Łukasz Struski

Semi-supervised model-based clustering with controlled clusters leakage

In this paper, we focus on finding clusters in partially categorized data sets. We propose a semi-supervised version of Gaussian mixture model, called C3L, which retrieves natural subgroups of given categories. In contrast to other semi-supervised models, C3L is parametrized by user-defined leakage level, which controls maximal inconsistency between initial categorization and resulting clustering. Our method can be implemented as a module in practical expert systems to detect clusters, which combine expert knowledge with true distribution of data. Moreover, it can be used for improving the results of less flexible clustering techniques, such as projection pursuit clustering. The paper presents extensive theoretical analysis of the model and fast algorithm for its efficient optimization. Experimental results show that C3L finds high quality clustering model, which can be applied in discovering meaningful groups in partially classified data.

Fast independent component analysis algorithm with a simple closed-form solution

Abstract In this paper we present WeICA, a fast ICA algorithm, which in its structure is similar to PCA and has the following features: • if there exists a coordinate system in which data is independent, then WeICA restores it, • the algorithm is affine invariant, • WeICA has a very simple and easy to implement closed-form solution, • the method allows for a dimensionality reduction, • the method can be updated on-line. WeICA substantially outperforms other state-of-the-art ICA methods with respect to time complexity, gives very good results in the case of dimension reduction and obtains satisfying restoring level.

Regression SVM for incomplete data

The use of machine learning methods in the case of incomplete data is an important task in many scientific fields, like medicine, biology, or face recognition. Typically, missing values are substituted with artificial values that are estimated from the known samples, and the classical machine learning algorithms are applied. Although this methodology is very common, it produces less informative data, because artificially generated values are treated in the same way as the known ones. In this paper, we consider a probabilistic representation of missing data, where each vector is identified with a Gaussian probability density function, modeling the uncertainty of absent attributes. This representation allows to construct an analogue of RBF kernel for incomplete data. We show that such a kernel can be successfully used in regression SVM. Experimental results confirm that our approach capture relevant information that is not captured by traditional imputation methods.