Search results for " Graph theory"

Graph Topology Learning and Signal Recovery Via Bayesian Inference

2019

The estimation of a meaningful affinity graph has become a crucial task for representation of data, since the underlying structure is not readily available in many applications. In this paper, a topology inference framework, called Bayesian Topology Learning, is proposed to estimate the underlying graph topology from a given set of noisy measurements of signals. It is assumed that the graph signals are generated from Gaussian Markov Random Field processes. First, using a factor analysis model, the noisy measured data is represented in a latent space and its posterior probability density function is found. Thereafter, by utilizing the minimum mean square error estimator and the Expectation M…

Robust Graph Topology Learning and Application in Stock Market Inference

2019

In many applications, there are multiple interacting entities, generating time series of data over the space. To describe the relation within the set of data, the underlying topology may be used. In many real applications, not only the signal/data of interest is measured in noise, but it is also contaminated with outliers. The proposed method, called RGTL, infers the graph topology from noisy measurements and removes these outliers simultaneously. Here, it is assumed that we have no information about the space graph topology, while we know that graph signal are sampled consecutively in time and thus the graph in time domain is given. The simulation results show that the proposed algorithm h…

Characteristic Topological Features of Promoter Capture Hi-C Interaction Networks

2020

Current Hi-C technologies for chromosome conformation capture allow to understand a broad spectrum of functional interactions between genome elements. Although significant progress has been made into analysis of Hi-C data to identify the biologically significant features, many questions still remain open. In this paper we describe analysis methods of Hi-C (specifically PCHi-C) interaction networks that are strictly focused on topological properties of these networks. The main questions we are trying to answer are: (1) can topological properties of interaction networks for different cell types alone be sufficient to distinguish between these types, and what the most important of such propert…

Biased graph walks for RDF graph embeddings

2017

Knowledge Graphs have been recognized as a valuable source for background information in many data mining, information retrieval, natural language processing, and knowledge extraction tasks. However, obtaining a suitable feature vector representation from RDF graphs is a challenging task. In this paper, we extend the RDF2Vec approach, which leverages language modeling techniques for unsupervised feature extraction from sequences of entities. We generate sequences by exploiting local information from graph substructures, harvested by graph walks, and learn latent numerical representations of entities in RDF graphs. We extend the way we compute feature vector representations by comparing twel…

Counterexamples to the Algebraic Closed Graph Theorem

1982

Quasi *-Algebras of Operators in Rigged Hilbert Spaces

2002

In this chapter, we will study families of operators acting on a rigged Hilbert space, with a particular interest in their partial algebraic structure. In Section 10.1 the notion of rigged Hilbert space D[t] ↪ H ↪ D × [t ×] is introduced and some examples are presented. In Section 10.2, we consider the space.L(D, D ×) of all continuous linear maps from D[t] into D × [t ×] and look for conditions under which (L(D, D ×), L +(D)) is a (topological) quasi *-algebra. Moreover the general problem of introducing in L(D, D ×) a partial multiplication is considered. In Section 10.3 representations of abstract quasi *-algebras into quasi*-algebras of operators are studied and the GNS-construction is …

Motives for reflections. Part one

2013

Facsimile of manuscript from the archive of Emanuels Grinbergs, University of Latvia. The article (in three pieces of manuscripts), written in Russian, contains some reflections on graph theory. It may be written in 1973.

Motives for reflections Addendum to part one

2013

The article (in three pieces of manuscripts), written in Russian, contains some reflections on graph theory. It may be written in 1973.

Joint Graph Learning and Signal Recovery via Kalman Filter for Multivariate Auto-Regressive Processes

2018

In this paper, an adaptive Kalman filter algorithm is proposed for simultaneous graph topology learning and graph signal recovery from noisy time series. Each time series corresponds to one node of the graph and underlying graph edges express the causality among nodes. We assume that graph signals are generated via a multivariate auto-regressive processes (MAR), generated by an innovation noise and graph weight matrices. Then we relate the state transition matrix of Kalman filter to the graph weight matrices since both of them can play the role of signal propagation and transition. Our proposed Kalman filter for MAR processes, called KF-MAR, runs three main steps; prediction, update, and le…

Motives for reflections. Part two

2013

E. Gringergs archive manuscripts may be found in the Library of the University of Latvia under https://lira.lanet.lv/F/98QNED45E7J5HDUHLY51HV43QNRX97XCQJPHQ9S6L7HX4FABFB-10883?func=find-b&request=E.Grinberga&find_code=TIT&x=32&y=13&filter_code_1=WLN&filter_request_1=&filter_code_2=WYR&filter_request_2=&filter_code_3=WYR&filter_request_3=&filter_code_4=WFM&filter_request_4=