A statistical approach to set classification by feature selection with applications to classification of histopathology images

SetSVM: An Approach to Set Classification in Nuclei-Based Cancer Detection

Due to the importance of nuclear structure in cancer diagnosis, several predictive models have been described for diagnosing a wide variety of cancers based on nuclear morphology. In many computer-aided diagnosis (CAD) systems, cancer detection tasks can be generally formulated as set classification problems, which can not be directly solved by classifying single instances. In this paper, we propose a novel set classification approach SetSVM to build a predictive model by considering any nuclei set as a whole without specific assumptions. SetSVM features highly discriminative power in cancer detection challenges in the sense that it not only optimizes the classifier decision boundary but also transfers discriminative information to set representation learning. During model training, these two processes are unified in the support vector machine (SVM) maximum separation margin problem. Experiment results show that SetSVM provides significant improvements compared with five commonly used approaches in cancer detection tasks utilizing 260 patients in total across three different cancer types, namely, thyroid cancer, liver cancer, and melanoma. In addition, we show that SetSVM enables visual interpretation of discriminative nuclear characteristics representing the nuclei set. These features make SetSVM a potentially practical tool in building accurate and interpretable CAD systems for cancer detection.

Entropy-based Correspondence Improvement of Interpolated Skeletal Models

Statistical analysis of shape representations relies on having good correspondence across a population. Improving correspondence yields improved statistics. Point distribution models (PDMs) are often used to represent object boundaries. Skeletal representations (s-reps) model object widths and boundary directions as well as boundary positions, so they should yield better correspondence. We present two methods: one for continuously interpolating a discretely-sampled skeletal model and one for improving correspondence by using this interpolation to shift skeletal samples to new positions. The interpolation operates by an extension of the mathematics of medial structures. As with Cates' boundary-based method, we evaluate correspondence in terms of regularity and shape-feature population entropies. Evaluation on both synthetic and real data shows that our method both improves correspondence of s-rep models fit to segmented lateral ventricles and that the combined boundary-and-skeletal PDMs implied by these optimized s-reps have better correspondence than optimized boundary PDMs.

Detection of spatial change points in the mean and covariances of multivariate simultaneous autoregressive models

In this paper, we propose a test procedure to detect change points of multidimensional autoregressive processes. The considered process differs from typical applied spatial autoregressive processes in that it is assumed to evolve from a predefined center into every dimension. Additionally, structural breaks in the process can occur at a certain distance from the predefined center. The main aim of this paper is to detect such spatial changes. In particular, we focus on shifts in the mean and the autoregressive parameter. The proposed test procedure is based on the likelihood-ratio approach. Eventually, the goodness-of-fit values of the estimators are compared for different shifts. Moreover, the empirical distribution of the test statistic of the likelihood-ratio test is obtained via Monte Carlo simulations. We show that the generalized Gumbel distribution seems to be a suitable limiting distribution of the proposed test statistic. Finally, we discuss the detection of lung cancer in computed tomography scans and illustrate the proposed test procedure.

Fitting Skeletal Object Models Using Spherical Harmonics Based Template Warping

We present a scheme that propagates a reference skeletal model (s-rep) into a particular case of an object, thereby propagating the initial shape-related layout of the skeleton-to-boundary vectors, called spokes. The scheme represents the surfaces of the template as well as the target objects by spherical harmonics and computes a warp between these via a thin plate spline. To form the propagated s-rep, it applies the warp to the spokes of the template s-rep and then statistically refines. This automatic approach promises to make s-rep fitting robust for complicated objects, which allows s-rep based statistics to be available to all. The improvement in fitting and statistics is significant compared with the previous methods and in statistics compared with a state-of-the-art boundary based method.