correlations, MuSiCNet enhances temporal representation quality while mitigating irregular sampling effects with practical implications for healthcare, climate, and other domains."

Abstract

Irregularly sampled multivariate time series (ISMTS) are prevalent in reality. Most existing methods treat ISMTS as synchronized regularly sampled time series with missing values, neglecting that the irregularities are primarily attributed to variations in sampling rates. In this paper, we introduce a novel perspective that irregularity is essentially relative in some senses. With sampling rates artificially determined from low to high, an irregularly sampled time series can be transformed into a hierarchical set of relatively regular time series from coarse to fine. We observe that additional coarse-grained relatively regular series not only mitigate the irregularly sampled challenges to some extent but also incorporate broad-view temporal information, thereby serving as a valuable asset for representation learning. Therefore, following the philosophy of learning that Seeing the big picture first, then delving into the details, we present the Multi-Scale and Multi-Correlation Attention Network (MuSiCNet) combining multiple scales to iteratively refine the ISMTS representation. Specifically, within each scale, we explore time attention and frequency correlation matrices to aggregate intra- and inter-series information, naturally enhancing the representation quality with richer and more intrinsic details. While across adjacent scales, we employ a representation rectification method containing contrastive learning and reconstruction results adjustment to further improve representation consistency. MuSiCNet is an ISMTS analysis framework that competitive with SOTA in three mainstream tasks consistently, including classification, interpolation, and forecasting.

Figures (3)

• Figure 1: Comparative visualization of multi-scale time series data with various sampling rates. Scale $L$ depicts the original selected representative time series in the P12 Dataset to show the inter- and intra-series irregularities. Scale $1$ to Scale $L-1$ illustrates the effect of applying different sampling rates from low to high.
• Figure 2: Overview of MuSiCNet framework, shown in (a), containing three main components for better representation learning, including hierarchical structure $\{X_{\text{mask}}^{(l)}\}_{l=1}^{L}$, representation learning using CorrNet within scale $\ell_{\text{cons}}^{(l)}$, and rectification operation across adjacent scales $\ell_{\text{recon}}^{(l)}$. (b) visualizes the encoding process in CorrNet for Scale $l$, which relies on $\tau_n^{(l)}$ to aggregates intra-series information, and then relies on $c_{d_i, (\cdot)}$ to fuse inter-series information from other variables for $d_i$-th dimension. (c) visualizes the calculation process of the correlation matrix, which transfers the time domain into the frequency domain with LSP, and then utilizes DTW to calculate the similarity weight.
• Figure 3: Visualization of various methods to extract the correlation matrix from P12 dataset. The darker the color, the more similar the relationship. (a) denotes the average pairwise observation rate (i.e., 1 minus missing rate), and (b) - (d) denotes the correlation matrices.