Tuesday, May 22, 2018

Incremental graph algorithms are different from parallel graph algorithms. The two are generally not combined because the approach is gather apply scatter at each vertex in the incremental algorithms while the approach in the latter is partitioning and communication overhead and sometimes including their hybrid variations.
Graph analysis is often compared with vector analysis. In the latter case,
dimensionality reduction is not necessarily a problem to solve. Increase in dimensions may even have marginal benefits. On the other hand, the cost savings in using lesser dimensions is actually quite significant.
This technique also eliminates noise by  choosing the dimensions as salient features. This means they improve visualization
Vectors have the advantage that they can participate in a change of point of reference which again can be used to improve visualization.
Eigen values and even vectors can be found for vectors which gives a totally different visualization and often simpler to view.
Dimensionality can also be reduced at multiple levels.
Further-more, the vectors can participate directly in data mining algorithms solving much of the categorization needs that text analysis seems to depend on if neural nets and other AI techniques are not involved or if we rely on document vectors instead of word vectors.
In this regard, graphs may have marginal benefits. However, there is no questioning that bi-partite approach for semantic embedding is better visualized and represented by graphs. When  graphs are visualized, they can be depicted with nodes having higher centrality at the core and those having lower centrality at the periphery.
Interestingly graphs can also be reduced. It is called hypergraph coarsening which is an approximation of the original structure of the graph. Coarsening can be iterative.  Succession of smaller hypergraphs tend to make incremental progress towards a coarser graph with less overall loss of information.  There are several methods. Pairs of vertices that are similar can be merged. Skip edges may be overlayed on the same graph to represent the coarser graph. Centrality may be adjusted based on weights of the edges removed from vertices that are removed without loss of path or connectivity among the fewer vertices.
Thus graph analysis gives a similar form of visualization while dimensionality reduction and vector analysis can enable myriad forms of visualization.


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