2,424 research outputs found
Evolutionary and variable step size strategies for multichannel filtered-x affine projection algorithms
This study is focused on the necessity to improve the performance of the affine projection (AP) algorithm for active
noise control (ANC) applications. The proposed algorithms are evaluated regarding their steady-state behaviour, their
convergence speed and their computational complexity. To this end, different strategies recently applied to the AP for channel
identification are proposed for multichannel ANC. These strategies are based either on a variable step size, an evolving
projection order, or the combination of both strategies. The developed efficient versions of the AP algorithm use the modified
filtered-x structure, which exhibits faster convergence than other filtering schemes. Simulation results show that the proposed
approaches exhibit better performance than the conventional AP algorithm and represent a meaningful choice for practical
multichannel ANC applications.This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0097, Spanish Ministerio de Ciencia e Innovacion TEC2009-13741 and Generalitat Valenciana PROMETEO 2009/2013.Gonzalez, A.; Albu, F.; Ferrer Contreras, M.; Diego Antón, MD. (2013). Evolutionary and variable step size strategies for multichannel filtered-x affine projection algorithms. IET Signal Processing. 7(6):471-476. https://doi.org/10.1049/iet-spr.2012.0213S47147676Shin, H.-C., Sayed, A. H., & Song, W.-J. (2004). Variable Step-Size NLMS and Affine Projection Algorithms. IEEE Signal Processing Letters, 11(2), 132-135. doi:10.1109/lsp.2003.821722Paleologu, C., Benesty, J., & Ciochina, S. (2008). A Variable Step-Size Affine Projection Algorithm Designed for Acoustic Echo Cancellation. IEEE Transactions on Audio, Speech, and Language Processing, 16(8), 1466-1478. doi:10.1109/tasl.2008.2002980Shin, H.-C., & Sayed, A. H. (2004). Mean-Square Performance of a Family of Affine Projection Algorithms. IEEE Transactions on Signal Processing, 52(1), 90-102. doi:10.1109/tsp.2003.820077Kong, S.-J., Hwang, K.-Y., & Song, W.-J. (2007). An Affine Projection Algorithm With Dynamic Selection of Input Vectors. IEEE Signal Processing Letters, 14(8), 529-532. doi:10.1109/lsp.2007.891325Seong-Eun Kim, Se-Jin Kong, & Woo-Jin Song. (2009). An Affine Projection Algorithm With Evolving Order. IEEE Signal Processing Letters, 16(11), 937-940. doi:10.1109/lsp.2009.2027638Kim, K.-H., Choi, Y.-S., Kim, S.-E., & Song, W.-J. (2011). An Affine Projection Algorithm With Periodically Evolved Update Interval. IEEE Transactions on Circuits and Systems II: Express Briefs, 58(11), 763-767. doi:10.1109/tcsii.2011.2168023Bouchard, M. (2003). Multichannel affine and fast affine projection algorithms for active noise control and acoustic equalization systems. IEEE Transactions on Speech and Audio Processing, 11(1), 54-60. doi:10.1109/tsa.2002.805642Kong, N., Shin, J., & Park, P. (2011). A two-stage affine projection algorithm with mean-square-error-matching step-sizes. Signal Processing, 91(11), 2639-2646. doi:10.1016/j.sigpro.2011.06.003MoonSoo Chang, NamWoong Kong, & PooGyeon Park. (2010). An Affine Projection Algorithm Based on Reuse Time of Input Vectors. IEEE Signal Processing Letters, 17(8), 750-753. doi:10.1109/lsp.2010.2053355Arablouei, R., & Doğançay, K. (2012). Affine projection algorithm with selective projections. Signal Processing, 92(9), 2253-2263. doi:10.1016/j.sigpro.2012.02.018Gonzalez, A., Ferrer, M., de Diego, M., & Piñero, G. (2012). An affine projection algorithm with variable step size and projection order. Digital Signal Processing, 22(4), 586-592. doi:10.1016/j.dsp.2012.03.00
On Characterizing the Data Access Complexity of Programs
Technology trends will cause data movement to account for the majority of
energy expenditure and execution time on emerging computers. Therefore,
computational complexity will no longer be a sufficient metric for comparing
algorithms, and a fundamental characterization of data access complexity will
be increasingly important. The problem of developing lower bounds for data
access complexity has been modeled using the formalism of Hong & Kung's
red/blue pebble game for computational directed acyclic graphs (CDAGs).
However, previously developed approaches to lower bounds analysis for the
red/blue pebble game are very limited in effectiveness when applied to CDAGs of
real programs, with computations comprised of multiple sub-computations with
differing DAG structure. We address this problem by developing an approach for
effectively composing lower bounds based on graph decomposition. We also
develop a static analysis algorithm to derive the asymptotic data-access lower
bounds of programs, as a function of the problem size and cache size
Numerical Verification of Affine Systems with up to a Billion Dimensions
Affine systems reachability is the basis of many verification methods. With
further computation, methods exist to reason about richer models with inputs,
nonlinear differential equations, and hybrid dynamics. As such, the scalability
of affine systems verification is a prerequisite to scalable analysis for more
complex systems. In this paper, we improve the scalability of affine systems
verification, in terms of the number of dimensions (variables) in the system.
The reachable states of affine systems can be written in terms of the matrix
exponential, and safety checking can be performed at specific time steps with
linear programming. Unfortunately, for large systems with many state variables,
this direct approach requires an intractable amount of memory while using an
intractable amount of computation time. We overcome these challenges by
combining several methods that leverage common problem structure. Memory is
reduced by exploiting initial states that are not full-dimensional and safety
properties (outputs) over a few linear projections of the state variables.
Computation time is saved by using numerical simulations to compute only
projections of the matrix exponential relevant for the verification problem.
Since large systems often have sparse dynamics, we use Krylov-subspace
simulation approaches based on the Arnoldi or Lanczos iterations. Our method
produces accurate counter-examples when properties are violated and, in the
extreme case with sufficient problem structure, can analyze a system with one
billion real-valued state variables
Some advances in the polyhedral model
Department Head: L. Darrell Whitley.2010 Summer.Includes bibliographical references.The polyhedral model is a mathematical formalism and a framework for the analysis and transformation of regular computations. It provides a unified approach to the optimization of computations from different application domains. It is now gaining wide use in optimizing compilers and automatic parallelization. In its purest form, it is based on a declarative model where computations are specified as equations over domains defined by "polyhedral sets". This dissertation presents two results. First is an analysis and optimization technique that enables us to simplify---reduce the asymptotic complexity---of such equations. The second is an extension of the model to richer domains called Ƶ-Polyhedra. Many equational specifications in the polyhedral model have reductions---application of an associative and commutative operator to collections of values to produce a collection of answers. Moreover, expressions in such equations may also exhibit reuse where intermediate values that are computed or used at different index points are identical. We develop various compiler transformations to automatically exploit this reuse and simplify the computational complexity of the specification. In general, there is an infinite set of applicable simplification transformations. Unfortunately, different choices may result in equivalent specifications with different asymptotic complexity. We present an algorithm for the optimal application of simplification transformations resulting in a final specification with minimum complexity. This dissertation also presents the Ƶ-Polyhedral model, an extension to the polyhedral model to more general sets, thereby providing a transformation framework for a larger set of regular computations. For this, we present a novel representation and interpretation of Ƶ-Polyhedra and prove a number of properties of the family of unions of Ƶ-Polyhedra that are required to extend the polyhedral model. Finally, we present value based dependence analysis and scheduling analysis for specifications in the Ƶ-Polyhedral model. These are direct extensions of the corresponding analyses of specifications in the polyhedral model. One of the benefits of our results in the Ƶ-Polyhedral model is that our abstraction allows the reuse of previously developed tools in the polyhedral model with straightforward pre- and post-processing
Simplifying Dependent Reductions in the Polyhedral Model
A Reduction -- an accumulation over a set of values, using an associative and
commutative operator -- is a common computation in many numerical computations,
including scientific computations, machine learning, computer vision, and
financial analytics.
Contemporary polyhedral-based compilation techniques make it possible to
optimize reductions, such as prefix sums, in which each component of the
reduction's output potentially shares computation with another component in the
reduction. Therefore an optimizing compiler can identify the computation shared
between multiple components and generate code that computes the shared
computation only once.
These techniques, however, do not support reductions that -- when phrased in
the language of the polyhedral model -- span multiple dependent statements. In
such cases, existing approaches can generate incorrect code that violates the
data dependences of the original, unoptimized program.
In this work, we identify and formalize the optimization of dependent
reductions as an integer bilinear program. We present a heuristic optimization
algorithm that uses an affine sequential schedule of the program to determine
how to simplfy reductions yet still preserve the program's dependences.
We demonstrate that the algorithm provides optimal complexity for a set of
benchmark programs from the literature on probabilistic inference algorithms,
whose performance critically relies on simplifying these reductions. The
complexities for 10 of the 11 programs improve siginifcantly by factors at
least of the sizes of the input data, which are in the range of to
for typical real application inputs. We also confirm the significance of
the improvement by showing speedups in wall-clock time that range from
to over
An Output-sensitive Algorithm for Computing Projections of Resultant Polytopes
We develop an incremental algorithm to compute the Newton polytope
of the resultant, aka resultant polytope, or its
projection along a given direction.
The resultant is fundamental in algebraic elimination and
in implicitization of parametric hypersurfaces.
Our algorithm exactly computes vertex- and halfspace-representations
of the desired polytope using an oracle producing resultant vertices in a
given direction.
It is output-sensitive as it uses one oracle call per vertex.
We overcome the bottleneck of determinantal predicates
by hashing, thus accelerating execution from to times.
We implement our algorithm using the experimental CGAL package {\tt
triangulation}.
A variant of the algorithm computes successively tighter inner and outer
approximations: when these polytopes have, respectively,
90\% and 105\% of the true volume, runtime is reduced up to times.
Our method computes instances of -, - or -dimensional polytopes
with K, K or vertices, resp., within hr.
Compared to tropical geometry software, ours is faster up to
dimension or , and competitive in higher dimensions
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