277,392 research outputs found
Cross-Entropy Clustering
We construct a cross-entropy clustering (CEC) theory which finds the optimal
number of clusters by automatically removing groups which carry no information.
Moreover, our theory gives simple and efficient criterion to verify cluster
validity.
Although CEC can be build on an arbitrary family of densities, in the most
important case of Gaussian CEC:
{\em -- the division into clusters is affine invariant;
-- the clustering will have the tendency to divide the data into
ellipsoid-type shapes;
-- the approach is computationally efficient as we can apply Hartigan
approach.}
We study also with particular attention clustering based on the Spherical
Gaussian densities and that of Gaussian densities with covariance s \I. In
the letter case we show that with converging to zero we obtain the
classical k-means clustering
Combinatorial Information Theory: I. Philosophical Basis of Cross-Entropy and Entropy
This study critically analyses the information-theoretic, axiomatic and
combinatorial philosophical bases of the entropy and cross-entropy concepts.
The combinatorial basis is shown to be the most fundamental (most primitive) of
these three bases, since it gives (i) a derivation for the Kullback-Leibler
cross-entropy and Shannon entropy functions, as simplified forms of the
multinomial distribution subject to the Stirling approximation; (ii) an
explanation for the need to maximize entropy (or minimize cross-entropy) to
find the most probable realization; and (iii) new, generalized definitions of
entropy and cross-entropy - supersets of the Boltzmann principle - applicable
to non-multinomial systems. The combinatorial basis is therefore of much
broader scope, with far greater power of application, than the
information-theoretic and axiomatic bases. The generalized definitions underpin
a new discipline of ``{\it combinatorial information theory}'', for the
analysis of probabilistic systems of any type.
Jaynes' generic formulation of statistical mechanics for multinomial systems
is re-examined in light of the combinatorial approach. (abbreviated abstract)Comment: 45 pp; 1 figure; REVTex; updated version 5 (incremental changes
Parallel Cross-Entropy Optimization
The cross-entropy (CE) method is a modern and effective optimization method well suited to parallel implementations. There is a vast array of problems today, some of which are highly complex and can take weeks or even longer to solve using current optimization techniques. This paper presents a general method for designing parallel CE algorithms for multiple instruction multiple data (MIVID) distributed memory machines using the message passing interface (MPI) library routines. We provide examples of its performance for two well-known test-cases: the (discrete) Max-Cut problem and (continuous) Rosenbrock problem. Speedup factors and a comparison to sequential CE methods are reported
Max-Pooling Loss Training of Long Short-Term Memory Networks for Small-Footprint Keyword Spotting
We propose a max-pooling based loss function for training Long Short-Term
Memory (LSTM) networks for small-footprint keyword spotting (KWS), with low
CPU, memory, and latency requirements. The max-pooling loss training can be
further guided by initializing with a cross-entropy loss trained network. A
posterior smoothing based evaluation approach is employed to measure keyword
spotting performance. Our experimental results show that LSTM models trained
using cross-entropy loss or max-pooling loss outperform a cross-entropy loss
trained baseline feed-forward Deep Neural Network (DNN). In addition,
max-pooling loss trained LSTM with randomly initialized network performs better
compared to cross-entropy loss trained LSTM. Finally, the max-pooling loss
trained LSTM initialized with a cross-entropy pre-trained network shows the
best performance, which yields relative reduction compared to baseline
feed-forward DNN in Area Under the Curve (AUC) measure
Asymptotic optimality of the cross-entropy method for Markov chain problems
The correspondence between the cross-entropy method and the zero-variance
approximation to simulate a rare event problem in Markov chains is shown. This
leads to a sufficient condition that the cross-entropy estimator is
asymptotically optimal.Comment: 13 pager; 3 figure
Optimal staffing under an annualized hours regime using Cross-Entropy optimization
This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis
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