Cervical cancer is the fourth leading cause of cancer-related deaths in women, especially in low to middle-income countries. Despite the outburst of recent scientific advances, there is no totally effective treatment, especially when diagnosed in an advanced stage. Screening tests, such as cytology or colposcopy, have been responsible for a substantial decrease in cervical cancer deaths. Cervical cancer automatic screening via Pap smear is a highly valuable cell imaging-based detection tool, where cells must be classified as being within one of a multitude of ordinal classes, ranging from abnormal to normal. Current approaches to ordinal inference for neural networks are found to not sufficiently take advantage of the ordinal problem or to be too uncompromising. A non-parametric ordinal loss for neuronal networks is proposed that promotes the output probabilities to follow a unimodal distribution. This is done by imposing a set of different constraints over all pairs of consecutive labels which allows for a more flexible decision boundary relative to approaches from the literature. Our proposed loss is contrasted against other methods from the literature by using a plethora of deep architectures. A first conclusion is the benefit of using non-parametric ordinal losses against parametric losses in cervical cancer risk prediction. Additionally, the proposed loss is found to be the top-performer in several cases. The best performing model scores an accuracy of 75.6% for seven classes and 81.3% for four classes.

Medical image quality assessment plays an important role not only in the design and manufacturing processes of image acquisition but also in the optimization of decision support systems. This work introduces a new deep ordinal learning approach for focus assessment in whole slide images. From the blurred image to the focused image there is an ordinal progression that contains relevant knowledge for more robust learning of the models. With this new method, it is possible to infer quality without losing ordinal information about focus since instead of using the nominal cross-entropy loss for training, ordinal losses were used. Our proposed model is contrasted against other state-of-the-art methods present in the literature. A first conclusion is a benefit of using data-driven methods instead of knowledge-based methods. Additionally, the proposed model is found to be the top-performer in several metrics. The best per-forming model scores an accuracy of 94.4% for a 12 classes classification problem in the FocusPath database.

In many real-world prediction tasks, the class labels contain information about the relative order between the labels that are not captured by commonly used loss functions such as multicategory cross-entropy. In ordinal regression, many works have incorporated ordinality into models and loss functions by promoting unimodality of the probability output. However, current approaches are based on heuristics, particularly non-parametric ones, which are still insufficiently explored in the literature. We analyze the set of unimodal distributions in the probability simplex, establishing fundamental properties and giving new perspectives to understand the ordinal regression problem. Two contributions are then proposed to incorporate the preference for unimodal distributions into the predictive model: 1) UnimodalNet, a new architecture that by construction ensures the output is a unimodal distribution, and 2) Wasserstein Regularization, a new loss term that relies on the notion of projection in a set to promote unimodality. Experiments show that the new architecture achieves top performance, while the proposed new loss term is very competitive while maintaining high unimodality.

Ordinal classification tasks are present in a large number of different domains. However, common losses for deep neural networks, such as cross-entropy, do not properly weight the relative ordering between classes. For that reason, many losses have been proposed in the literature, which model the output probabilities as following a unimodal distribution. This manuscript reviews many of these losses on three different datasets and suggests a potential improvement that focuses the unimodal constraint on the neighborhood around the true class, allowing for a more flexible distribution, aptly called quasi-unimodal loss. For this purpose, two constraints are proposed: A first constraint concerns the relative order of the top-three probabilities, and a second constraint ensures that the remaining output probabilities are not higher than the top three. Therefore, gradient descent focuses on improving the decision boundary around the true class in detriment to the more distant classes. The proposed loss is found to be competitive in several cases.