Diffusion tensor imaging (DTI) allows the simultaneous measurement of several diffusion indices that provide complementary information on the substrate of white matter alterations in neurodegenerative diseases. These indices include fractional anisotropy (FA) as measure of fiber tract integrity, and the mode of anisotropy (Mode) reflecting differences in the shape of the diffusion tensor. We used a multivariate approach based on joint independent component analysis of FA and Mode in a large sample of 138 subjects with Alzheimer's disease (AD) dementia, 37 subjects with cerebrospinal fluid biomarker positive mild cognitive impairment (MCI-AD), and 153 healthy elderly controls from the European DTI Study on Dementia to comprehensively study alterations of microstructural white matter integrity in AD dementia and predementia AD. We found a parallel decrease of FA and Mode in intracortically projecting fiber tracts, and a parallel increase of FA and Mode in the corticospinal tract in AD patients compared to controls. Subjects with MCI-AD showed a similar, but spatially more restricted pattern of diffusion changes. Our findings suggest an early axonal degeneration in intracortical projecting fiber tracts in dementia and predementia stages of AD. An increase of Mode, parallel to an increase of FA, in the corticospinal tract suggests a more linear shape of diffusion due to loss of crossing fibers along relatively preserved cortico-petal and cortico-fugal fiber tracts in AD. Supporting this interpretation, we found three populations of fiber tracts, namely cortico-petal and cortico-fugal, commissural, and intrahemispherically projecting fiber tracts, in the peak area of parallel FA and Mode increase.