Point Information Gain and Multidimensional Data Analysis

We generalize the Point information gain (PIG) and derived quantities, i.e. Point information entropy (PIE) and Point information entropy density (PIED), for the case of R\'enyi entropy and simulate the behavior of PIG for typical distributions. We also use these methods for the analysis of multidimensional datasets. We demonstrate the main properties of PIE/PIED spectra for the real data on the example of several images, and discuss possible further utilization in other fields of data processing.Comment: 16 pages, 6 figure

change point detection in mortality data

Background: Mortality refers to death that occurs within a population. It is linked to many factors such as age, sex, race, occupation and social class. Change in the pattern of mortality trend can affect the population standards of living and health care. This event makes a change point is occurred in mortality rates. The aim of this study is to detect change point in Iranian mortality data during1970 to 2007. Methods: We use several frequencies and Bayesian methods to estimate the change point in mortality data by Poisson model. Results: All methods show that a change has been occurred in mortality rates of Iran at year 1993. Conclusion: Results showed that pattern and rate of mortality before and after change point is not similar

Visual and interactive exploration of point data

Point data, such as Unit Postcodes (UPC), can provide very detailed information at fine scales of resolution. For instance, socio-economic attributes are commonly assigned to UPC. Hence, they can be represented as points and observable at the postcode level. Using UPC as a common field allows the concatenation of variables from disparate data sources that can potentially support sophisticated spatial analysis. However, visualising UPC in urban areas has at least three limitations. First, at small scales UPC occurrences can be very dense making their visualisation as points difficult. On the other hand, patterns in the associated attribute values are often hardly recognisable at large scales. Secondly, UPC can be used as a common field to allow the concatenation of highly multivariate data sets with an associated postcode. Finally, socio-economic variables assigned to UPC (such as the ones used here) can be non-Normal in their distributions as a result of a large presence of zero values and high variances which constrain their analysis using traditional statistics. This paper discusses a Point Visualisation Tool (PVT), a proof-of-concept system developed to visually explore point data. Various well-known visualisation techniques were implemented to enable their interactive and dynamic interrogation. PVT provides multiple representations of point data to facilitate the understanding of the relations between attributes or variables as well as their spatial characteristics. Brushing between alternative views is used to link several representations of a single attribute, as well as to simultaneously explore more than one variable. PVT’s functionality shows how the use of visual techniques embedded in an interactive environment enable the exploration of large amounts of multivariate point data

Generalized Convolutional Neural Networks for Point Cloud Data

The introduction of cheap RGB-D cameras, stereo cameras, and LIDAR devices has given the computer vision community 3D information that conventional RGB cameras cannot provide. This data is often stored as a point cloud. In this paper, we present a novel method to apply the concept of convolutional neural networks to this type of data. By creating a mapping of nearest neighbors in a dataset, and individually applying weights to spatial relationships between points, we achieve an architecture that works directly with point clouds, but closely resembles a convolutional neural net in both design and behavior. Such a method bypasses the need for extensive feature engineering, while proving to be computationally efficient and requiring few parameters

Power of change-point tests for long-range dependent data

We investigate the power of the CUSUM test and the Wilcoxon change-point tests for a shift in the mean of a process with long-range dependent noise. We derive analytic formulas for the power of these tests under local alternatives. These results enable us to calculate the asymptotic relative efficiency (ARE) of the CUSUM test and the Wilcoxon change point test. We obtain the surprising result that for Gaussian data, the ARE of these two tests equals 1, in contrast to the case of i.i.d. noise when the ARE is known to be 3/π.Herold Dehling and Aeneas Rooch were supported in part by the German Research Foundation (DFG) through the Collaborative Research Center SFB 823 Statistical Modelling of Nonlinear Dynamic Processes. Murad S. Taqqu was supported in part by NSF grant DMS-1309009 at Boston University. (SFB 823 - German Research Foundation (DFG); DMS-1309009 - NSF at Boston University)Published versio