Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data.

Area of Science:

• Statistics
• Biostatistics
• Machine Learning

Background:

• Multi-source functional block-wise missing data are increasingly common in healthcare.
• Existing dimension reduction methods often treat high-dimensional data as covariates, limiting their application in classification.

Purpose of the Study:

• To propose a novel multinomial imputed-factor Logistic regression model for classification with multi-source functional block-wise missing data.
• To develop efficient dimension reduction techniques for extracting important information from complex medical datasets.

Main Methods:

• Univariate Functional Principal Component Analysis (FPCA) on observable data.
• Imputation of missing functional principal component scores using conditional mean and multiple block-wise imputation.
• Construction of multi-source principal component scores and canonical scores.
• Establishment of a multinomial imputed-factor Logistic regression model.

Main Results:

• The proposed model effectively handles multi-source functional block-wise missing data.
• Imputed functional principal component scores and canonical scores serve as effective covariates.
• Numerical simulations and real-world data analysis (ADNI) demonstrate the method's efficacy.

Conclusions:

• The novel multinomial imputed-factor Logistic regression model provides a robust solution for classification problems with complex missing data patterns.
• The imputation strategies and dimension reduction techniques are crucial for accurate information extraction in medical big data.