From Intelligent Perception
Officially: Ayasdi "specializes in analysis and visualization of large structured (microarrays, proteomics, seismology) and unstructured datasets (graphs, networks, text)." (From LinkedIn)
Funding: $1.53 million in September 2010.
Ayasdi's software is called Iris. The founders are the people from the Computational Topology group at Stanford so, presumably, at least some of the underlying methods are the same as the ones of JPlex, i.e., persistent homology.
There is a very well produced video on YouTube that explains in detail how the software operates. You get to see a color coded graph that you can manipulate with the mouse. However, the question "what does it do?" remains even after watching it.
A group of PhDs...
First, Gunnar Carlsson, PhD, Co-Founder and President was instrumental in the development of computational topology in the last few years with "NSF funding and as the lead PI on the DARPA “Topological Data Analysis”...".
The actual coding and software development comes from elsewhere. These are his former students: Gurjeet Singh, PhD, Co-Founder and CEO, and Harlan Sexton, PhD, Co-Founder.
The main push of Ayasdi seems to be bioinformatics. Pek Lum, PhD, Vice President, Life Sciences, "is developing the vision and business strategy".
The company already has its own lobbyist. Ben Mann, PhD, Director, Federal Operations, "heads up Ayasdi’s initiatives with government agencies". In the NSF, as a Program Director, he "created and funded novel mathematics programs". In DARPA, a Program Manager, "his Topological Data Analysis Program used sophisticated methods from algebraic topology and geometry to analyze massive data sets". So, he is paid by a company created to commercialize the research he funded, with taxpayers' money, until very recently. Did somebody say "military-industrial complex"?
Ayasdi filed a patent application: "Systems and methods for visualization of data analysis", US2010/023771. A few quotes below (there is only one mention of homology in the text).
"Clustering is often too blunt an instrument to identify important relationships in the data. Similarly, previous methods of linear regression, projection pursuit, principal component analysis, and multidimensional scaling often do not reveal important relationships. Existing linear algebraic and analytic methods are too sensitive to large scale distances and, as a result, lose detail."
"Further, even if the data is analyzed, sophisticated experts are often necessary to interpret and understand the output of previous methods. Although some previous methods allow graphs depicting some relationships in the data, the graphs are not interactive and require considerable time for a team of such experts to understand the relationships. Further, the output of previous methods does not allow for exploratory data analysis where the analysis can be quickly modified to discover new relationships. Rather, previous methods require the formulation of a hypothesis before testing."
"The output may be a simplicial complex, from which one can extract its 1-skeleton. The nodes of the complex may be partial clusters, (i.e., clusters constructed from subsets of S specified as the preimages of sets in the given covering of the reference space R). "
"...the analysis module 220 may compute simplicial complexes of any dimension (by a variety of rules) on nodes, and apply techniques from homology theory to the graphs to help users understand a structure in an automatic (or semi-automatic) way."