Learning Low Dimensional Manifold Representation of Scanning Laser Polarimetry Data From Healthy and Glaucomatous Eyes

Abstract

Abstract: : Purpose: Recently, optimization using machine learning classifiers (MLC) has been used in an attempt to decrease the complexity of imaging data and to demonstrate the viability of MLC analyses for glaucoma detection. Currently, only supervised learning techniques (where the diagnosis is known during the learning phase) have been employed. In this study, we apply a new unsupervised (no labeled information given) technique, non–linear manifold learning using the ISOMAP algorithm, to scanning laser polarimetry (SLP) data to learn the mapping from the complex high dimensional representation to a simpler low dimensional representation of these data . We then assess the ability of ISOMAP derived and reduced dimensional data sets to classify and interpret eyes as healthy or glaucomatous. Methods: The ISOMAP algorithm (Tenenbaum et al., Science, 2000) is used to map the 64–dimensional (64 circumpapillary retinal nerve fiber layer thickness measurements) SLP data from 164 eyes (92 glaucoma by repeatable VF defects and 72 healthy) into a low–dimensional representation. This algorithm transforms the original 64 dimensional data into 1 to 10 lower dimensions. A subset of the first 1 to 10 features of each dimensions is used as input to a classifier (support vector machine) to determine the ability of the dimensions to classify glaucomatous and healthy eyes. The classification performance of each dimension is tested by determining areas under ROC curves using 10–partition cross–validation. We also compared the performance of each axis to that of the original 64–dimensional data set. Results: Areas under the ROC curves were 0.881 using the first dimension and 0.882 using the first 2 dimensions, respectively. These ROC curve areas were not significantly different from the ROC curve obtained using the 64–dimensional data set which is 0.911. Areas under ROC did not improve significantly with more than 1 dimensions. Conclusions: The ISOMAP method for unsupervised learning of a lower dimensional mapping of SLP data captures informative features. This manifold learning approach preserves good classification performance since it seems to learn the intrinsic structure of SLP data in only one dimensions. The learned mapping also provides additional information about how machine learning determines useful features for detecting healthy or glaucomatous eyes.

Keywords: imaging methods (CT, FA, ICG, MRI, OCT, RTA, SLO, ultrasound) • optic disc • computational modeling