Data Science and Advanced Analytics (DSAA), 2015. 36678 2015. IEEE International Conference on
Following the great success of DSAA’2014 in Shanghai, the 2015 IEEE International Conference on Data Science and Advanced Analytics (IEEE DSAA’2015), to be held on 19-21 October 2015 in Paris, has seen the significant growth of the number of submissions, participates, sponsors and key stakeholders. Without any doubt, DSAA has been recognized to be the first and most influential event in the data science and analytics focused community. Data driven scientific discovery and innovation and practical development, applications and economy have been increasingly recognized as the major trend of future IT and business. Data science, big data and advanced analytics play the most important role in driving data innovation and economy. DSAA thus carries a critical role in substantially promoting and strengthening the above trends and results.
In many Data Analysis tasks, one deals with data that are presented in high-dimensional spaces. In practice original high-dimensional data are transformed into lower-dimensional representations (features) preserving certain subject-driven data properties such as distances or geodesic distances, angles, etc. Preserving as much as possible available information contained in the original high-dimensional data is also an important and desirable property of the representation. The real-world high-dimensional data typically lie on or near a certain unknown low-dimensional manifold (Data manifold) embedded in an ambient high-dimensional `observation' space, so in this article we assume this Manifold assumption to be fulfilled. An exact isometric manifold embedding in a low-dimensional space is possible in certain special cases only, so we consider the problem of constructing a `locally isometric and conformal' embedding, which preserves distances and angles between close points. We propose a new geometrically motivated locally isometric and conformal representation method, which employs Tangent Manifold Learning technique consisting in sample-based estimation of tangent spaces to the unknown Data manifold. In numerical experiments, the proposed method compares favourably with popular Manifold Learning methods in terms of isometric and conformal embedding properties as well as of accuracy of Data manifold reconstruction from the sample.