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## Learning Algorithms for Human–Machine Interfaces

Fonte: PubMed
Publicador: PubMed

Tipo: Artigo de Revista Científica

EN

Relevância na Pesquisa

26.25%

The goal of this study is to create and examine machine learning algorithms that adapt in a controlled and cadenced way to foster a harmonious learning environment between the user and the controlled device. To evaluate these algorithms, we have developed a simple experimental framework. Subjects wear an instrumented data glove that records finger motions. The high-dimensional glove signals remotely control the joint angles of a simulated planar two-link arm on a computer screen, which is used to acquire targets. A machine learning algorithm was applied to adaptively change the transformation between finger motion and the simulated robot arm. This algorithm was either LMS gradient descent or the Moore–Penrose (MP) pseudoinverse transformation. Both algorithms modified the glove-to-joint angle map so as to reduce the endpoint errors measured in past performance. The MP group performed worse than the control group (subjects not exposed to any machine learning), while the LMS group outperformed the control subjects. However, the LMS subjects failed to achieve better generalization than the control subjects, and after extensive training converged to the same level of performance as the control subjects. These results highlight the limitations of coadaptive learning using only endpoint error reduction.

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## Accurate solution of structured least squares problems via rank-revealing decompositions

Fonte: Society for Industrial and Applied Mathematics
Publicador: Society for Industrial and Applied Mathematics

Tipo: info:eu-repo/semantics/publishedVersion; info:eu-repo/semantics/article

Publicado em /07/2013
ENG

Relevância na Pesquisa

66.72%

#Accurate solutions#least squares problems#multiplicative perturbation theory#rank revealing decompositions#structured matrices#Moore–Penrose pseudoinverse.#Matemáticas

Least squares problems min(x) parallel to b - Ax parallel to(2) where the matrix A is an element of C-mXn (m >= n) has some particular structure arise frequently in applications. Polynomial data fitting is a well-known instance of problems that yield highly structured matrices, but many other examples exist. Very often, structured matrices have huge condition numbers kappa(2)(A) = parallel to A parallel to(2) parallel to A(dagger)parallel to(2) (A(dagger) is the Moore-Penrose pseudoinverse of A) and therefore standard algorithms fail to compute accurate minimum 2-norm solutions of least squares problems. In this work, we introduce a framework that allows us to compute minimum 2-norm solutions of many classes of structured least squares problems accurately, i.e., with errors parallel to(x) over cap (0) - x(0)parallel to(2)/parallel to x(0)parallel to(2) = O(u), where u is the unit roundoff, independently of the magnitude of kappa(2)(A) for most vectors b. The cost of these accurate computations is O(n(2)m) flops, i.e., roughly the same cost as standard algorithms for least squares problems. The approach in this work relies in computing first an accurate rank-revealing decomposition of A, an idea that has been widely used in recent decades to compute...

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## A higher Boltzmann distribution

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.25%

#Mathematics - Algebraic Topology#Mathematical Physics#Mathematics - Probability#Primary: 92E10, 18G35, 57M15, 80A50, Secondary: 05C05, 05C21, 05E45,
82C31

We characterize the classical Boltzmann distribution as the unique solution
to a certain combinatorial Hodge theory problem in homological degree zero on a
finite graph. By substituting for the graph a CW complex of dimension d, we are
able to define, by direct analogy, a higher dimensional Boltzmann distribution
as a certain (d-1)-cycle on the real cellular chain complex which is
characterized by appropriate constraints. We then give an explicit summation
formula for this cycle. Lastly, we explain how this circle of ideas relates to
the authors' Higher Kirchhoff Network Theorem.; Comment: Fixed a sign mistake in the definition of the master operator and in
the statement of the summation formula for the Moore-Penrose pseudoinverse

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## Optimal linear Glauber model

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.25%

Contrary to the actual nonlinear Glauber model (NLGM), the linear Glauber
model (LGM) is exactly solvable, although the detailed balance condition is not
generally satisfied. This motivates us to address the issue of writing the
transition rate ($w_j$) in a best possible linear form such that the mean
squared error in satisfying the detailed balance condition is least. The
advantage of this work is that, by studying the LGM analytically, we will be
able to anticipate how the kinetic properties of an arbitrary Ising system
depend on the temperature and the coupling constants. The analytical
expressions for the optimal values of the parameters involved in the linear
$w_j$ are obtained using a simple Moore-Penrose pseudoinverse matrix. This
approach is quite general, in principle applicable to any system and can
reproduce the exact results for one dimensional Ising system. In the continuum
limit, we get a linear time-dependent Ginzburg-Landau (TDGL) equation from the
Glauber's microscopic model of non-conservative dynamics. We analyze the
critical and dynamic properties of the model, and show that most of the
important results obtained in different studies can be reproduced by our new
mathematical approach. We will also show in this paper that the effect of
magnetic field can easily be studied within our approach; in particular...

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## Regularized Computation of Approximate Pseudoinverse of Matrices Using Low-Rank Tensor Train Decompositions

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.46%

We propose a new method for low-rank approximation of Moore-Penrose
pseudoinverses (MPPs) of large-scale matrices using tensor networks. The
computed pseudoinverses can be useful for solving or preconditioning
large-scale overdetermined or underdetermined systems of linear equations. The
computation is performed efficiently and stably based on the modified
alternating least squares (MALS) scheme using low-rank tensor train (TT)
decomposition. The large-scale optimization problem is reduced to sequential
smaller-scale problems for which any standard and stable algorithms can be
applied. Regularization technique is further introduced in order to alleviate
ill-posedness and obtain low-rank solutions. Numerical simulation results
illustrate that the pseudoinverses of a wide class of nonsquare or nonsymmetric
matrices admit good approximate low-rank TT approximations. It is demonstrated
that the computational cost of the proposed method is only logarithmic in the
matrix size given that the TT-ranks of a data matrix and its approximate
pseudoinverse are bounded. It is illustrated that a strongly nonsymmetric
convection-diffusion problem can be efficiently solved by using the
preconditioners computed by the proposed method.; Comment: 26 pages

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## Fast Computation of Moore-Penrose Inverse Matrices

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 30/04/2008

Relevância na Pesquisa

46.65%

Many neural learning algorithms require to solve large least square systems
in order to obtain synaptic weights. Moore-Penrose inverse matrices allow for
solving such systems, even with rank deficiency, and they provide minimum-norm
vectors of synaptic weights, which contribute to the regularization of the
input-output mapping. It is thus of interest to develop fast and accurate
algorithms for computing Moore-Penrose inverse matrices. In this paper, an
algorithm based on a full rank Cholesky factorization is proposed. The
resulting pseudoinverse matrices are similar to those provided by other
algorithms. However the computation time is substantially shorter, particularly
for large systems.; Comment: Number of pages: 5. Typo page 26 line 3: one must read W=G^+F
(instead of W=G^+W, which does not make sense!)

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## A comparative study of Gaussian Graphical Model approaches for genomic data

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/07/2011

Relevância na Pesquisa

36.25%

The inference of networks of dependencies by Gaussian Graphical models on
high-throughput data is an open issue in modern molecular biology. In this
paper we provide a comparative study of three methods to obtain small sample
and high dimension estimates of partial correlation coefficients: the
Moore-Penrose pseudoinverse (PINV), residual correlation (RCM) and
covariance-regularized method $(\ell_{2C})$. We first compare them on simulated
datasets and we find that PINV is less stable in terms of AUC performance when
the number of variables changes. The two regularized methods have comparable
performances but $\ell_{2C}$ is much faster than RCM. Finally, we present the
results of an application of $\ell_{2C}$ for the inference of a gene network
for isoprenoid biosynthesis pathways in Arabidopsis thaliana.; Comment: 7 pages, 1 figure, RevTex4, version to appear in the proceedings of
1st International Workshop on Pattern Recognition, Proteomics, Structural
Biology and Bioinformatics: PR PS BB 2011, Ravenna, Italy, 13 September 2011

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## Optimal control theory with arbitrary superpositions of waveforms

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Relevância na Pesquisa

36.25%

Standard optimal control methods perform optimization in the time domain.
However, many experimental settings demand the expression of the control signal
as a superposition of given waveforms, a case that cannot easily be
accommodated using time-local constraints. Previous approaches [1,2] have
circumvented this difficulty by performing optimization in a parameter space,
using the chain rule to make a connection to the time domain. In this paper, we
present an extension to Optimal Control Theory which allows gradient-based
optimization for superpositions of arbitrary waveforms directly in a
time-domain subspace. Its key is the use of the Moore-Penrose pseudoinverse as
an efficient means of transforming between a time-local and waveform-based
descriptions. To illustrate this optimization technique, we study the
parametrically driven harmonic oscillator as model system and reduce its
energy, considering both Hamiltonian dynamics and stochastic dynamics under the
influence of a thermal reservoir. We demonstrate the viability and efficiency
of the method for these test cases and find significant advantages in the case
of waveforms which do not form an orthogonal basis.; Comment: 16 pages, 6 figures

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## The Moore-Penrose Pseudoinverse. A Tutorial Review of the Theory

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/10/2011

Relevância na Pesquisa

67.23%

In the last decades the Moore-Penrose pseudoinverse has found a wide range of
applications in many areas of Science and became a useful tool for physicists
dealing, for instance, with optimization problems, with data analysis, with the
solution of linear integral equations, etc. The existence of such applications
alone should attract the interest of students and researchers in the
Moore-Penrose pseudoinverse and in related sub jects, like the singular values
decomposition theorem for matrices. In this note we present a tutorial review
of the theory of the Moore-Penrose pseudoinverse. We present the first
definitions and some motivations and, after obtaining some basic results, we
center our discussion on the Spectral Theorem and present an algorithmically
simple expression for the computation of the Moore-Penrose pseudoinverse of a
given matrix. We do not claim originality of the results. We rather intend to
present a complete and self-contained tutorial review, useful for those more
devoted to applications, for those more theoretically oriented and for those
who already have some working knowledge of the sub ject.; Comment: 23 pages

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## A Ring Isomorphism and corresponding Pseudoinverses

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/10/2008

Relevância na Pesquisa

36.46%

This paper studies the set of $n\times n$ matrices for which all row and
column sums equal zero. By representing these matrices in a lower dimensional
space, it is shown that this set is closed under addition and multiplication,
and furthermore is isomorphic to the set of arbitrary $(n-1)\times (n-1)$
matrices. The Moore-Penrose pseudoinverse corresponds with the true inverse,
(when it exists), in this lower dimension and an explicit representation of
this pseudoinverse in terms of the lower dimensional space is given. This
analysis is then extended to non-square matrices with all row or all column
sums equal to zero.; Comment: 9 Pages

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