Density-based Isometric Mapping
Bardia Yousefi Mélina Khansari Ryan Trask Patrick Tallon Carina Carino Arman Afrasiyabi Vikas Kundra Lan Ma Lei Ren Keyvan Farahani Michelle Hershman
The isometric mapping method employs the shortest path algorithm to estimate
the Euclidean distance between points on High dimensional (HD) manifolds. This
may not be sufficient for weakly uniformed HD data as it could lead to
overestimating distances between far neighboring points, resulting in
inconsistencies between the intrinsic (local) and extrinsic (global) distances
during the projection. To address this issue, we modify the shortest path
algorithm by adding a novel constraint inspired by the Parzen-Rosenblatt (PR)
window, which helps to maintain the uniformity of the constructed shortest-path
graph in Isomap. Multiple imaging datasets overall of 72,236 cases, 70,000
MINST data, 1596 from multiple Chest-XRay pneumonia datasets, and three NSCLC
CT/PET datasets with a total of 640 lung cancer patients, were used to
benchmark and validate PR-Isomap. 431 imaging biomarkers were extracted from
each modality. Our results indicate that PR-Isomap projects HD attributes into
a lower-dimensional (LD) space while preserving information, visualized by the
MNIST dataset indicating the maintaining local and global distances. PR-Isomap
achieved the highest comparative accuracies of 80.9% (STD:5.8) for pneumonia
and 78.5% (STD:4.4), 88.4% (STD:1.4), and 61.4% (STD:11.4) for three NSCLC
datasets, with a confidence interval of 95% for outcome prediction. Similarly,
the multivariate Cox model showed higher overall survival, measured with
c-statistics and log-likelihood test, of PR-Isomap compared to other
dimensionality reduction methods. Kaplan Meier survival curve also signifies
the notable ability of PR-Isomap to distinguish between high-risk and low-risk
patients using multimodal imaging biomarkers preserving HD imaging
characteristics for precision medicine.