# A novel approach for fusion of heterogeneous sources of data

arXiv: https://arxiv.org/abs/1803.00138 · HTML: https://mlsanity.com/paper/1803.00138/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2018.

## Built on by (most cited first, 14 of 14)

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- [Maximum Covariance Unfolding Regression: A Novel Covariate-based Manifold Learning Approach for Point Cloud Data](https://mlsanity.com/paper/2303.17852/) (2023)
- [Tensor-based process control and monitoring for semiconductor manufacturing with unstable disturbances](https://mlsanity.com/paper/2401.17573/) (2024)
- [Tensorized Multi-Task Learning for Personalized Modeling of Heterogeneous Individuals with High-Dimensional Data](https://mlsanity.com/paper/2508.15676/) (2025)
- [Low-Rank and Structured Sparse Tensor Decomposition for Anomaly Detection in Multivariate Functional Data](https://mlsanity.com/paper/2610.06930/) (2026)

## Abstract (arXiv)

With advancements in sensor technology, a heterogeneous set of data, containing samples of scalar, waveform signal, image, or even structured point cloud are becoming increasingly popular. Developing a statistical model, representing the behavior of the underlying system based upon such a heterogeneous set of data can be used in monitoring, control, and optimization of the system. Unfortunately, available methods only focus on the scalar and curve data and do not provide a general framework that can integrate different sources of data to construct a model. This paper poses the problem of estimating a process output, measured by a scalar, curve, an image, or a point cloud by a set of heterogeneous process variables such as scalar process setting, sensor readings, and images. We introduce a general approach in which each set of input data (predictor) as well as the output measurements are represented by tensors. We formulate a linear regression model between the input and output tensors and estimate the parameters by minimizing a least square loss function. In order to avoid overfitting and to reduce the number of parameters to be estimated, we decompose the model parameters using several bases, spanning the input and output spaces. Next, we learn both the bases and their spanning coefficients when minimizing the loss function using an alternating least square (ALS) algorithm. We show that such a minimization has a closed-form solution in each iteration and can be computed very efficiently. Through several simulation and case studies, we evaluate the performance of the proposed method. The results reveal the advantage of the proposed method over some benchmarks in the literature in terms of the mean square prediction error.