Heitor S. Ramos

Eduarda T. C. Chagas, Alejandro. C. Frery, Juliana Gambini et al.

The ultimate purpose of the statistical analysis of ordinal patterns is to characterize the distribution of the features they induce. In particular, knowing the joint distribution of the pair Entropy-Statistical Complexity for a large class of time series models would allow statistical tests that are unavailable to date. Working in this direction, we characterize the asymptotic distribution of the empirical Shannon's Entropy for any model under which the true normalized Entropy is neither zero nor one. We obtain the asymptotic distribution from the Central Limit Theorem (assuming large time series), the Multivariate Delta Method, and a third-order correction of its mean value. We discuss the applicability of other results (exact, first-, and second-order corrections) regarding their accuracy and numerical stability. Within a general framework for building test statistics about Shannon's Entropy, we present a bilateral test that verifies if there is enough evidence to reject the hypothesis that two signals produce ordinal patterns with the same Shannon's Entropy. We applied this bilateral test to the daily maximum temperature time series from three cities (Dublin, Edinburgh, and Miami) and obtained sensible results.

Pedro H. Barros, Fabiane Queiroz, Flavio Figueredo et al.

We propose a novel deep metric learning method. Differently from many works on this area, we defined a novel latent space obtained through an autoencoder. The new space, namely S-space, is divided into different regions that describe the positions where pairs of objects are similar/dissimilar. We locate makers to identify these regions. We estimate the similarities between objects through a kernel-based t-student distribution to measure the markers' distance and the new data representation. In our approach, we simultaneously estimate the markers' position in the S-space and represent the objects in the same space. Moreover, we propose a new regularization function to avoid similar markers to collapse altogether. We present evidences that our proposal can represent complex spaces, for instance, when groups of similar objects are located in disjoint regions. We compare our proposal to 9 different distance metric learning approaches (four of them are based on deep-learning) on 28 real-world heterogeneous datasets. According to the four quantitative metrics used, our method overcomes all the nine strategies from the literature.

I. Cardoso-Pereira, J. B. Borges, P. H. Barros et al.

The analysis of GPS trajectories is a well-studied problem in Urban Computing and has been used to track people. Analyzing people mobility and identifying the transportation mode used by them is essential for cities that want to reduce traffic jams and travel time between their points, thus helping to improve the quality of life of citizens. The trajectory data of a moving object is represented by a discrete collection of points through time, i.e., a time series. Regarding its interdisciplinary and broad scope of real-world applications, it is evident the need of extracting knowledge from time series data. Mining this type of data, however, faces several complexities due to its unique properties. Different representations of data may overcome this. In this work, we propose the use of a feature retained from the Ordinal Pattern Transition Graph, called the probability of self-transition for transportation mode classification. The proposed feature presents better accuracy results than Permutation Entropy and Statistical Complexity, even when these two are combined. This is the first work, to the best of our knowledge, that uses Information Theory quantifiers to transportation mode classification, showing that it is a feasible approach to this kind of problem.

María Elena Buemi, Alejandro C. Frery, Heitor S. Ramos

Stack filters are a special case of non-linear filters. They have a good performance for filtering images with different types of noise while preserving edges and details. A stack filter decomposes an input image into stacks of binary images according to a set of thresholds. Each binary image is then filtered by a Boolean function, which characterizes the filter. Adaptive stack filters can be computed by training using a prototype (ideal) image and its corrupted version, leading to optimized filters with respect to a loss function. In this work we propose the use of training with selected samples for the estimation of the optimal Boolean function. We study the performance of adaptive stack filters when they are applied to speckled imagery, in particular to Synthetic Aperture Radar (SAR) images. This is done by evaluating the quality of the filtered images through the use of suitable image quality indexes and by measuring the classification accuracy of the resulting images. We used SAR images as input, since they are affected by speckle noise that makes classification a difficult task.

Maria E. Buemi, Marta Mejail, Julio Jacobo et al.

Stack filters are a special case of non-linear filters. They have a good performance for filtering images with different types of noise while preserving edges and details. A stack filter decomposes an input image into several binary images according to a set of thresholds. Each binary image is then filtered by a Boolean function, which characterizes the filter. Adaptive stack filters can be designed to be optimal; they are computed from a pair of images consisting of an ideal noiseless image and its noisy version. In this work we study the performance of adaptive stack filters when they are applied to Synthetic Aperture Radar (SAR) images. This is done by evaluating the quality of the filtered images through the use of suitable image quality indexes and by measuring the classification accuracy of the resulting images.