Learning Manifolds Transformation for Classification of Standard Automated Perimetry

Abstract

Abstract: : Purpose: We evaluated the effects of nonlinear transformation by unsupervised learning manifolds of high dimensional standard automated perimetry (SAP) data. A theoretical advantage of transformation with learning manifolds is improved mapping of data to the low dimensions. Methods: Learning manifold methods find a complex surface within high–dimensional data that maximizes interesting information and develops a nonlinear transformation to flatten that complex surface in a way that preserves in the low–dimension output the geometrical structure of the high–dimensional input. The learning manifold process was accomplished with the Isomap algorithm (Tenenbaum et al, Science, 2000) on 52 field locations in a single SAP field from 189 normal eyes and 156 eyes with glaucomatous optic neuropathy (GON) and 5 to 16 SAP fields in 191 eyes with GON, totaling 1872 SAP fields. The learned transformation was used to map the 52–dimensional input in 189 normal eyes and 156 eyes with GON into 1 to 6 axes. The 1 to 6 axes became input for supervised learning with support vector machines with Gaussian kernels (SVMg). The SVMg performance was tested by area under ROC curves generated with 10–partition cross validation. Results: There was no significant difference in ROC areas from SVMg trained on 2 through 6 dimensions after manifold transformation nor between SVMg trained on 6 dimensions after manifold transformation (0.90) compared to the full 52 dimensions before manifold transformation (0.91). Conclusions: This type of geometry–preserving dimension reduction can be further processed in diverse ways. Low dimensions mapped from the initial 52 dimensions by unsupervised learning with manifold transformation retained sufficient information that post–transformation classification with SVMg did not lose performance. Other potential posttransformation applications include detection of progression in sequential visual fields with posttransformation processing, such as variational Bayesian Independent Component Analysis.

Keywords: perimetry • visual fields • computational modeling