258 research outputs found
Piecewise rigid curve deformation via a Finsler steepest descent
This paper introduces a novel steepest descent flow in Banach spaces. This
extends previous works on generalized gradient descent, notably the work of
Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient
allows one to take into account a prior on deformations (e.g., piecewise rigid)
in order to favor some specific evolutions. We define a Finsler gradient
descent method to minimize a functional defined on a Banach space and we prove
a convergence theorem for such a method. In particular, we show that the use of
non-Hilbertian norms on Banach spaces is useful to study non-convex
optimization problems where the geometry of the space might play a crucial role
to avoid poor local minima. We show some applications to the curve matching
problem. In particular, we characterize piecewise rigid deformations on the
space of curves and we study several models to perform piecewise rigid
evolution of curves
Toeplitz Inverse Covariance-Based Clustering of Multivariate Time Series Data
Subsequence clustering of multivariate time series is a useful tool for
discovering repeated patterns in temporal data. Once these patterns have been
discovered, seemingly complicated datasets can be interpreted as a temporal
sequence of only a small number of states, or clusters. For example, raw sensor
data from a fitness-tracking application can be expressed as a timeline of a
select few actions (i.e., walking, sitting, running). However, discovering
these patterns is challenging because it requires simultaneous segmentation and
clustering of the time series. Furthermore, interpreting the resulting clusters
is difficult, especially when the data is high-dimensional. Here we propose a
new method of model-based clustering, which we call Toeplitz Inverse
Covariance-based Clustering (TICC). Each cluster in the TICC method is defined
by a correlation network, or Markov random field (MRF), characterizing the
interdependencies between different observations in a typical subsequence of
that cluster. Based on this graphical representation, TICC simultaneously
segments and clusters the time series data. We solve the TICC problem through
alternating minimization, using a variation of the expectation maximization
(EM) algorithm. We derive closed-form solutions to efficiently solve the two
resulting subproblems in a scalable way, through dynamic programming and the
alternating direction method of multipliers (ADMM), respectively. We validate
our approach by comparing TICC to several state-of-the-art baselines in a
series of synthetic experiments, and we then demonstrate on an automobile
sensor dataset how TICC can be used to learn interpretable clusters in
real-world scenarios.Comment: This revised version fixes two small typos in the published versio
Total variation regularization of multi-material topology optimization
This work is concerned with the determination of the diffusion coefficient
from distributed data of the state. This problem is related to homogenization
theory on the one hand and to regularization theory on the other hand. An
approach is proposed which involves total variation regularization combined
with a suitably chosen cost functional that promotes the diffusion coefficient
assuming prespecified values at each point of the domain. The main difficulty
lies in the delicate functional-analytic structure of the resulting
nondifferentiable optimization problem with pointwise constraints for functions
of bounded variation, which makes the derivation of useful pointwise optimality
conditions challenging. To cope with this difficulty, a novel reparametrization
technique is introduced. Numerical examples using a regularized semismooth
Newton method illustrate the structure of the obtained diffusion coefficient.
Group Lasso with Overlaps: the Latent Group Lasso approach
We study a norm for structured sparsity which leads to sparse linear
predictors whose supports are unions of prede ned overlapping groups of
variables. We call the obtained formulation latent group Lasso, since it is
based on applying the usual group Lasso penalty on a set of latent variables. A
detailed analysis of the norm and its properties is presented and we
characterize conditions under which the set of groups associated with latent
variables are correctly identi ed. We motivate and discuss the delicate choice
of weights associated to each group, and illustrate this approach on simulated
data and on the problem of breast cancer prognosis from gene expression data
Synthesis for Testability by Two-Clock Control
In previous studies clock control has been inserted after design to improve the testability of a sequential circuit. In this paper we propose a two-clock control scheme that is included as a part of the logic synthesis of a finite state machine (fsm). The scheme has low area overhead and competes well with scan methods in its ability to initialize and observe circuit states. The states of the machine are assigned a pair of binary values using a novel split coding system. The purpose of the encoding is to ease navigation between any pair of states using a combination of normal and test-mode transitions. We require a Hamiltonian cycle to exist in the state transition graph. Our investigation of the fsm benchmark shows that either such a cycle already exists or can be created with the insertion of a small number of transition edges. We also present synthesis results to show that the area penalty is small
External optimal control of fractional parabolic PDEs
In this paper we introduce a new notion of optimal control, or source
identification in inverse, problems with fractional parabolic PDEs as
constraints. This new notion allows a source/control placement outside the
domain where the PDE is fulfilled. We tackle the Dirichlet, the Neumann and the
Robin cases. For the fractional elliptic PDEs this has been recently
investigated by the authors in \cite{HAntil_RKhatri_MWarma_2018a}. The need for
these novel optimal control concepts stems from the fact that the classical PDE
models only allow placing the source/control either on the boundary or in the
interior where the PDE is satisfied. However, the nonlocal behavior of the
fractional operator now allows placing the control in the exterior. We
introduce the notions of weak and very-weak solutions to the parabolic
Dirichlet problem. We present an approach on how to approximate the parabolic
Dirichlet solutions by the parabolic Robin solutions (with convergence rates).
A complete analysis for the Dirichlet and Robin optimal control problems has
been discussed. The numerical examples confirm our theoretical findings and
further illustrate the potential benefits of nonlocal models over the local
ones.Comment: arXiv admin note: text overlap with arXiv:1811.0451
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