Fig 1.
Illustration of the linear regression (LR), transformed-target principal component regression (TTPCR), and partial least squares (PLS) methods.
Note that while only one general diagram is shown for each model, for SORS in fact many models are trained until the optimal model is found for reconstruction from S = 1, 2, …, 53 to 54 locations. In TTPCR, the second PCA layer is trained once and frozen for all cases of S. This contrasts with PLS, where both layers are optimized for each model.
Fig 2.
Point-wise RMSE as a function of the embedding dimension (number of principal components) with TTPCR and PLS after testing 36 locations in a reliable responder (3% false positive and 3% false negative).
(Left) Cross-validation results with a small (20%) training dataset. Testing error is much larger than training error when the embedding dimension is large. (Right) Cross-validation results with a large (90%) training dataset. Testing error is similar to training error. TTPCR performs similarly to PLS in all cases.
Fig 3.
Point-wise RMSE (A and C) and number of trials (B and D) as a function of number of tested locations with TTPCR, LR, Quadrant, and Mean. Cross-validation results of using 20% for training (A and B, small dataset) and 90% for training (C and D, large dataset).
Fig 4.
Distribution of point-wise RMSE (A, C, E) and test duration (B, D, F) after training on the small dataset using TTPCR and LR in different disease severities. When both are terminated after 36 locations, TTPCR(36) (blue) achieves lower RMSE than LR(36) (orange) (p<0.0001 for all severities). LR(46) (green) is able to achieve similar accuracy as TTPCR(36) (blue) but is 29% longer on average (p<0.0001 for all severities).
Fig 5.
Order of locations tested in the SORS algorithm using four different reconstruction models.
The first four locations are marked in red, the next 16 locations in blue, and the following 16 locations in green. Top row, left: Using the mean (hill-of-vision) estimator for untested locations in SORS essentially results in testing locations with the largest variances to locations with the smallest variances. Right: The traditional quadrant growth map first tests the four quadrant centers (marked in red), and then “grows” their deviations from normal values to neighboring locations. Bottom row, left to right: LR, TTPCR, and PLS models learn a sequentially optimized order of testing based on the training data. In the presented sequences, both TTPCR and PLS used an 8-dimensional embedding, while LR is 54-dimensional.
Fig 6.
(Left) Point-wise RMSE of PCA reconstruction as a function of embedding dimension. Principal components were trained on the full dataset and then the PCA reconstruction error is evaluated on all, mild (MD>−6 dB), moderate (−12<MD<−6 dB), and severe (MD<−12 dB) data. (Right) Visualization of the top four principal components superimposed on the Garway-Heath visual field sectors.