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Sparse representation has been widely used in data compression, signal and image denoising, dimensionality reduction and computer vision. While overcomplete dictionaries are required for sparse representation of multidimensional data, orthogonal bases represent one-dimensional data well. In this paper, we propose a data-driven sparse representation using orthonormal bases under the lossless compression constraint. We show that imposing such constraint under the Minimum Description Length (MDL) principle leads to a unique and optimal sparse representation for one-dimensional data, which results in discriminative features useful for data discovery.

While Internet of Things (IoT) devices and sensors create continuous streams of information, Big Data infrastructures are deemed to handle the influx of data in real-time. One type of such a continuous stream of information is time series data. Due to the richness of information in time series and inadequacy of summary statistics to encapsulate structures and patterns in such data, development of new approaches to learn time series is of interest. In this paper, we propose a novel method, called pattern tree, to learn patterns in the times-series using a binary-structured tree. While a pattern tree can be used for many purposes such as lossless compression, prediction and anomaly detection, in this paper we focus on its application in time series estimation and forecasting. In comparison to other methods, our proposed pattern tree method improves the mean squared error of estimation.

Automating classification and segmentation process of abnormal regions in different body organs has a crucial role in most of medical imaging applications such as funduscopy, endoscopy, and dermoscopy. Detecting multiple abnormalities in each type of images is necessary for better and more accurate diagnosis procedure and medical decisions. In recent years portable medical imaging devices such as capsule endoscopy and digital dermatoscope have been introduced and made the diagnosis procedure easier and more efficient. However, these portable devices have constrained power resources and limited computational capability. To address this problem, we propose a bifurcated structure for convolutional neural networks performing both classification and segmentation of multiple abnormalities simultaneously. The proposed network is first trained by each abnormality separately. Then the network is trained using all abnormalities. In order to reduce the computational complexity, the network is redesigned to share some features which are common among all abnormalities. Later, these shared features are used in different settings (directions) to segment and classify the abnormal region of the image. Finally, results of the classification and segmentation directions are fused to obtain the classified segmentation map. Proposed framework is simulated using four frequent gastrointestinal abnormalities as well as three dermoscopic lesions and for evaluation of the proposed framework the results are compared with the corresponding ground truth map. Properties of the bifurcated network like low complexity and resource sharing make it suitable to be implemented as a part of portable medical imaging devices.

Heart rate variability (HRV) is a vital measure of the autonomic nervous system functionality and a key indicator of cardiovascular condition. This paper proposes a novel method, called pattern tree which is an extension of Willem's context tree to real-valued data, to investigate HRV via an atypicality framework. In a previous paper atypicality was developed as method for mining and discovery in "Big Data," which requires a universal approach. Using the proposed pattern tree as a universal source coder in this framework led to discovery of arrhythmias and unknown patterns in HRV Holter Monitoring., Comment: 5 pages

A central question in the era of 'big data' is what to do with the enormous amount of information. One possibility is to characterize it through statistics, e.g., averages, or classify it using machine learning, in order to understand the general structure of the overall data. The perspective in this paper is the opposite, namely that most of the value in the information in some applications is in the parts that deviate from the average, that are unusual, atypical. We define what we mean by 'atypical' in an axiomatic way as data that can be encoded with fewer bits in itself rather than using the code for the typical data. We show that this definition has good theoretical properties. We then develop an implementation based on universal source coding, and apply this to a number of real world data sets., Comment: 40 pages

The aim of atypicality is to extract small, rare, unusual and interesting pieces out of big data. This complements statistics about typical data to give insight into data. In order to find such "interesting" parts of data, universal approaches are required, since it is not known in advance what we are looking for. We therefore base the atypicality criterion on codelength. In a prior paper we developed the methodology for discrete-valued data, and the the current paper extends this to real-valued data. This is done by using minimum description length (MDL). We show that this shares a number of theoretical properties with the discrete-valued case. We develop the methodology for a number of "universal" signal processing models, and finally apply them to recorded hydrophone data., Comment: 13 pages, two columns