Abstract
PurposeThe variational Bayesian independent component analysis-mixture model (VIM), an unsupervised machine-learning classifier, was used to automatically separate Matrix Frequency Doubling Technology (FDT) perimetry data into clusters of healthy and glaucomatous eyes, and to identify axes representing statistically independent patterns of defect in the glaucoma clusters.MethodsFDT measurements were obtained from 1,190 eyes with normal FDT results and 786 eyes with abnormal FDT results from the UCSD-based Diagnostic Innovations in Glaucoma Study (DIGS) and African Descent and Glaucoma Evaluation Study (ADAGES). For all eyes, VIM input was 52 threshold test points from the 24-2 test pattern, plus age.ResultsFDT mean deviation was −1.00 dB (S.D. = 2.80 dB) and −5.57 dB (S.D. = 5.09 dB) in FDT-normal eyes and FDT-abnormal eyes, respectively (p<0.001). VIM identified meaningful clusters of FDT data and positioned a set of statistically independent axes through the mean of each cluster. The optimal VIM model separated the FDT fields into 3 clusters. Cluster N contained primarily normal fields (1109/1190, specificity 93.1%) and clusters G1 and G2 combined, contained primarily abnormal fields (651/786, sensitivity 82.8%). For clusters G1 and G2 the optimal number of axes were 2 and 5, respectively. Patterns automatically generated along axes within the glaucoma clusters were similar to those known to be indicative of glaucoma. Fields located farther from the normal mean on each glaucoma axis showed increasing field defect severity.ConclusionsVIM successfully separated FDT fields from healthy and glaucoma eyes without a priori information about class membership, and identified familiar glaucomatous patterns of loss.
Highlights
A number of previous studies have used supervised machinelearning techniques to separate healthy from glaucomatous eyes successfully, based on visual function and optical imaging data. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] In several instances, machine-learning classifiers (MLCs) have outperformed commercially available software-generated parameters at this task. [6,7,8,15,18] Supervised MLCs are trained with labeled examples of class membership, preferably based on a teaching label other than the test being assessed
Independent component analysis (ICA) has proven highly successful for noise reduction in a wide range of applications. [26,27,28] there are data distributions where components are nonlinearly related or clustered such that they are difficult to describe by a single ICA model, for example, perimetric visual field results from a mixture of healthy and glaucomatous eyes
Previous studies using unsupervised classifiers to identify patterns of visual field defect in glaucoma eyes used glaucomatous optic neuropathy (GON), as determined by stereophotograph assessment, as an indicator of disease. [23,24] Because some eyes with GON have normal appearing visual fields and some eyes with abnormal visual fields do not have glaucomatous optic neuropathy, and since the goal of this study was to understand the structure of the data rather than diagnosis, in particular to find axes that represented visual field patterns within the data, we considered that the truth values used to validate the clusters that best separated glaucoma and normal eyes should be based on FTD visual field results instead of GON
Summary
A number of previous studies have used supervised machinelearning techniques to separate healthy from glaucomatous eyes successfully, based on visual function and optical imaging data. [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] In several instances, machine-learning classifiers (MLCs) have outperformed commercially available software-generated parameters at this task. [6,7,8,15,18] Supervised MLCs are trained with labeled examples of class membership (e.g., healthy or glaucoma), preferably based on a teaching label other than the test being assessed. [8] For example the presence of glaucomatous optic neuropathy (GON) can indicate which eyes have glaucoma when assessing visual field-based MLCs, and the presence of visual field defects can indicate which eyes have glaucoma when assessing optical imaging-based MLCs. [21] The MLCs ‘‘learn’’ to separate healthy and glaucomatous eyes in a training set and the performance (i.e., diagnostic accuracy) of each MLC is assessed on a separate test set not used during training (often using k-fold cross validation, holdout method, or bootstrapping).An alternate class of MLCs, based on unsupervised learning, has been employed to identify healthy and glaucomatous eyes, based on visual field data. [22,23,24] Unsupervised learning is a technique that discerns how the data are organized by learning to separate data into statistically independent groups by cluster analysis, or into representative axes by component analysis, without a priori information regarding class membership. [26,27,28] there are data distributions where components are nonlinearly related or clustered such that they are difficult to describe by a single ICA model, for example, perimetric visual field results from a mixture of healthy and glaucomatous eyes. In these cases, nonlinear mixture model ICA can extend the linear ICA model by learning multiple ICA models and weighting them in a probabilistic (i.e., Bayesian) manner. The variational Bayesian framework helps to capture the number of axes in the local axis set and reduces computational complexity. [29] The amalgamation of all these processes is the unsupervised variational Bayesian independent component analysis-mixture model (called VIM)
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