Censored Least Squares for Imputing Missing Values in PARAFAC Tensor Factorization.

Area of Science:

• Biomedical data analysis
• Multidimensional array processing
• Computational biology

Background:

• Tensor factorization is a dimensionality reduction technique for multidimensional arrays, valuable in biomedical research for pattern identification.
• Missing data presents a significant challenge in tensor factorization, potentially affecting the accuracy of reconstructed data.
• Existing methods like alternating least squares and direct optimization have limitations, including bias and slow computation.

Purpose of the Study:

• To propose and evaluate censored least squares as a superior method for tensor factorization with missing data.
• To compare the performance of censored least squares against traditional methods using biological datasets.
• To assess the accuracy and computational efficiency of different tensor imputation algorithms.

Main Methods:

• Application of censored least squares (CLS) for tensor factorization on four biological datasets.
• Comparison of CLS with alternating least squares (ALS) with prefilled values and direct optimization (DO).
• Benchmarking imputation error and the ability to infer masked values to evaluate missing data handling.

Main Results:

• Censored least squares demonstrated superior performance in handling missing values across multiple biological datasets.
• CLS exhibited higher accuracy and faster convergence rates compared to ALS and DO.
• The method proved effective in reconstructing complete tensors and inferring masked data points.

Conclusions:

• Censored least squares is well-suited for analyzing high-dimensional biological data with missing values.
• CLS offers improved accuracy and computational efficiency for tensor factorization in biomedical applications.
• This approach enhances the reliability of insights derived from incomplete biomedical datasets.