Jakob J. Verbeek

THE GLOBAL K-MEANS CLUSTERING ALGORITHM

We present the global k-means algorithm which is an incremental approach to clustering that dynamically adds one cluster center at a time through a deterministic global search procedure consisting of N (with N being the size of the data set) executions of the k-means algorithm from suitable initial positions. We also propose modifications of the method to reduce the computational load without significantly affecting solution quality. The proposed clustering methods are tested on well-known data sets and they compare favorably to the k-means algorithm with random restarts.

Efficient greedy learning of Gaussian mixture models

This article concerns the greedy learning of gaussian mixtures. In the greedy approach, mixture components are inserted into the mixture one aftertheother.We propose a heuristic for searching for the optimal component to insert. In a randomized manner, a set of candidate new components is generated. For each of these candidates, we find the locally optimal new component and insert it into the existing mixture. The resulting algorithm resolves the sensitivity to initialization of state-of-the-art methods, like expectation maximization, and has running time linear in the number of data points and quadratic in the (final) number of mixture components. Due to its greedy nature, the algorithm can be particularly useful when the optimal number of mixture components is unknown. Experimental results comparing the proposed algorithm to other methods on density estimation and texture segmentation are provided.

A k-segments algorithm for finding principal curves

We propose an incremental method to find principal curves. Line segments are fitted and connected to form polygonal lines (PLs). New segments are inserted until a performance criterion is met. Experimental results illustrate the performance of the method compared to other existing approaches.

Self-organizing mixture models

We present an expectation-maximization (EM) algorithm that yields topology preserving maps of data based on probabilistic mixture models. Our approach is applicable to any mixture model for which we have a normal EM algorithm. Compared to other mixture model approaches to self-organizing maps (SOMs), the function our algorithm maximizes has a clear interpretation: it sums data log-likelihood and a penalty term that enforces self-organization. Our approach allows principled handling of missing data and learning of mixtures of SOMs. We present example applications illustrating our approach for continuous, discrete, and mixed discrete and continuous data.

Active Appearance-Based Robot Localization Using Stereo Vision

A vision-based robot localization system must be robust: able to keep track of the position of the robot at any time even if illumination conditions change and, in the extreme case of a failure, able to efficiently recover the correct position of the robot. With this objective in mind, we enhance the existing appearance-based robot localization framework in two directions by exploiting the use of a stereo camera mounted on a pan-and-tilt device. First, we move from the classical passive appearance-based localization framework to an active one where the robot sometimes executes actions with the only purpose of gaining information about its location in the environment. Along this line, we introduce an entropy-based criterion for action selection that can be efficiently evaluated in our probabilistic localization system. The execution of the actions selected using this criterion allows the robot to quickly find out its position in case it gets lost. Secondly, we introduce the use of depth maps obtained with the stereo cameras. The information provided by depth maps is less sensitive to changes of illumination than that provided by plain images. The main drawback of depth maps is that they include missing values: points for which it is not possible to reliably determine depth information. The presence of missing values makes Principal Component Analysis (the standard method used to compress images in the appearance-based framework) unfeasible. We describe a novel Expectation-Maximization algorithm to determine the principal components of a data set including missing values and we apply it to depth maps. The experiments we present show that the combination of the active localization with the use of depth maps gives an efficient and robust appearance-based robot localization system.

Coordinating Principal Component Analyzers

Mixtures of Principal Component Analyzers can be used to model high dimensional data that lie on or near a low dimensional manifold. By linearly mapping the PCA subspaces to one global low dimensional space, we obtain a global low dimensional coordinate system for the data. As shown by Roweis et al., ensuring consistent global low-dimensional coordinates for the data can be expressed as a penalized likelihood optimization problem. We show that a restricted form of the Mixtures of Probabilistic PCA model allows for a more efficient algorithm. Experimental results are provided to illustrate the viability method.

Gaussian fields for semi-supervised regression and correspondence learning

Gaussian fields (GF) have recently received considerable attention for dimension reduction and semi-supervised classification. In this paper we show how the GF framework can be used for semi-supervised regression on high-dimensional data. We propose an active learning strategy based on entropy minimization and a maximum likelihood model selection method. Furthermore, we show how a recent generalization of the LLE algorithm for correspondence learning can be cast into the GF framework, which obviates the need to choose a representation dimensionality.

A Soft k-Segments Algorithm for Principal Curves

We propose a new method to find principal curves for data sets. The method repeats three steps until a stopping criterion is met. In the first step, k (unconnected) line segments are fitted on the data. The second step connects the segments to form a polygonal line, and evaluates the quality of the resulting polygonal line. The third step inserts a new line segment.We compare the performance of our new method with other existing methods to find principal curves.

Enhancing appearance-based robot localization using sparse disparity maps

In this paper, we enhance appearance-based robot localization by using disparity maps. Disparity maps provide the same type of information as range based sensors (distance to objects) and thus, they are likely to be less sensitive to changes of illumination than plain images, that are the source of information generally used in appearance-based localization. The main drawback of disparity maps is that they can include very noisy depth values: points for which the algorithms can not determine reliable depth information. These noisy values have to be discarded resulting in missing values. The presence of missing values makes principal component analysis (the standard method used to compress images in the appearance-based framework) unfeasible. We describe a novel expectation-maximization algorithm to determine the principal components of a data set including missing values and we apply it to disparity maps. The results we present show that disparity maps are a valid alternative to increase the robustness of appearance-based localization.