Paper:
Robust Feature-Sample Linear Discriminant Analysis for Brain Disorders Diagnosis
A wide spectrum of discriminative methods is increasingly used in diverse applications for classification or regression tasks. However, many existing discriminative methods assume that the input data is nearly noise-free, which limits their applications to solve real-world problems. Particularly for disease diagnosis, the data acquired by the neuroimaging devices are always prone to different sources of noise. Robust discriminative models are somewhat scarce and only a few attempts have been made to make them robust against noise or outliers. These methods focus on detecting either the sample-outliers or feature-noises. Moreover, they usually use unsupervised de-noising procedures, or separately de-noise the training and the testing data. All these factors may induce biases in the learning process, and thus limit its performance. In this paper, we propose a classification method based on the least-squares formulation of linear discriminant analysis, which simultaneously detects the sample-outliers and feature-noises. The proposed method operates under a semi-supervised setting, in which both labeled training and unlabeled testing data are incorporated to form the intrinsic geometry of the sample space. Therefore, the violating samples or feature values are identified as sample-outliers or feature-noises, respectively. We test our algorithm on one synthetic and two brain neurodegenerative databases (particularly for Parkinson's disease and Alzheimer's disease). The results demonstrate that our method outperforms all baseline and state-of-the-art methods, in terms of both accuracy and the area under the ROC curve.

Review:
This work was vaguely interesting as it proposed handling noisy features and labels within a semi-supervised pattern recognition framework.In medicine, a proportion of labels are often wrong (eg a diagnosis of Alzheimer's disease is often incorrect).In terms of originality, there are many papers on the subject of improving classification accuracy using the ADNI (Alzheimer's disease, AD) dataset, although not as many using the PPMI (Parkinson's disease, PD) database.It would perhaps have been interesting to see if the proposed method generalises to other sorts of data beyond diagnoses using MRI.It could also be interesting to assess the behaviour of the approach if some of the training data are deliberately mislabelled.This could be future work though.This manuscript builds on the Huang et al paper on Robust regression, which I have not read. The approach involves various settings, which were determined via a nested cross-validation procedure.This should mean that the estimated classification accuracies are relatively unbiased.For the PD dataset, there were 56 normal controls and 56 patients.Classification accuracy was 84.1%, which was higher than for the other methods.The dataset was relatively small, so it's difficult to say whether this was a statistical fluke. For the AD dataset, the proposed method also appeared to perform best, although the accuracy was not so much better than for the other methods.This could easily have been down to chance.Accuracies are not really high enough for clinical applications, but this may be down to incorrect diagnoses of patients involved.If the method had been probabilistic, then prediction could perhaps be combined with other sources of information, but this is not the case here.There is not even any mention of sensitivity and specificity, which could be used to adjust for the fact that in the real world, the prior probability of having a disease is not 0.5 (or whatever the proportions are in the training data).The manuscript uses the ADNI dataset, but does not appear to comply with their data use agreement.I do not personally approve of the requirements imposed by ADNI, and I do not know if NIPS has an editorial policy on this sort of thing.I do not see how equation 1 gets around the N > d problem, as there is no regularization involved.I do not understand why the authors propose the use of k-NN to determine class labels after having performed LDA.Figure 1 is not needed and does not add anything to the work.In the "Contributions", the authors say they "build a robust discriminative classification model".My understanding of LDA is that it is fundamentally generative, which models two Gaussian distributions that share their covariance matrices.The framework here seems to be discriminative though, treating classification as a regression problem.In equations 2 and 3, is the 1 superscript needed in $|| H (Y_{tr} - \beta X_{tr}) ||_1^1$ ?On page 4, the paper says that the first term of equation 3 contains a quadratic optimization step.This does not make sense, as the equation does not contain steps.The first term is an l_1 norm. The step from equation 3 to equation 5 needs some more rigorous justification.It currently seems like an ad hoc procedure.On page 8, the manuscript says "The magnitude of the coefficients would show the significance of contribution for that specific feature".This is not a statistical significance, and it is not clinical significance.Perhaps refer to the "relevance", rather than "significance".