Grażyna Szkatuła

An approach to dimensionality reduction in time series

Many methods of dimensionality reduction of data series (time series) have been introduced over the past decades. Some of them rely on a symbolic representation of the original data, however in this case the obtained dimensionality reduction is not substantial. In this paper, we introduce a new approach referred to as Symbolic Essential Attributes Approximation (SEAA) to reduce the dimensionality of multidimensional time series. In such a way we form a new nominal representation of the original data series. The approach is based on the concept of data series envelopes and essential attributes generated by a multilayer neural network. The real-valued attributes are discretized, and in this way symbolic data series representation is formed. The SEAA generates a vector of nominal values of new attributes which form the compressed representation of original data series. The nominal attributes are synthetic, and while not being directly interpretable, they still retain important features of the original data series. A validation of usefulness of the proposed dimensionality reduction is carried out for classification and clustering tasks. The experiments have shown that even for a significant reduction of dimensionality, the new representation retains information about the data series sufficient for classification and clustering of the time series.

An integer programming approach to inductive learning using genetic and greedy algorithms

In this paper we propose an inductive learning method, IP2, to derive classification rules that correctly describe most of the examples belonging to a class and do not describe most of the examples not belonging to this class. A pre-analysis of data is included that assigns higher weights to those values of attributes which occur more often in the positive than in the negative examples. The inductive learning problem is represented as a modification of the set covering problem which are solved by an integer programming based algorithm using elements of a greedy algorithm or a genetic algorithm. The results are very encouraging and are illustrated on thyroid cancer and coronary heard disease problems.

A softened formulation of inductive learning and its use for coronary disease data

We present an improved inductive learning method to derive classification rules that correctly describe most of the examples belonging to a class and do not describe most of the examples not belonging to this class. The problem is represented as a modification of the set covering problems solved by a genetic algorithm. Its is employed to medical data on coronary disease, and the results seem to be encouraging.

On Perturbation Measure of Sets : Properties

In this paper we describe a new measure of remoteness between sets described by nominal values. The introduced measures of perturbation of one set by another are considered instead of commonly used distance between two sets. The operations of the set theory are operated and the considered measures describe changes of the perturbed second set by adding the first one or vice versa. The values of the measure of sets’ perturbation are range between 0 and 1, and in general, are not symmetric – it means that the perturbation of one set by another is not the same as the perturbation of the second set by the first one.

On Perturbation Measure of Clusters: Application

In this paper we developed a new methodology for grouping objects described by nominal attributes. We introduced a measure of perturbation of one cluster by another cluster in order to create a junction of clusters. The developed method is hierarchical and agglomerative and can be characterized both by high speed of computation as well as surprising good accuracy of clustering. keywords cluster analysis, nominal attributes, sets theory.

Forecasting voting behaviour using machine learning – Poland in transition

The aim of the paper is to apply some inductive learning method from examples (which gives explicit decision rules of “if-then” type) to forecast the voting behaviour of individual members of the Polish Parliament. Results obtained are both interesting and promising.

A clustering algorithm based on distinguishability for nominal attributes

In this paper we developed a new methodology for grouping objects described by nominal attributes. We introduced a definition of conditions domination within each pair of cluster, and next the measure of ω-distinguishability of clusters for creating a junction of clusters. The developed method is hierarchical and agglomerative one and can be characterized both by high speed of computation as well as extremely good accuracy of clustering.

Nominal time series representation for the clustering problem

In this paper we considered time series dimension reduction for clustering problem. The techniques of reduction of dimension of time series is based on the concept of envelopes, aggregation of the envelopes and extracting essential attributes. Essential attributes were nominalized. The reduced representation of time series is characterized by nominal attributes. For such representation of time series we applied a definition of conditions domination within each pair of clusters. We proposed a hierarchical agglomerative approach to clustering nominal data. There is considered a case of data series clustering problem as an illustrative example.

An inductive learning algorithm with a partial completeness and consistence via a modified set covering problem

We present an inductive learning algorithm that allows for a partial completeness and consistence, i.e. that derives classification rules correctly describing, e.g, most of the examples belonging to a class and not describing most of the examples not belonging to this class. The problem is represented as a modification of the set covering problem that is solved by a greedy algorithm. The approach is illustrated on some medical data.

On Bilateral Matching between Multisets

In the paper we defined a new measure of remoteness between multisets. The development of the measure is based on the definition of sets perturbation originally developed by the authors. The sets perturbation definition is here extended to multisets perturbation, it means perturbation of one multiset by another multiset and/or vice-versa. In general these two measures are different, it means asymmetrical, and therefore can be called the bilateral measure of matching between two multisets. Therefore the measure cannot be considered as a distance between multisets.