Related papers: Object oriented data analysis: Sets of trees
Much of statistics relies upon four key elements: a law of large numbers, a calculus to operationalize stochastic convergence, a central limit theorem, and a framework for constructing local approximations. These elements are…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
The basic objective of data visualization is to provide an efficient graphical display for summarizing and reasoning about quantitative information. During the last decades, political science has accumulated a large corpus of various kinds…
We describe a new logical data model, called the concept-oriented model (COM). It uses mathematical functions as first-class constructs for data representation and data processing as opposed to using exclusively sets in conventional…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Real-world processes often involve interdependent objects that also carry data values, such as integers, reals, or strings. However, existing process formalisms fall short to combine key modeling features, such as tracking object…
Deep learning approaches to object detection have achieved reliable detection of specific object classes in images. However, extending a model's detection capability to new object classes requires large amounts of annotated training data,…
In machine learning it is common to interpret each data point as a vector in Euclidean space. However the data may actually be functional i.e.\ each data point is a function of some variable such as time and the function is discretely…
The utilization of statistical methods an their applications within the new field of study known as Topological Data Analysis has has tremendous potential for broadening our exploration and understanding of complex, high-dimensional data…
Modern-day problems in statistics often face the challenge of exploring and analyzing complex non-Euclidean object data that do not conform to vector space structures or operations. Examples of such data objects include covariance matrices,…
Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
Unsupervised object discovery is commonly interpreted as the task of localizing and/or categorizing objects in visual data without the need for labeled examples. While current object recognition methods have proven highly effective for…
Samples of dynamic or time-varying networks and other random object data such as time-varying probability distributions are increasingly encountered in modern data analysis. Common methods for time-varying data such as functional data…
In this paper are briefly outlined the motivations, mathematical ideas in use, pre-formalization and assumptions, object-as-functor construction, `soft' types and concept constructions, case study for concepts based on variable domains,…
Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are…
Data clustering is an approach to seek for structure in sets of complex data, i.e., sets of "objects". The main objective is to identify groups of objects which are similar to each other, e.g., for classification. Here, an introduction to…
The Internet of Things (IoT) envisions a world-wide, interconnected network of smart physical entities. These physical entities generate a large amount of data in operation and as the IoT gains momentum in terms of deployment, the combined…
Processes tend to interact with other processes and operate on various objects of different types. These objects can influence each other creating dependencies between sub-processes. Analyzing the conformance of such complex processes…
This paper is based on a previous publication [29]. Our work extends exception mining and outlier detection to the case of object-relational data. Object-relational data represent a complex heterogeneous network [12], which comprises…