4,983 research outputs found
Robust PCA by Manifold Optimization
Robust PCA is a widely used statistical procedure to recover a underlying
low-rank matrix with grossly corrupted observations. This work considers the
problem of robust PCA as a nonconvex optimization problem on the manifold of
low-rank matrices, and proposes two algorithms (for two versions of
retractions) based on manifold optimization. It is shown that, with a proper
designed initialization, the proposed algorithms are guaranteed to converge to
the underlying low-rank matrix linearly. Compared with a previous work based on
the Burer-Monterio decomposition of low-rank matrices, the proposed algorithms
reduce the dependence on the conditional number of the underlying low-rank
matrix theoretically. Simulations and real data examples confirm the
competitive performance of our method
Nonlinear stability of planar rarefaction wave to the three-dimensional Boltzmann equation
We investigate the time-asymptotic stability of planar rarefaction wave for
the three-dimensional Boltzmann equation, based on the micro-macro
decomposition introduced in [24, 22] and our new observations on the underlying
wave structures of the equation to overcome the difficulties due to the wave
propagation along the transverse directions and its interactions with the
planar rarefaction wave. Note that this is the first stability result of planar
rarefaction wave for 3D Boltzmann equation, while the corresponding results for
the shock and contact discontinuities are still completely open.Comment: 45pages. We correct some typoes. The paper will be published on
Kinetic and Related Model
Understanding changes in teacher beliefs and identity formation: A case study of three novice teachers in Hong Kong
Novice teachers often undergo an identity shift from learner to teacher. Along this process, their instructional beliefs change considerably which in turn affect their teacher identity formation. Drawing on
data collected mainly through interviews with three novice English teachers formore than one year, the present study examines their firstyear teaching experience in Hong Kong secondary schools, focusing
on changes of their English teaching beliefs and the impact of these changes on their identity construction. Findings reveal that while the teachers’ initial teaching beliefs were largely shaped in their prior school learning and learning-to-teach experience, these beliefs changed and were reshaped a great deal when encountering various contextual realities, and these changes further influenced their views on their teacher identity establishment, unfortunately in a more negative
than positive direction. The study sheds light on the importance of institutional support in affording opportunities for novice teachers’ workplace learning and professional development
Randomized hybrid linear modeling by local best-fit flats
The hybrid linear modeling problem is to identify a set of d-dimensional
affine sets in a D-dimensional Euclidean space. It arises, for example, in
object tracking and structure from motion. The hybrid linear model can be
considered as the second simplest (behind linear) manifold model of data. In
this paper we will present a very simple geometric method for hybrid linear
modeling based on selecting a set of local best fit flats that minimize a
global l1 error measure. The size of the local neighborhoods is determined
automatically by the Jones' l2 beta numbers; it is proven under certain
geometric conditions that good local neighborhoods exist and are found by our
method. We also demonstrate how to use this algorithm for fast determination of
the number of affine subspaces. We give extensive experimental evidence
demonstrating the state of the art accuracy and speed of the algorithm on
synthetic and real hybrid linear data.Comment: To appear in the proceedings of CVPR 201
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