deletions | additions       diff --git a/Related Work.tex b/Related Work.tex  index 32614fc..244bc70 100644  --- a/Related Work.tex  +++ b/Related Work.tex 
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Signal processing on graphs as defined in \cite{Shuman} is an emergent field that extends high-dimensional data analysis to networks and other irregular domains. The graph spectral frequency domain is processed by fundamental operations such as filtering, translation, modulation, dilation and downsampling. A graph signal is defined by a finite collection of samples at each graph vertex. To compute information at each graph node a small neighbourhood of the vertex is considered. The graph Laplacian and its eigenvectors and eigenvalues encodes the graph connectivity. The graph Laplacian eigenvector corresponding to lower eigenvalues are smoother. Other graphs matrices are the normalized graph Laplacian and the random walk matrix. More research has to be done to know when to use each matrix. The authors define generalized operators for signals in graphs. Extensions include: analyzing directed graphs and vertexes with a time serie associated.  \cite{Shuman_vertex-frequencyanalysis} in In  another article: \cite{Shuman_vertex-frequencyanalysis}  "Vertex-Frequency Analysis on Graphs" defines the windowed Fourier transform that probably could be used for Twitter The authors of \cite{Miller_2013} propose the use of detection and estimation theory as defined for vector spaces with Gaussian noise in the context of graph analytics framework creating a new research area at the intersection of this domains. It is applied in the situational awareness cyber security to detect suspicious activity. Small subsets of vertices whose interactions do not fit the typical behaviour are identified. Relationships modeled as a graph are dificult to be analized in the Detection Theory framework. Translation and scaling are difficult to define for combinatorial and discrete graphs.  \cite{Miller_2012} describes the D4M architecture for handling large graphs. Analizes the Web of Science database and finds clutter and identifies emerging clusters in the eigenspace of graph residuals. "Future work will include developing automated methods to filter away clutter in the graph data, incorporating metadata into our models of graph residuals, and analyzing multi-graphs in which different types of edges correspond to different relationships."  \cite{Miller_2010} identifies a couple of graph problems that can be solved using signal processing: subgraph finding in a larger graph can be solved with match filtering for signal detection; very dense subgraph detection; frequency occuring subgraph or a certain behavioral pattern; The subgraph matching is further analysed in the framework of detection theory. 
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\cite{Dong_2014}  \cite{Nurwidyantoro}  \cite{Pohl_2013}  \cite{Gao_2013}  \cite{Ramanathan_2014}  \cite{Coifman_2006} is a math theoretical article in wich it is shown that in the context of manifolds, graphs, data sets and general metric spaces, diffusion processes and Markov processes can be analyzed in  a multiscale fashion very much in the spirit of classical wavelet analysis. It is proposed fast and stable algorithms for constructing orthonormal bases for the multiscale approximation spaces, and it is shown that there is an efficient scaling function and wavelet transform. 
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\subsection{Social Networks}  \cite{Campbell_2014} studies the following problems: community detection, relational learning, leadership role prediction. Co-occurences of entities is used to form a graph from text. A more refined approach is to extract relationships fromtext. from text.  A schema with entity types and attributes is described. A graphical query language is used to analyze the entity graph. \cite{Sizov_2010} studies authority ranking on social networks. The use of hashtags are indicative of emergent semantics in modern social networks as in \cite{Dellschaft_2009}. The authors formaly define social graphs and the application of tensors for authority ranking. A SocialWeb graph is defined as a graph G = ( V, L, E, linkType ) where V is the set of users in the community, L is the set of literals (e.g., hashtags), and E is the set of relations between users in V . Additionally, the function linkType : E -> L returns the annotation from L that relates two users. User X links to user Y by edge of type Z iff a) X follows Y (in the common sense of Twitter) and b) both X and Y have recently used the hashtag Z in their own postings/tweets. The authors describe the data collection and transformation processes for Twitter.