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RESEARCH PROJECTS
A Preconditioned Hybrid SVD Method for Large-Scale problems
The
computation of a few singular triplets of large,
sparse matrices is a challenging task, especially
when the smallest magnitude singular values are
needed in high accuracy. Most recent efforts try to
address this problem through variations of the
Lanczos bidiagonalization method, but they are still
challenged even for medium matrix sizes due to the
difficulty of the problem. We
propose a novel SVD approach that can take advantage
of preconditioning and of any well designed
eigensolver to compute both largest and smallest
singular triplets. Accuracy and efficiency is
achieved through a hybrid, two-stage meta-method,
PHSVDS. In the first stage, PHSVDS solves the normal
equations up to the best achievable accuracy. If
further accuracy is required, the method switches
automatically to an eigenvalue problem with the
augmented matrix. Thus it combines the advantages of
the two stages, faster convergence and accuracy,
respectively. For the augmented matrix, solving the
interior eigenvalue is facilitated by a proper use
of the good initial guesses from the first stage and
an efficient implementation of the refined
projection method. We also discuss how to
precondition PHSVDS and to cope with some issues
that arise. Numerical experiments illustrate the
efficiency and robustness of the method.
Papers: SIAM
SISC (Flagship Journal in Scientific Computing,
5-Year Impact Factor: 2.40), SC15
Poster, SC15
Doctoral Showcase
Software: PRIMME_SVDS
(GitHub) (Providing C, Python, Matlab and Fortran
interfaces)
- Fast Trace Estimator for Large Sparse Matrix Inverse
Determining
the trace of a matrix that is implicitly
available through a function is a
computationally challenging task that arises in
a number of applications. For the common
function of the inverse of a large, sparse
matrix, the standard approach is based on a
Monte Carlo method which converges slowly.
We
present a different approach by exploiting the
pattern correlation between the diagonal of the
inverse of the matrix and the diagonal of some
approximate inverse that can be computed
inexpensively. We leverage various sampling and
fitting techniques to fit the diagonal of the
approximation to the diagonal of the inverse.
Based on a dynamic evaluation of the variance,
the proposed method can be used as a variance
reduction method for Monte Carlo in some cases.
Furthermore, the presented method may serve as a
standalone kernel for providing a fast trace
estimate with a small number of samples. An
extensive set of experiments with various
technique combinations demonstrates the
effectiveness of our method in some real
applications.
Papers:
JCOMP
(5-Year Impact Factor: 3.120), second-round
review
- Real Time Blob-Filaments Detection and Tracking in Fusion Plamsa Big Data
Magnetic
fusion could provide an inexhaustible, clean, and safe solution to the
global energy needs. The success of magnetically-confined fusion
reactors demands steady-state plasma confinement which is challenged by
the blob-filaments driven by the edge turbulence. Real-time analysis
can be used to monitor the progress of fusion experiments and prevent
catastrophic events. However, terabytes of data are generated over
short time periods in fusion experiments. Timely access to and
analyzing this amount of data demands properly responding to extreme
scale computing and big data challenges.
In this paper, we apply outlier detection techniques to
effectively tackle the fusion blob detection problem on
extremely large parallel machines. We present a
real-time region outlier detection algorithm to
efficiently find blobs in fusion experiments and
simulations. In addition, we propose an efficient scheme
to track the movement of region outliers over time. We
have implemented our algorithms with hybrid MPI/OpenMP
and demonstrated the accuracy and efficiency of the
proposed blob detection and tracking methods with a set
of data from the XGC1 fusion simulation code. Our tests
illustrate that we can achieve linear time speedup and
complete blob detection in two or three milliseconds
using Edison, a Cray XC30 system at NERSC.
Papers: IEEE
Transaction
on Big Data (TBD), second-round review. BDAC-14,
SC14
Poster
Software: Big data analytics component in ICEE
HPC demo: SC14
- Scale Up Large-Scale Kernel Machine Using Random Features for Speech Recognition
Recent evidences suggest that the performance of kernel
methods may match that of deep neural networks (DNNs),
which have been the state-of-the-art approach for speech
recognition.
In this work, we present an improvement of the kernel
ridge regression, and show that our proposal is
computationally advantageous. Our approach performs
classifications by using the one-vs-one scheme, which,
under certain assumptions, reduces the costs of the
one-vs-rest scheme by asymptotically a factor of c in
training time and c in memory consumption. Here, c is
the number of classes and it is typically on the order
of hundreds and thousands for speech recognition. We
demonstrate empirical results on the benchmark corpus
TIMIT. In particular, the classification accuracy is one
to two percentages higher (in the absolute term) than
the best of the kernel methods and of the DNNs, and the
speech recognition accuracy is highly comparable.
Papers: ICASSP
2016, KDD16
(in submission)
Software: coming soon.
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