23 research outputs found
Recommended from our members
Sparse kernel density estimation technique based on zero-norm constraint
A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance
Reducing Spatial Data Complexity for Classification Models
Intelligent data analytics gradually becomes a day-to-day reality of today's businesses. However, despite rapidly
increasing storage and computational power current state-of-the-art predictive models still can not handle massive and noisy
corporate data warehouses. What is more adaptive and real-time operational environment requires multiple models to be
frequently retrained which fiirther hinders their use. Various data reduction techniques ranging from data sampling up to
density retention models attempt to address this challenge by capturing a summarised data structure, yet they either do
not account for labelled data or degrade the classification performance of the model trained on the condensed dataset. Our
response is a proposition of a new general framework for reducing the complexity of labelled data by means of controlled
spatial redistribution of class densities in the input space. On the example of Parzen Labelled Data Compressor (PLDC) we
demonstrate a simulatory data condensation process directly inspired by the electrostatic field interaction where the data are
moved and merged following the attracting and repelling interactions with the other labelled data. The process is controlled
by the class density function built on the original data that acts as a class-sensitive potential field ensuring preservation of
the original class density distributions, yet allowing data to rearrange and merge joining together their soft class partitions.
As a result we achieved a model that reduces the labelled datasets much further than any competitive approaches yet with
the maximum retention of the original class densities and hence the classification performance. PLDC leaves the reduced
dataset with the soft accumulative class weights allowing for efficient online updates and as shown in a series of experiments
if coupled with Parzen Density Classifier (PDC) significantly outperforms competitive data condensation methods in terms of
classification performance at the comparable compression levels
Recommended from our members
Sparse density estimator with tunable kernels
A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators
A variable metric forward--backward method with extrapolation
Forward-backward methods are a very useful tool for the minimization of a
functional given by the sum of a differentiable term and a nondifferentiable
one and their investigation has experienced several efforts from many
researchers in the last decade. In this paper we focus on the convex case and,
inspired by recent approaches for accelerating first-order iterative schemes,
we develop a scaled inertial forward-backward algorithm which is based on a
metric changing at each iteration and on a suitable extrapolation step. Unlike
standard forward-backward methods with extrapolation, our scheme is able to
handle functions whose domain is not the entire space. Both {an convergence rate estimate on the objective function values and the
convergence of the sequence of the iterates} are proved. Numerical experiments
on several {test problems arising from image processing, compressed sensing and
statistical inference} show the {effectiveness} of the proposed method in
comparison to well performing {state-of-the-art} algorithms
Recommended from our members
Probability density estimation with tunable kernels using orthogonal forward regression
A generalized or tunable-kernel model is proposed for probability density function estimation based on an orthogonal forward regression procedure. Each stage of the density estimation process determines a tunable kernel, namely, its center vector and diagonal covariance matrix, by minimizing a leave-one-out test criterion. The kernel mixing weights of the constructed sparse density estimate are finally updated using the multiplicative nonnegative quadratic programming algorithm to ensure the nonnegative and unity constraints, and this weight-updating process additionally has the desired ability to further reduce the model size. The proposed tunable-kernel model has advantages, in terms of model generalization capability and model sparsity, over the standard fixed-kernel model that restricts kernel centers to the training data points and employs a single common kernel variance for every kernel. On the other hand, it does not optimize all the model parameters together and thus avoids the problems of high-dimensional ill-conditioned nonlinear optimization associated with the conventional finite mixture model. Several examples are included to demonstrate the ability of the proposed novel tunable-kernel model to effectively construct a very compact density estimate accurately
Multiple Resolution Nonparametric Classifiers
Bayesian discriminant functions provide optimal classification decision boundaries in the sense of minimizing the average error rate. An operational assumption is that the probability density functions for the individual classes are either known a priori or can be estimated from the data through the use of estimating techniques. The use of Parzen- windows is a popular and theoretically sound choice for such estimation. However, while the minimal average error rate can be achieved when combining Bayes Rule with Parzen-window density estimation, the latter is computationally costly to the point where it may lead to unacceptable run-time performance. We present the Multiple Resolution Nonparametric (MRN) classifier as a new approach for significantly reducing the computational cost of using Parzen-window density estimates without sacrificing the virtues of Bayesian discriminant functions. Performance is evaluated against a standard Parzen-window classifier on several common datasets