IP protection

1

Please provide a short description of the state-of-the-art and/or current trends in the field? How does the result fit into it?

The manifold learning approach assumes that the data belong to a low dimensional manifold embedded in the construct a graph encoding the interrelations of the data. Then, the task is to properly unfold this graph and embed it in a low dimensional space. The advantage of this approach is that complex overlapping geometries, clusters, and data of non-linear nature can be effectively represented. Additionally, in cases where the graph is naturally available as in the Web the methods can be applied directly. A typical list of graph-based manifold learning methods includes: Isomap, MVU, Diffusion maps, LLE , Laplacian Eigenmap , Hessian LLE , LTSA. They involve eigen-analysis, graph traversal techniques and other computationally demanding op- erations, which are in general sensitive to the scale of the graph. A comparison in terms of time complexity with respect to the graph size |V |. All of them are of polynomial complexity O(|V|2) or O(|V |3). Although the complexity is reasonable and benefits from the sparsity of the graphs as we scale up they become incomputable. Of them particular interest has the Laplacian Eigenmap because it has a natural tendency to enhance the formation of the communities. A (Web) community can be considered as a coherent cluster of pages that has significantly more hyper-links pointing among pages belonging to the community itself than the rest of the graph. This structural attribute emerges from the fact that pages with common subject often reference one another as related sources. A user, that enters a Web community, is “trapped” in the sense that the probability of visiting a page outside the com- munity is lower, because of the fewer outgoing hyper- links.

 

 

2

What is the problem/need/knowledge gap that the research result is responding to?  How was it addressed before?

The problem of large has been resolved using the manifold. A manifold is a topological space that only locally exhibits flat conventional geometry. On global scale, it demonstrates profound structural hyper-organization. In the space of a manifold the conventional Euclidean distances are less important as they do not capture the manifold’s geometry. Consider, as toy example, the Archimedes’ spiral manifold. The spiral itself comprises of a swarm of 1000 points in a 2D space coordinate. Although we can evaluate the Euclidean distance from point labelled 1 to 2, the result would be contrary to our intuition. A more appropriate distance evaluation should incorporate the intrinsic geometry of the manifold by imitating a “walk” on the manifold, from point 1 to 2. In order to perform a walk on the manifold, a graph that connects nearby points in the space is formed. The graph encodes local relations, building essentially a graph of the data. The graph itself limits the ways in which the data points can be accessed from one another since “communication” is possible only through the available edges.

 

 

3

What is the potential for further research?

Future research directions may include time varying networks and content/label- loaded graphs. The time-varying maximum flow problem is to find the maximum flow in a time-varying network. A time-varying network is the network which the transit time and the capacity of an arc are functions of the departure time at the beginning node of an arc. The earliest (or the latest) maximum flow is the maximum flow could be sent from the source node to the sink node in the time-varying network within the given time duration with the earliest (or the latest) arrival time. Assuming that the transit time and the capacity of an arc are positive integers, and waiting at any node is prohibited except the source node. The problem is known to be NP-complete.

 

 

4

What is the proposed method of IPR-protection? (patent, license, trademark etc.)

The adoption of the Creative Commons licensing model is suggested for Mani-Web

·       overcomes the rigidity of the “All Rights Reserved” status and introduces the “Some Rights Reserved” status

·       includes terms and clauses for open distribution of content

·       is easy to use by an author or right-holder to grant permissions for any use of their works

·       has no cost

·       is enhanced by technological elements, i.e. meta-data software code

·       is applicable to all sorts of creative works

 

5

What are the steps that need to be taken in order to secure the IPR-protection? What is the cost of IPR-protection?

Creative Commons licensing model a design of the platform in the form a blueprint is required and an application for license.

 

6

What is you overall assessment of the scientific maturity of the research result?

 

The manifold algorithm has been implemented and is matured having the following constituents. The algorithm itself consists of three phases namely maniReduce(), maniReconstruct(), and maniMap() (The appearance of ’()’ will denote Functions). The complete listing of the code is available in Figure 1 (using Matlab syntax, ready to copy-paste). The outline of the algorithm is this: Select a few boundary-nodes, construct a reduced-graph using the boundary-nodes, produce a Laplacian Eignemap for the reduced-graph, and finally extrapolate the map for all nodes. The result is a map of all nodes in a (Euclidean) coordinate space with only marginal error against the original Laplacian Eigenmap. Then, by selecting the 2nd,3rd (and optionally 4th) dimensions we produce a low-dimensional image of the original graph.

 

 

KEYWORDS QUANTITATIVE ASSESSMENT (0-5).

Please put X as appropriate.

1

2

3

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5

Scientific maturity

 

 

 

 

x

Synergies

 

 

 

 

x

State-of-the-art/innovation

 

 

 

 

x

IPR-potential

 

 

 

 

x

 

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