Feature-based time-series analysis

This work presents an introduction to feature-based time-series analysis. The time series as a data type is first described, along with an overview of the interdisciplinary time-series analysis literature. I then summarize the range of feature-based representations for time series that have been developed to aid interpretable insights into time-series structure. Particular emphasis is given to emerging research that facilitates wide comparison of feature-based representations that allow us to understand the properties of a time-series dataset that make it suited to a particular feature-based representation or analysis algorithm. The future of time-series analysis is likely to embrace approaches that exploit machine learning methods to partially automate human learning to aid understanding of the complex dynamical patterns in the time series we measure from the world.Comment: 28 pages, 9 figure

Adaptive Segmentation of Knee Radiographs for Selecting the Optimal ROI in Texture Analysis

The purposes of this study were to investigate: 1) the effect of placement of region-of-interest (ROI) for texture analysis of subchondral bone in knee radiographs, and 2) the ability of several texture descriptors to distinguish between the knees with and without radiographic osteoarthritis (OA). Bilateral posterior-anterior knee radiographs were analyzed from the baseline of OAI and MOST datasets. A fully automatic method to locate the most informative region from subchondral bone using adaptive segmentation was developed. We used an oversegmentation strategy for partitioning knee images into the compact regions that follow natural texture boundaries. LBP, Fractal Dimension (FD), Haralick features, Shannon entropy, and HOG methods were computed within the standard ROI and within the proposed adaptive ROIs. Subsequently, we built logistic regression models to identify and compare the performances of each texture descriptor and each ROI placement method using 5-fold cross validation setting. Importantly, we also investigated the generalizability of our approach by training the models on OAI and testing them on MOST dataset.We used area under the receiver operating characteristic (ROC) curve (AUC) and average precision (AP) obtained from the precision-recall (PR) curve to compare the results. We found that the adaptive ROI improves the classification performance (OA vs. non-OA) over the commonly used standard ROI (up to 9% percent increase in AUC). We also observed that, from all texture parameters, LBP yielded the best performance in all settings with the best AUC of 0.840 [0.825, 0.852] and associated AP of 0.804 [0.786, 0.820]. Compared to the current state-of-the-art approaches, our results suggest that the proposed adaptive ROI approach in texture analysis of subchondral bone can increase the diagnostic performance for detecting the presence of radiographic OA

Evidence functions: a compositional approach to information

The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection.Peer Reviewe

Evidence functions: a compositional approach to information

The discrete case of Bayes’ formula is considered the paradigm of information acquisition. Prior and posterior probability functions, as well as likelihood functions, called evidence functions, are compositions following the Aitchison geometry of the simplex, and have thus vector character. Bayes’ formula becomes a vector addition. The Aitchison norm of an evidence function is introduced as a scalar measurement of information. A fictitious fire scenario serves as illustration. Two different inspections of affected houses are considered. Two questions are addressed: (a) which is the information provided by the outcomes of inspections, and (b) which is the most informative inspection.Peer ReviewedPostprint (author's final draft

On the Prior and Posterior Distributions Used in Graphical Modelling

Graphical model learning and inference are often performed using Bayesian techniques. In particular, learning is usually performed in two separate steps. First, the graph structure is learned from the data; then the parameters of the model are estimated conditional on that graph structure. While the probability distributions involved in this second step have been studied in depth, the ones used in the first step have not been explored in as much detail. In this paper, we will study the prior and posterior distributions defined over the space of the graph structures for the purpose of learning the structure of a graphical model. In particular, we will provide a characterisation of the behaviour of those distributions as a function of the possible edges of the graph. We will then use the properties resulting from this characterisation to define measures of structural variability for both Bayesian and Markov networks, and we will point out some of their possible applications.Comment: 28 pages, 6 figure