15,951 research outputs found
Differential Performance Debugging with Discriminant Regression Trees
Differential performance debugging is a technique to find performance
problems. It applies in situations where the performance of a program is
(unexpectedly) different for different classes of inputs. The task is to
explain the differences in asymptotic performance among various input classes
in terms of program internals. We propose a data-driven technique based on
discriminant regression tree (DRT) learning problem where the goal is to
discriminate among different classes of inputs. We propose a new algorithm for
DRT learning that first clusters the data into functional clusters, capturing
different asymptotic performance classes, and then invokes off-the-shelf
decision tree learning algorithms to explain these clusters. We focus on linear
functional clusters and adapt classical clustering algorithms (K-means and
spectral) to produce them. For the K-means algorithm, we generalize the notion
of the cluster centroid from a point to a linear function. We adapt spectral
clustering by defining a novel kernel function to capture the notion of linear
similarity between two data points. We evaluate our approach on benchmarks
consisting of Java programs where we are interested in debugging performance.
We show that our algorithm significantly outperforms other well-known
regression tree learning algorithms in terms of running time and accuracy of
classification.Comment: To Appear in AAAI 201
Kernel discriminant analysis and clustering with parsimonious Gaussian process models
This work presents a family of parsimonious Gaussian process models which
allow to build, from a finite sample, a model-based classifier in an infinite
dimensional space. The proposed parsimonious models are obtained by
constraining the eigen-decomposition of the Gaussian processes modeling each
class. This allows in particular to use non-linear mapping functions which
project the observations into infinite dimensional spaces. It is also
demonstrated that the building of the classifier can be directly done from the
observation space through a kernel function. The proposed classification method
is thus able to classify data of various types such as categorical data,
functional data or networks. Furthermore, it is possible to classify mixed data
by combining different kernels. The methodology is as well extended to the
unsupervised classification case. Experimental results on various data sets
demonstrate the effectiveness of the proposed method
Classification methods for Hilbert data based on surrogate density
An unsupervised and a supervised classification approaches for Hilbert random
curves are studied. Both rest on the use of a surrogate of the probability
density which is defined, in a distribution-free mixture context, from an
asymptotic factorization of the small-ball probability. That surrogate density
is estimated by a kernel approach from the principal components of the data.
The focus is on the illustration of the classification algorithms and the
computational implications, with particular attention to the tuning of the
parameters involved. Some asymptotic results are sketched. Applications on
simulated and real datasets show how the proposed methods work.Comment: 33 pages, 11 figures, 6 table
Adaptive Graph via Multiple Kernel Learning for Nonnegative Matrix Factorization
Nonnegative Matrix Factorization (NMF) has been continuously evolving in
several areas like pattern recognition and information retrieval methods. It
factorizes a matrix into a product of 2 low-rank non-negative matrices that
will define parts-based, and linear representation of nonnegative data.
Recently, Graph regularized NMF (GrNMF) is proposed to find a compact
representation,which uncovers the hidden semantics and simultaneously respects
the intrinsic geometric structure. In GNMF, an affinity graph is constructed
from the original data space to encode the geometrical information. In this
paper, we propose a novel idea which engages a Multiple Kernel Learning
approach into refining the graph structure that reflects the factorization of
the matrix and the new data space. The GrNMF is improved by utilizing the graph
refined by the kernel learning, and then a novel kernel learning method is
introduced under the GrNMF framework. Our approach shows encouraging results of
the proposed algorithm in comparison to the state-of-the-art clustering
algorithms like NMF, GrNMF, SVD etc.Comment: This paper has been withdrawn by the author due to the terrible
writin
A Simple Iterative Algorithm for Parsimonious Binary Kernel Fisher Discrimination
By applying recent results in optimization theory variously known as optimization transfer or majorize/minimize algorithms, an algorithm for binary, kernel, Fisher discriminant analysis is introduced that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The problem is converted into a smooth optimization that can be solved iteratively with no greater overhead than iteratively re-weighted least-squares. The result is simple, easily programmed and is shown to perform, in terms of both accuracy and parsimony, as well as or better than a number of leading machine learning algorithms on two well-studied and substantial benchmarks
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