A Novel Approach to Perform Linear Discriminant Analyses for a 4-way Alzheimer's Disease Diagnosis Based on an Integration of Pearson’s Correlation Coefficients and Empirical Cumulative Distribution Function

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Abstract The diagnosis of Alzheimer's disease (AD) in his prodromal stage is a major topic. About 50% of the well-known Mild Cognitive Impairment (MCI) cohort are estimated to develop AD, and the reasons for conversion or not are still unknown. An efficient diagnosis of the earlier (EMCI) and later (LMCI) cohorts among normal control subjects (CN) is still a big research challenge. Encouraged by the available data provided by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database, we aim to develop a 4-way framework for multi-class diagnosis. One of the standard methods for supervised classification is Linear Discriminant Analysis (LDA). In contrast to the traditional method based on Principal Component Analysis (PCA) followed by LDA, the current paper proposes a novel approach where optimal LDA subspace is integrated with Pearson’s correlation coefficient (PCC) method to overcome the singularity problem resulting in the case of an underdetermined dataset. We choose, for innovation, to operate the brain connectivity reconstructed from diffusion-weighted imaging modality. First, Diffusion Tensor and Magnetic Resonance brain images of 229 subjects have been preprocessed, their correspondent brain connectivity maps have been required, and connections inside and between hemispheres have been extracted. Second, correlation coefficients between features and classes have been determined, and empirical cumulative distribution functions have been reconstructed (ECDF). Features concerned by the transformation into the LDA space are those exhibiting a cumulative frequency above a determined percentile of the ECDF, in condition to guarantee the non-singularity of the within-class variance matrix. Finally, different machine learning algorithms have been performed and evaluated thanks to the repeated five-fold Cross-Validation procedure. Compared to other methods, the originality of this work is that an accuracy of 100% has been achieved for the LMCI class diagnosis. Furthermore, the connectivity between hemispheres has been identified as a biomarker for disease diagnosis.

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