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Negative-Unlabeled Learning for Diffusion MRI1Department of Informatics, Technical University of Munich, Garching, Germany, 2CUBRIC, Cardiff University, Cardiff, United Kingdom, 3Department of Neurology and Psychiatry, Sapienza University of Rome, Rome, Italy, 4Division of Psychological Medicine and Clinical Neurosciences, Cardiff University, Cardiff, United Kingdom
Synopsis
Machine learning strongly enhances diffusion MRI in terms of acquisition speed and quality of results. Different machine learning tasks are applicable in different situations: labels for training might be available only for healthy data or only for common but not rare diseases; training labels might be available voxel-wise, or only scan-wise. This leads to various tasks beyond supervised learning. Here we examine whether it is possible to perform accurate voxel-wise MS lesion detection if only scan-wise training labels are used. We use negative-unlabeled learning (an equivalent of positive-unlabeled learning) and achieve an AUC of 0.77.
Introduction
Diffusion MRI provides valuable information about microstructural tissue properties. The classical processing pipeline uses physical/mathematical representations that are suboptimally simplistic (discard information) and rely on unstable fitting that requires long scan times. Recent methods based on machine learning circumvent these drawbacks. They do not rely on unstable fitting1,2,3,4,5 and extract features from diffusion-space (q-space) data in an optimized (rather than handcrafted) way1,4,5. Such methods exist for different situations/tasks: To predict voxel-wise microstructural properties (such as disease effects) in test data when training data with voxel-wise labels are available1; to detect voxel-wise “novelty” (e.g. disease effects) in test data when only “normal”-labeled (e.g. healthy) training data are available2,3,4; to predict scan-wise properties (e.g. disease) in test data when training data with scan-wise labels are available5; to get fine-grained (voxel-wise) predictions from coarse-grained (scan-wise) training labels5.The latter corresponds to different machine-learning tasks, depending on whether the information is used that (a) voxels belonging to one scan can be grouped into a “bag” of voxels, (b) all voxels from healthy-control scans are healthy, (c) which features indicate disease may depend on context (features in other voxels). Using (a,c) but not (b) corresponds to weakly-supervised learning, e.g. class-activation maps5. Using (a,b) corresponds to multiple-instance learning. Using (b) but instead of (a,c) grouping voxels into only two “bags” based on their scan-label is negative-unlabeled learning. Here we use the latter to detect multiple-sclerosis (MS) lesions without using voxel-wise training labels. Figure 1 shows an overview of methods.Methods
Data: 94 MS patients and 26 healthy controls, each with six b=0 images and 40 diffusion-weighted images (6+40 “channels”), bmax=1200s/mm², SE-EPI, voxel size 1.8mm×1.8mm×2.4mm, matrix 128×128, 57 slices, TE=94.5ms, TR=16s, motion/distortion-corrected6. Human raters marked MS lesions. To facilitate neural network training, we perform so-called feature scaling by dividing each channel by the corresponding channel mean taken over all scans. To prevent overfitting on intensity values, we also divide each scan by its mean intensity, and multiply it by a random scalar between 0.8 and 1.2 during each training epoch.
Negative-Unlabeled Learning: We examine whether it is possible to perform accurate voxel-wise MS lesion detection if only scan-wise training labels are used. We treat every voxel as a sample, with its features being the q-space measurements. We distinguish a set of negative samples (all voxels from healthy controls) and a set of unlabeled samples (patient scans consisting of lesions and healthy voxels without labels). Using such training data is called negative-unlabeled learning7, or equivalently (by renaming the classes) positive-unlabeled learning. When labeling the unlabeled set entirely as positive (hence introducing some “label-noise”) and optimizing the area under the ROC curve (AUC) is equivalent to supervised learning with AUC optimization8. Here we optimize mean-squared-error instead of AUC, which usually yields similar results. We expect a prediction around 1 for lesions and around 0.78 (due to class imbalance and neural networks averaging out label-noise) for healthy voxels.
Training: We used a convolutional network: four layers with 128, 256, 512, and 1 filter, respectively, all filter sizes 1×1×1, ReLU, mean-squared-error loss (and quality evaluation) only on segmented9,10 brain voxels. We used 60% of scans for training, 20% for early stopping, 20% for testing.
Results & Discussion
Figure 2 shows output maps from the test set together with corresponding histograms for novelty detection2,3, negative-unlabeled learning, and voxel-wise supervised learning1. As expected, supervised learning1 yields best AUC (0.91) across voxels of all test scans due to using the largest amount of information for training (correct labels for all training voxels). Negative-unlabeled learning yields overall good AUC (0.77). It uses more information (distribution of unlabeled positives) than novelty detection, but surprisingly is outperformed by it (AUC=0.89). One might suspect that “label-noise” incites negative-unlabeled learning to become sensitive to subtle MS features of normal-appearing white matter in patients, causing false-positives (in terms of lesion labels). However, high predictions also reach far into grey matter. Non-deep learning can be better for certain data, but since deep q-space novelty detection outperforms4 its non-deep counterpart, the deep nature of negative-unlabeled learning is unlikely to be the issue in this case. We were not able to tune class-activation maps5 to achieve good AUC. Their cost function is similar to negative-unlabeled learning, but the difference between them appears to influence results considerably. For all these reasons we conclude that more research on these families of methods is necessary.Acknowledgements
No acknowledgement found.References
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