280 research outputs found
Sparse machine learning methods with applications in multivariate signal processing
This thesis details theoretical and empirical work that draws from two main subject areas: Machine
Learning (ML) and Digital Signal Processing (DSP). A unified general framework is given for the application
of sparse machine learning methods to multivariate signal processing. In particular, methods that
enforce sparsity will be employed for reasons of computational efficiency, regularisation, and compressibility.
The methods presented can be seen as modular building blocks that can be applied to a variety
of applications. Application specific prior knowledge can be used in various ways, resulting in a flexible
and powerful set of tools. The motivation for the methods is to be able to learn and generalise from a set
of multivariate signals.
In addition to testing on benchmark datasets, a series of empirical evaluations on real world
datasets were carried out. These included: the classification of musical genre from polyphonic audio
files; a study of how the sampling rate in a digital radar can be reduced through the use of Compressed
Sensing (CS); analysis of human perception of different modulations of musical key from
Electroencephalography (EEG) recordings; classification of genre of musical pieces to which a listener
is attending from Magnetoencephalography (MEG) brain recordings. These applications demonstrate
the efficacy of the framework and highlight interesting directions of future research
Study of manifold geometry using multiscale non-negative kernel graphs
Modern machine learning systems are increasingly trained on large amounts of data embedded in high-dimensional spaces. Often this is done without analyzing the structure of the dataset. In this work, we propose a framework to study the geometric structure of the data. We make use of our recently introduced non-negative kernel (NNK) regression graphs to estimate the point density, intrinsic dimension, and linearity of the data manifold (curvature). We further generalize the graph construction and geometric estimation to multiple scales by iteratively merging neighborhoods in the input data. Our experiments demonstrate the effectiveness of our proposed approach over other baselines in estimating the local geometry of the data manifolds on synthetic and real datasets.Our work was supported in part by DARPA grant (FA8750-19-2-1005) in the Learning with Less Labels (LwLL) program.Peer ReviewedPostprint (author's final draft
Study of Manifold Geometry using Multiscale Non-Negative Kernel Graphs
Modern machine learning systems are increasingly trained on large amounts of
data embedded in high-dimensional spaces. Often this is done without analyzing
the structure of the dataset. In this work, we propose a framework to study the
geometric structure of the data. We make use of our recently introduced
non-negative kernel (NNK) regression graphs to estimate the point density,
intrinsic dimension, and the linearity of the data manifold (curvature). We
further generalize the graph construction and geometric estimation to multiple
scale by iteratively merging neighborhoods in the input data. Our experiments
demonstrate the effectiveness of our proposed approach over other baselines in
estimating the local geometry of the data manifolds on synthetic and real
datasets
Backward Reachability Analysis of Perturbed Continuous-Time Linear Systems Using Set Propagation
Backward reachability analysis computes the set of states that reach a target
set under the competing influence of control input and disturbances. Depending
on their interplay, the backward reachable set either represents all states
that can be steered into the target set or all states that cannot avoid
entering it -- the corresponding solutions can be used for controller synthesis
and safety verification, respectively. A popular technique for backward
reachable set computation solves Hamilton-Jacobi-Isaacs equations, which scales
exponentially with the state dimension due to gridding the state space. In this
work, we instead use set propagation techniques to design backward reachability
algorithms for linear time-invariant systems. Crucially, the proposed
algorithms scale only polynomially with the state dimension. Our numerical
examples demonstrate the tightness of the obtained backward reachable sets and
show an overwhelming improvement of our proposed algorithms over
state-of-the-art methods regarding scalability, as systems with well over a
hundred states can now be analyzed.Comment: 16 page
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