Hassan A. Kingravi

A methodological approach to the classification of dermoscopy images

In this paper a methodological approach to the classification of pigmented skin lesions in dermoscopy images is presented. First, automatic border detection is performed to separate the lesion from the background skin. Shape features are then extracted from this border. For the extraction of color and texture related features, the image is divided into various clinically significant regions using the Euclidean distance transform. This feature data is fed into an optimization framework, which ranks the features using various feature selection algorithms and determines the optimal feature subset size according to the area under the ROC curve measure obtained from support vector machine classification. The issue of class imbalance is addressed using various sampling strategies, and the classifier generalization error is estimated using Monte Carlo cross validation. Experiments on a set of 564 images yielded a specificity of 92.34% and a sensitivity of 93.33%.

A comparative study of efficient initialization methods for the k-means clustering algorithm

K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. In this paper, we first present an overview of these methods with an emphasis on their computational efficiency. We then compare eight commonly used linear time complexity initialization methods on a large and diverse collection of data sets using various performance criteria. Finally, we analyze the experimental results using non-parametric statistical tests and provide recommendations for practitioners. We demonstrate that popular initialization methods often perform poorly and that there are in fact strong alternatives to these methods.

Nonlinear vector filtering for impulsive noise removal from color images

A comprehensive survey of 48 filters for impulsive noise removal from color images is presented. The filters are formulated using a uniform notation and categorized into 8 families. The performance of these filters is compared on a large set of images that cover a variety of domains using three effectiveness and one efficiency criteria. In order to ensure a fair efficiency comparison, a fast and accurate approximation for the inverse cosine function is introduced. In addition, commonly used distance measures (Minkowski, angular, and directional-distance) are analyzed and evaluated. Finally, suggestions are provided on how to choose a filter given certain requirements.

Deterministic Initialization of the K-Means Algorithm Using Hierarchical Clustering

K-means is undoubtedly the most widely used partitional clustering algorithm. Unfortunately, due to its gradient descent nature, this algorithm is highly sensitive to the initial placement of the cluster centers. Numerous initialization methods have been proposed to address this problem. Many of these methods, however, have superlinear complexity in the number of data points, making them impractical for large data sets. On the other hand, linear methods are often random and/or order-sensitive, which renders their results unrepeatable. Recently, Su and Dy proposed two highly successful hierarchical initialization methods named Var-Part and PCA-Part that are not only linear, but also deterministic (nonrandom) and order-invariant. In this paper, we propose a discriminant analysis based approach that addresses a common deficiency of these two methods. Experiments on a large and diverse collection of data sets from the UCI machine learning repository demonstrate that Var-Part and PCA-Part are highly competitive with one of the best random initialization methods to date, i.e. k-means++, and that the proposed approach significantly improves the performance of both hierarchical methods.

Reproducing Kernel Hilbert Space Approach for the Online Update of Radial Bases in Neuro-Adaptive Control

Classical gradient based adaptive laws in model reference adaptive control for uncertain nonlinear dynamical systems with a Radial Basis Function (RBF) neural networks adaptive element do not guarantee that the network weights stay bounded in a compact neighborhood of the ideal weights without Persistently Exciting (PE) system signals or a-priori known bounds on ideal weights. Recent work has shown, however, that an adaptive controller using specifically recorded data concurrently with instantaneous data can guarantee such boundedness without requiring PE signals. However, in this work, the assumption has been that the RBF network centers are fixed, which requires some domain knowledge of the uncertainty. We employ a Reproducing Kernel Hilbert Space theory motivated online algorithm for updating the RBF centers to remove this assumption. Along with showing the boundedness of the resulting neuro-adaptive controller, a connection is also made between PE signals and kernel methods. Simulation results show improved performance.

Bayesian Nonparametric Adaptive Control Using Gaussian Processes

Most current model reference adaptive control (MRAC) methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are fixed a priori, often through expert judgment. An example of such an adaptive element is radial basis function networks (RBFNs), with RBF centers preallocated based on the expected operating domain. If the system operates outside of the expected operating domain, this adaptive element can become noneffective in capturing and canceling the uncertainty, thus rendering the adaptive controller only semiglobal in nature. This paper investigates a Gaussian process-based Bayesian MRAC architecture (GP-MRAC), which leverages the power and flexibility of GP Bayesian nonparametric models of uncertainty. The GP-MRAC does not require the centers to be preallocated, can inherently handle measurement noise, and enables MRAC to handle a broader set of uncertainties, including those that are defined as distributions over functions. We use stochastic stability arguments to show that GP-MRAC guarantees good closed-loop performance with no prior domain knowledge of the uncertainty. Online implementable GP inference methods are compared in numerical simulations against RBFN-MRAC with preallocated centers and are shown to provide better tracking and improved long-term learning.

Fast colour space transformations using minimax approximations

Colour space transformations are frequently used in image processing, graphics and visualisation applications. In many cases, these transformations are complex non-linear functions, which prohibit their use in time-critical applications. A new approach called minimax approximations for colour space transformations (MACT) is presented. The authors demonstrate MACT on three commonly used colour space transformations. Extensive experiments on a large and diverse image set and comparisons with well-known multidimensional look-up table interpolation methods show that MACT achieves an excellent balance among four criteria: ease of implementation, memory usage, accuracy and computational speed.

Model Reference Adaptive Control using Nonparametric Adaptive Elements

Most current model reference adaptive control methods rely on parametric adaptive elements, in which the number of parameters of the adaptive element are xed a-priori, often through expert judgment. Examples of such adaptive elements are the commonly used Radial Basis Function Neural Networks (RBF-NN) with centers allocated a priori based on the expected operating domain. If the system operates outside of the expected operating domain, such adaptive elements can become non-eective, thus rendering the adaptive controller only semi-global in nature. This paper investigates two classes of nonparametric adaptive elements, that is, adaptive elements whose number of parameters grow in response to data. This includes RBF adaptive elements with centers that are allocated dynamically as the system evolves using a Kernel linear independence test, and Gaussian Processes based adaptive elements which generalize the notion of Gaussian Distribution to function approximation. We show that these nonparametric adaptive elements result in good closed loop performance without requiring any prior knowledge about the domain of the uncertainty. These results indicate that the use of such nonparametric adaptive elements can improve the global stability properties adaptive controllers.

On Euclidean norm approximations

Euclidean norm calculations arise frequently in scientific and engineering applications. Several approximations for this norm with differing complexity and accuracy have been proposed in the literature. Earlier approaches [1-3] were based on minimizing the maximum error. Recently, Seol and Cheun [4] proposed an approximation based on minimizing the average error. In this paper, we first examine these approximations in detail, show that they fit into a single mathematical formulation, and compare their average and maximum errors. We then show that the maximum errors given by Seol and Cheun are significantly optimistic.

Bayesian nonparametric adaptive control of time-varying systems using Gaussian processes

Real-world dynamical variations make adaptive control of time-varying systems highly relevant. However, most adaptive control literature focuses on analyzing systems where the uncertainty is represented as a weighted linear combination of fixed number of basis functions, with constant weights. One approach to modeling time variations is to assume time varying ideal weights, and use difference integration to accommodate weight variation. However, this approach reactively suppresses the uncertainty, and has little ability to predict system behavior locally. We present an alternate formulation by leveraging Bayesian nonparametric Gaussian Process adaptive elements. We show that almost surely bounded adaptive controllers for a class of nonlinear time varying system can be formulated by incorporating time as an additional input to the Gaussian kernel. Analysis and simulations show that the learning-enabled local predictive ability of our adaptive controllers significantly improves performance.