Tang, R., Kolda, T., & Zhang, A. R. (2024). Tensor Decomposition with Unaligned Observations. arXiv preprint arXiv:2410.14046.
This paper addresses the limitations of existing tensor decomposition methods in handling unaligned observations, particularly common in longitudinal multivariate data where measurements are not taken at uniform time points across subjects. The authors aim to develop a new tensor decomposition framework that effectively analyzes such data while preserving its inherent structure and minimizing information loss.
The authors propose a novel tensor decomposition framework called "tensor decomposition with unaligned observations." This framework utilizes functions in a reproducing kernel Hilbert space (RKHS) to represent the mode with unaligned observations. They introduce a versatile loss function compatible with various data types, including binary, integer-valued, and positive-valued data. To optimize the decomposition, they propose an algorithm based on alternating minimization, further enhanced by stochastic gradient descent and sketching techniques for improved computational efficiency.
The proposed framework effectively handles unaligned observations in tensor decomposition, overcoming the limitations of existing methods that require aligned data or introduce bias through data preprocessing. The use of RKHS allows for capturing complex relationships within the data, while the versatile loss function accommodates different data types. The proposed optimization algorithms, incorporating stochastic gradient descent and sketching, significantly reduce computational time without compromising accuracy.
The "tensor decomposition with unaligned observations" framework offers a powerful tool for analyzing longitudinal multivariate data with irregular measurement timings. Its ability to handle unaligned data directly, without relying on potentially biased preprocessing steps, makes it particularly valuable for real-world applications. The proposed computational methods ensure its feasibility for analyzing large-scale datasets.
This research significantly advances the field of tensor decomposition by introducing a framework specifically designed for unaligned observations, a common challenge in many practical applications. This framework, along with the proposed efficient computational methods, has the potential to enhance data analysis in various domains, including healthcare, social sciences, and finance, where longitudinal multivariate data with irregular measurements are prevalent.
While the proposed framework demonstrates promising results, future research could explore its application to higher-order tensors and investigate the theoretical properties of the estimators in greater depth. Additionally, exploring other types of reproducing kernels and loss functions tailored for specific data characteristics could further enhance the framework's applicability and performance.
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by Runshi Tang,... : arxiv.org 10-21-2024
https://arxiv.org/pdf/2410.14046.pdfDaha Derin Sorular