טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentSchwartz Ariel
SubjectIntrinsic Isometric Manifold Learning with Application
to Localization in Sensor Networks
DepartmentDepartment of Electrical Engineering
Supervisor Professor Ronen Talmon
Full Thesis textFull thesis text - English Version


Abstract

Data lying on manifolds commonly appear in machine learning, signal processing and data analysis. It is often the case that although these manifolds are low-dimensional, they are embedded in an ambient space of a much higher dimension. Manifold learning techniques aim to eliminate the need for data processing in high-dimension; this is often accomplished by building alternative low-dimensional representations of the data while preserving, as much as possible, some of its observed properties. These observed properties are usually related to the geometric structure of the observed data samples. In this work, we propose to deviate from this standard practice. Instead of learning the structure of the observed manifold, we view the observed data only as a proxy to a latent unobserved intrinsic manifold for which we aim to build a geometry preserving representation. In particular, we propose a new manifold learning method which uses the push-forward metric, between the latent intrinsic manifold and the observed manifold, in order to compute geometric properties on the observed data manifold as if they were computed directly on the underlying latent intrinsic manifold. We show that by using this intrinsic metric and under certain conditions, learning an intrinsic and isometric data representation which respects the latent manifold geometry is possible with only minimal prior model assumptions. We further propose a method for robust estimation of the push-forward metric from observed data without knowledge of the system model using artificial neural networks. Finally, we show that the proposed approach can be successfully applied to the problem of indoor localization in ad-hoc sensor networks of unknown type. In particular, we demonstrate that we can discover the physical space and infer a non-linear function which maps sensor measurements to a location in the physical space allowing us to localize an agent, all without knowing a-priori the nature of the connection between the agent location and the sensor measurements.