Deep ROC Analysis and AUC as Balanced Average Accuracy, for Improved Classifier Selection, Audit and Explanation.

Optimal performance is desired for decision-making in any field with binary classifiers and diagnostic tests, however common performance measures lack depth in information. The area under the receiver operating characteristic curve (AUC) and the area under the precision recall curve are too general because they evaluate all decision thresholds including unrealistic ones. Conversely, accuracy, sensitivity, specificity, positive predictive value and the F1 score are too specific-they are measured at a single threshold that is optimal for some instances, but not others, which is not equitable. In between both approaches, we propose deep ROC analysis to measure performance in multiple groups of predicted risk (like calibration), or groups of true positive rate or false positive rate. In each group, we measure the group AUC (properly), normalized group AUC, and averages of: sensitivity, specificity, positive and negative predictive value, and likelihood ratio positive and negative. The measurements can be compared between groups, to whole measures, to point measures and between models. We also provide a new interpretation of AUC in whole or part, as balanced average accuracy, relevant to individuals instead of pairs. We evaluate models in three case studies using our method and Python toolkit and confirm its utility.

A new concordant partial AUC and partial c statistic for imbalanced data in the evaluation of machine learning algorithms.

BACKGROUND: In classification and diagnostic testing, the receiver-operator characteristic (ROC) plot and the area under the ROC curve (AUC) describe how an adjustable threshold causes changes in two types of error: false positives and false negatives. Only part of the ROC curve and AUC are informative however when they are used with imbalanced data. Hence, alternatives to the AUC have been proposed, such as the partial AUC and the area under the precision-recall curve. However, these alternatives cannot be as fully interpreted as the AUC, in part because they ignore some information about actual negatives. METHODS: We derive and propose a new concordant partial AUC and a new partial c statistic for ROC data-as foundational measures and methods to help understand and explain parts of the ROC plot and AUC. Our partial measures are continuous and discrete versions of the same measure, are derived from the AUC and c statistic respectively, are validated as equal to each other, and validated as equal in summation to whole measures where expected. Our partial measures are tested for validity on a classic ROC example from Fawcett, a variation thereof, and two real-life benchmark data sets in breast cancer: the Wisconsin and Ljubljana data sets. Interpretation of an example is then provided. RESULTS: Results show the expected equalities between our new partial measures and the existing whole measures. The example interpretation illustrates the need for our newly derived partial measures. CONCLUSIONS: The concordant partial area under the ROC curve was proposed and unlike previous partial measure alternatives, it maintains the characteristics of the AUC. The first partial c statistic for ROC plots was also proposed as an unbiased interpretation for part of an ROC curve. The expected equalities among and between our newly derived partial measures and their existing full measure counterparts are confirmed. These measures may be used with any data set but this paper focuses on imbalanced data with low prevalence. FUTURE WORK: Future work with our proposed measures may: demonstrate their value for imbalanced data with high prevalence, compare them to other measures not based on areas; and combine them with other ROC measures and techniques.

Median Robust Extended Local Binary Pattern for Texture Classification.

Local binary patterns (LBP) are considered among the most computationally efficient high-performance texture features. However, the LBP method is very sensitive to image noise and is unable to capture macrostructure information. To best address these disadvantages, in this paper, we introduce a novel descriptor for texture classification, the median robust extended LBP (MRELBP). Different from the traditional LBP and many LBP variants, MRELBP compares regional image medians rather than raw image intensities. A multiscale LBP type descriptor is computed by efficiently comparing image medians over a novel sampling scheme, which can capture both microstructure and macrostructure texture information. A comprehensive evaluation on benchmark data sets reveals MRELBP's high performance-robust to gray scale variations, rotation changes and noise-but at a low computational cost. MRELBP produces the best classification scores of 99.82%, 99.38%, and 99.77% on three popular Outex test suites. More importantly, MRELBP is shown to be highly robust to image noise, including Gaussian noise, Gaussian blur, salt-and-pepper noise, and random pixel corruption.

BRINT: binary rotation invariant and noise tolerant texture classification.

In this paper, we propose a simple, efficient, yet robust multiresolution approach to texture classification-binary rotation invariant and noise tolerant (BRINT). The proposed approach is very fast to build, very compact while remaining robust to illumination variations, rotation changes, and noise. We develop a novel and simple strategy to compute a local binary descriptor based on the conventional local binary pattern (LBP) approach, preserving the advantageous characteristics of uniform LBP. Points are sampled in a circular neighborhood, but keeping the number of bins in a single-scale LBP histogram constant and small, such that arbitrarily large circular neighborhoods can be sampled and compactly encoded over a number of scales. There is no necessity to learn a texton dictionary, as in methods based on clustering, and no tuning of parameters is required to deal with different data sets. Extensive experimental results on representative texture databases show that the proposed BRINT not only demonstrates superior performance to a number of recent state-of-the-art LBP variants under normal conditions, but also performs significantly and consistently better in presence of noise due to its high distinctiveness and robustness. This noise robustness characteristic of the proposed BRINT is evaluated quantitatively with different artificially generated types and levels of noise (including Gaussian, salt and pepper, and speckle noise) in natural texture images.

A new Mercer sigmoid kernel for clinical data classification.

In classification with Support Vector Machines, only Mercer kernels, i.e. valid kernels, such as the Gaussian RBF kernel, are widely accepted and thus suitable for clinical data. Practitioners would also like to use the sigmoid kernel, a non-Mercer kernel, but its range of validity is difficult to determine, and even within range its validity is in dispute. Despite these shortcomings the sigmoid kernel is used by some, and two kernels in the literature attempt to emulate and improve upon it. We propose the first Mercer sigmoid kernel, that is therefore trustworthy for the classification of clinical data. We show the similarity between the Mercer sigmoid kernel and the sigmoid kernel and, in the process, identify a normalization technique that improves the classification accuracy of the latter. The Mercer sigmoid kernel achieves the best mean accuracy on three clinical data sets, detecting melanoma in skin lesions better than the most popular kernels; while with non-clinical data sets it has no significant difference in median accuracy as compared with the Gaussian RBF kernel. It consistently classifies some points correctly that the Gaussian RBF kernel does not and vice versa.

Frozen-state hierarchical annealing.

There is significant interest in the synthesis of discrete-state random fields, particularly those possessing structure over a wide range of scales. However, given a model on some finest, pixellated scale, it is computationally very difficult to synthesize both large- and small-scale structures, motivating research into hierarchical methods. In this paper, we propose a frozen-state approach to hierarchical modeling, in which simulated annealing is performed on each scale, constrained by the state estimates at the parent scale. This approach leads to significant advantages in both modeling flexibility and computational complexity. In particular, a complex structure can be realized with very simple, local, scale-dependent models, and by constraining the domain to be annealed at finer scales to only the uncertain portions of coarser scales; the approach leads to huge improvements in computational complexity. Results are shown for a synthesis problem in porous media.

Texture classification from random features.

Inspired by theories of sparse representation and compressed sensing, this paper presents a simple, novel, yet very powerful approach for texture classification based on random projection, suitable for large texture database applications. At the feature extraction stage, a small set of random features is extracted from local image patches. The random features are embedded into a bag-of-words model to perform texture classification; thus, learning and classification are carried out in a compressed domain. The proposed unconventional random feature extraction is simple, yet by leveraging the sparse nature of texture images, our approach outperforms traditional feature extraction methods which involve careful design and complex steps. We have conducted extensive experiments on each of the CUReT, the Brodatz, and the MSRC databases, comparing the proposed approach to four state-of-the-art texture classification methods: Patch, Patch-MRF, MR8, and LBP. We show that our approach leads to significant improvements in classification accuracy and reductions in feature dimensionality.

Decoupled active contour (DAC) for boundary detection.

The accurate detection of object boundaries via active contours is an ongoing research topic in computer vision. Most active contours converge toward some desired contour by minimizing a sum of internal (prior) and external (image measurement) energy terms. Such an approach is elegant, but suffers from a slow convergence rate and frequently misconverges in the presence of noise or complex contours. To address these limitations, a decoupled active contour (DAC) is developed which applies the two energy terms separately. Essentially, the DAC consists of a measurement update step, employing a Hidden Markov Model (HMM) and Viterbi search, and then a separate prior step, which modifies the updated curve based on the relative strengths of the measurement uncertainty and the nonstationary prior. By separating the measurement and prior steps, the algorithm is less likely to misconverge; furthermore, the use of a Viterbi optimizer allows the method to converge far more rapidly than energy-based iterative solvers. The results clearly demonstrate that the proposed approach is robust to noise, can capture regions of very high curvature, and exhibits limited dependence on contour initialization or parameter settings. Compared to five other published methods and across many image sets, the DAC is found to be faster with better or comparable segmentation accuracy.

Extended-Hungarian-JPDA: exact single-frame stem cell tracking.

The fields of bioinformatics and biotechnology rely on the collection, processing and analysis of huge numbers of biocellular images, including cell features such as cell size, shape, and motility. Thus, cell tracking is of crucial importance in the study of cell behaviour and in drug and disease research. Such a multitarget tracking is essentially an assignment problem, NP-hard, with the solution normally found in practice in a reduced hypothesis space. In this paper we introduce a novel approach to find the exact association solution over time for single-frame scan-back stem cell tracking. Our proposed method employs a class of linear programming optimization methods known as the Hungarian method to find the optimal joint probabilistic data association for nonlinear dynamics and non-Gaussian measurements. The proposed method, an optimal joint probabilistic data association approach, has been successfully applied to track hematopoietic stem cells.