36 research outputs found
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Applied Harmonic Analysis and Data Science (hybrid meeting)
Data science has become a field of major importance for science and technology
nowadays and poses a large variety of
challenging mathematical questions.
The area
of applied harmonic analysis has a significant impact on such problems by providing methodologies
both for theoretical questions and for a wide range of applications
in signal and image processing and machine learning.
Building on the success of three previous workshops on applied harmonic analysis in 2012, 2015 and 2018,
this workshop focused
on several exciting novel directions such as mathematical theory of
deep learning, but also reported progress on long-standing open problems in the field
Recommended from our members
Deconvolution Problems for Structured Sparse Signal
This dissertation studies deconvolution problems of how structured sparse signals appear in nature, science and engineering. We discuss about the intrinsic solution to the problem of short-and-sparse deconvolution, how these solutions structured the optimization problem, and how do we design an efficient and practical algorithm base on aforementioned analytical findings. To fully utilized the information of structured sparse signals efficiently, we also propose a sensing method while the sampling acquisition is expansive, and study its sample limit and algorithms for signal recovery with limited samples
International Conference on Continuous Optimization (ICCOPT) 2019 Conference Book
The Sixth International Conference on Continuous Optimization took place on the campus of the Technical University of Berlin, August 3-8, 2019. The ICCOPT is a flagship conference of the Mathematical Optimization Society (MOS), organized every three years. ICCOPT 2019 was hosted by the Weierstrass Institute for Applied Analysis and Stochastics (WIAS) Berlin. It included a Summer School and a Conference with a series of plenary and semi-plenary talks, organized and contributed sessions, and poster sessions.
This book comprises the full conference program. It contains, in particular, the scientific program in survey style as well as with all details, and information on the social program, the venue, special meetings, and more
A User-assisted Approach to Multiple Instrument Music Transcription
PhDThe task of automatic music transcription has been studied for several decades
and is regarded as an enabling technology for a multitude of applications such
as music retrieval and discovery, intelligent music processing and large-scale
musicological analyses. It refers to the process of identifying the musical content
of a performance and representing it in a symbolic format. Despite its long
research history, fully automatic music transcription systems are still error prone
and often fail when more complex polyphonic music is analysed. This gives
rise to the question in what ways human knowledge can be incorporated in the
transcription process.
This thesis investigates ways to involve a human user in the transcription
process. More specifically, it is investigated how user input can be employed
to derive timbre models for the instruments in a music recording, which are
employed to obtain instrument-specific (parts-based) transcriptions.
A first investigation studies different types of user input in order to derive
instrument models by means of a non-negative matrix factorisation framework.
The transcription accuracy of the different models is evaluated and a method is
proposed that refines the models by allowing each pitch of each instrument to
be represented by multiple basis functions.
A second study aims at limiting the amount of user input to make the
method more applicable in practice. Different methods are considered to estimate
missing non-negative basis functions when only a subset of basis functions can
be extracted based on the user information.
A method is proposed to track the pitches of individual instruments over time
by means of a Viterbi framework in which the states at each time frame contain
several candidate instrument-pitch combinations. A transition probability is
employed that combines three different criteria: the frame-wise reconstruction
error of each combination, a pitch continuity measure that favours similar pitches
in consecutive frames, and an explicit activity model for each instrument. The
method is shown to outperform other state-of-the-art multi-instrument tracking
methods.
Finally, the extraction of instrument models that include phase information
is investigated as a step towards complex matrix decomposition. The phase
relations between the partials of harmonic sounds are explored as a time-invariant
property that can be employed to form complex-valued basis functions. The
application of the model for a user-assisted transcription task is illustrated with a saxophone example.QMU
Speech dereverberation and speaker separation using microphone arrays in realistic environments
This thesis concentrates on comparing novel and existing dereverberation and speaker
separation techniques using multiple corpora, including a new corpus collected using
a microphone array. Many corpora currently used for these techniques are recorded
using head-mounted microphones in anechoic chambers. This novel corpus contains
recordings with noise and reverberation made in office and workshop environments.
Novel algorithms present a different way of approximating the reverberation, producing results that are competitive with existing algorithms.
Dereverberation is evaluated using seven correlation-based algorithms and applied to two different corpora. Three of these are novel algorithms (Hs NTF, Cauchy
WPE and Cauchy MIMO WPE). Both non-learning and learning algorithms are
tested, with the learning algorithms performing better.
For single and multi-channel speaker separation, unsupervised non-negative matrix factorization (NMF) algorithms are compared using three cost functions combined with sparsity, convolution and direction of arrival. The results show that the
choice of cost function is important for improving the separation result. Furthermore, six different supervised deep learning algorithms are applied to single channel
speaker separation. Historic information improves the result. When comparing
NMF to deep learning, NMF is able to converge faster to a solution and provides a
better result for the corpora used in this thesis
Relating Spontaneous Activity and Cognitive States via NeuroDynamic Modeling
Stimulus-free brain dynamics form the basis of current knowledge concerning functional integration and segregation within the human brain. These relationships are typically described in terms of resting-state brain networks—regions which spontaneously coactivate. However, despite the interest in the anatomical mechanisms and biobehavioral correlates of stimulus-free brain dynamics, little is known regarding the relation between spontaneous brain dynamics and task-evoked activity. In particular, no computational framework has been previously proposed to unite spontaneous and task dynamics under a single, data-driven model. Model development in this domain will provide new insight regarding the mechanisms by which exogeneous stimuli and intrinsic neural circuitry interact to shape human cognition. The current work bridges this gap by deriving and validating a new technique, termed Mesoscale Individualized NeuroDynamic (MINDy) modeling, to estimate large-scale neural population models for individual human subjects using resting-state fMRI. A combination of ground-truth simulations and test-retest data are used to demonstrate that the approach is robust to various forms of noise, motion, and data processing choices. The MINDy formalism is then extended to simultaneously estimating neural population models and the neurovascular coupling which gives rise to BOLD fMRI. In doing so, I develop and validate a new optimization framework for simultaneously estimating system states and parameters. Lastly, MINDy models derived from resting-state data are used to predict task-based activity and remove the effects of intrinsic dynamics. Removing the MINDy model predictions from task fMRI, enables separation of exogenously-driven components of activity from their indirect consequences (the model predictions). Results demonstrate that removing the predicted intrinsic dynamics improves detection of event-triggered and sustained responses across four cognitive tasks. Together, these findings validate the MINDy framework and demonstrate that MINDy models predict brain dynamics across contexts. These dynamics contribute to the variance of task-evoked brain activity between subjects. Removing the influence of intrinsic dynamics improves the estimation of task effects
Global Optimality in Representation Learning
A majority of data processing techniques across a wide range of technical disciplines require a representation of the data that is meaningful for the task at hand in order to succeed. In some cases one has enough prior knowledge about the problem that a fixed transformation of the data or set of features can be pre-calculated, but for most challenging problems with high dimensional data, it is often not known what representation of the data would give the best performance. To address this issue, the field of representation learning seeks to learn meaningful representations directly from data and includes methods such as matrix factorization, tensor factorization, and neural networks. Such techniques have achieved considerable empirical success in many fields, but common to a vast majority of these approaches are the significant disadvantages that 1) the associated optimization problems are typically non-convex due to a multilinear form or other convexity destroying transformation and 2) one is forced to specify the size of the learned representation a priori.
This thesis presents a very general framework which allows for the mathematical analysis of a wide range of non-convex representation learning problems. The framework allows the derivation of sufficient conditions to guarantee that a local minimizer of the non-convex optimization problem is a global minimizer and that from any initialization it is possible to find a global minimizer using a purely local descent algorithm. Further, the framework also allows for a wide range of regularization to be incorporated into the model to capture known features of data and to adaptively fit the size of the learned representation to the data instead of defining it a priori. Multiple implications of this work are discussed as they relate to modern practices in deep learning, and the advantages of the approach are demonstrated in applications of automated spatio-temporal segmentation of neural calcium imaging data and reconstructing hyperspectral image volumes from compressed measurements