Visualization of Non-vectorial Data Using Twin Kernel Embedding

2006 ◽  
Author(s):  
Yi Guo ◽  
Junbin Gao ◽  
Paul Kwan
Keyword(s):  
Vectorial Data

GRAPH CLASSIFICATION BASED ON VECTOR SPACE EMBEDDING

2009 ◽  
Vol 23 (06) ◽  
pp. 1053-1081 ◽  
Author(s):  
KASPAR RIESEN ◽  
HORST BUNKE
Keyword(s):  
Data Sets ◽  
Object Representations ◽  
Graph Classification ◽  
Graph Edit Distance ◽  
Graph Kernels ◽  
Symbolic Data ◽  
Representational Power ◽  
High Degree ◽  
Vectorial Data ◽  
Representation Formalism

Graphs provide us with a powerful and flexible representation formalism for pattern classification. Many classification algorithms have been proposed in the literature. However, the vast majority of these algorithms rely on vectorial data descriptions and cannot directly be applied to graphs. Recently, a growing interest in graph kernel methods can be observed. Graph kernels aim at bridging the gap between the high representational power and flexibility of graphs and the large amount of algorithms available for object representations in terms of feature vectors. In the present paper, we propose an approach transforming graphs into n-dimensional real vectors by means of prototype selection and graph edit distance computation. This approach allows one to build graph kernels in a straightforward way. It is not only applicable to graphs, but also to other kind of symbolic data in conjunction with any kind of dissimilarity measure. Thus it is characterized by a high degree of flexibility. With several experimental results, we prove the robustness and flexibility of our new method and show that our approach outperforms other graph classification methods on several graph data sets of diverse nature.

Fuzzy Clustering Methods for Categorical Multivariate Data Based on q-Divergence

2018 ◽  
Vol 22 (4) ◽  
pp. 524-536 ◽  
Author(s):  
Tadafumi Kondo ◽  
◽  
Yuchi Kanzawa
Keyword(s):  
Conventional Method ◽  
Fuzzy Clustering ◽  
Optimization Problems ◽  
Clustering Algorithms ◽  
Multivariate Data ◽  
Clustering Methods ◽  
Kl Divergence ◽  
Fuzzy Clustering Methods ◽  
Conventional Methods ◽  
Vectorial Data

This paper presents two fuzzy clustering algorithms for categorical multivariate data based on q-divergence. First, this study shows that a conventional method for vectorial data can be explained as regularizing another conventional method using q-divergence. Second, based on the known results that Kullback-Leibler (KL)-divergence is generalized into the q-divergence, and two conventional fuzzy clustering methods for categorical multivariate data adopt KL-divergence, two fuzzy clustering algorithms for categorical multivariate data that are based on q-divergence are derived from two optimization problems built by extending the KL-divergence in these conventional methods to the q-divergence. Through numerical experiments using real datasets, the proposed methods outperform the conventional methods in term of clustering accuracy.

FlowVis — a CAD based solution for the graphical post-processing of scalar and vectorial data

1997 ◽  
Vol 12 (2-3) ◽  
pp. 161-168 ◽  
Author(s):  
A.M.G. Lopes
Keyword(s):  
Post Processing ◽  
Vectorial Data

SELF-ORGANIZING MAP-BASED DISCOVERY AND VISUALIZATION OF HUMAN ENDOGENOUS RETROVIRAL SEQUENCE GROUPS

2005 ◽  
Vol 15 (03) ◽  
pp. 163-179 ◽  
Author(s):  
MERJA OJA ◽  
GÖRAN O. SPERBER ◽  
JONAS BLOMBERG ◽  
SAMUEL KASKI
Keyword(s):  
Human Genome ◽  
Common Origin ◽  
Self Organizing Map ◽  
Visualization Method ◽  
Bootstrap Procedure ◽  
Human Genes ◽  
Vectorial Data ◽  
Self Organizing

About 8 per cent of the human genome consists of human endogenous retroviral sequences (HERVs), which are remains from ancient infections. The HERVs may give rise to transcripts or affect the expression of human genes. The first step in understanding HERV function is to classify HERVs into families. In this work we study the relationships of existing HERV families and detect potentially new HERV families. A Median Self-Organizing Map (SOM), a SOM for non-vectorial data, is used to group and visualize a collection of 3661 HERVs. The SOM-based analysis is complemented with estimates of the reliability of the results. A novel trustworthiness visualization method is used to estimate which parts of the SOM visualization are reliable and which not. The reliability of extracted interesting HERV groups is verified by a bootstrap procedure suitable for SOM visualization-based analysis. The SOM detects a group of epsilonretroviral sequences and a group of ERV9, HERVW, and HUERSP3 sequences which suggests that ERV9 and HERVW sequences may have a common origin.

Estimating and modeling spatio-temporal complex-valued covariance functions

2021 ◽  
Author(s):  
Sabrina Maggio ◽  
Donato Posa ◽  
Sandra De Iaco ◽  
Claudia Cappello
Keyword(s):  
Complex Data ◽  
Temporal Dependence ◽  
Covariance Functions ◽  
Covariance Models ◽  
Unit Of Measurement ◽  
Oceanographic Data ◽  
Spatio Temporal ◽  
Complex Valued ◽  
Vectorial Data

<p><span><span>Oceanographic data belong to the wide class of vectorial data, for which the decomposition in modulus and direction is meaningful, and the vectorial components are characterized by homogeneous quantities, with the same unit of measurement. Another feature of oceanographic data is that they exhibit spatio-temporal dependence.<br>In Geostatistics, such data can be properly modelled by recalling the theory of complex-valued random fields. However, in the literature, only techniques for modeling and predicting the spatial evolution of these phenomena were proposed; while the temporal dependence was analyzed separately from the spatial one, or just time-varying complex covariance models were used. Thus, the novelty of this paper regards some advances of the complex formalism for analyzing complex data in space-time and new classes of spatio-temporal complex covariance models.<br>A case study on spatio-temporal complex estimating and modeling with oceanographic data is provided and a comparison between two classes of complex covariance models is also proposed.</span></span></p>

Complex-Valued Random Fields for Vectorial Data: Estimating and Modeling Aspects

2013 ◽  
Vol 45 (5) ◽  
pp. 557-573 ◽  
Author(s):  
S. De Iaco ◽  
D. Posa ◽  
M. Palma
Keyword(s):  
Random Fields ◽  
Complex Valued ◽  
Vectorial Data

scholarly journals Dynamics and Topographic Organization of Recursive Self-Organizing Maps

2006 ◽  
Vol 18 (10) ◽  
pp. 2529-2567 ◽  
Author(s):  
Peter Tiňo ◽  
Igor Farkaš ◽  
Jort van Mourik
Keyword(s):  
Receptive Fields ◽  
Topographic Maps ◽  
Sequential Data ◽  
Self Organizing Map ◽  
Self Organizing Maps ◽  
Fixed Input ◽  
Feedback Connections ◽  
Superior Memory ◽  
Vectorial Data ◽  
Self Organizing

Recently there has been an outburst of interest in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, there is no general consensus as to how best to process sequences using topographic maps, and this topic remains an active focus of neurocomputational research. The representational capabilities and internal representations of the models are not well understood. Here, we rigorously analyze a generalization of the self-organizing map (SOM) for processing sequential data, recursive SOM(RecSOM) (Voegtlin, 2002), as a nonautonomous dynamical system consisting of a set of fixed input maps. We argue that contractive fixed-input maps are likely to produce Markovian organizations of receptive fields on the RecSOM map. We derive bounds on parameter β (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed-input maps is guaranteed. Some generalizations of SOM contain a dynamic module responsible for processing temporal contexts as an integral part of the model. We show that Markovian topographic maps of sequential data can be produced using a simple fixed (nonadaptable) dynamic module externally feeding a standard topographic model designed to process static vectorial data of fixed dimensionality (e.g., SOM). However, by allowing trainable feedback connections, one can obtain Markovian maps with superior memory depth and topography preservation. We elaborate on the importance of non-Markovian organizations in topographic maps of sequential data.

Analysis Of Vectorial Data

1962 ◽  
Vol Vol. 32 ◽  
Author(s):  
Richard Steinmetz
Keyword(s):  
Vectorial Data
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