@ARTICLE{Grochowski12,
author = {Marek Grochowski},
title = {Simple Incremental Instance Selection Wrapper for Classification},
journal = {Lecture Notes in Computer Science},
booktitle = {ICAISC (2)},
editor = {Leszek Rutkowski and Ryszard Tadeusiewicz and Lotfi A. Zadeh and Jacek M. \.{Z}urada},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
year = {2012},
pages = {64-72},
volume = {7268},
ee = {http://dx.doi.org/10.1007/978-3-642-29350-4_8},
file = {http://www.fizyka.umk.pl/~grochu/data/articles/12-ICAISC-IISW.pdf},
abstract = {Instance selection methods are very useful data mining tools for dealing with large data sets. There exist many instance selection algorithms capable for significant reduction of training data size for particular classifier without generalization degradation. In opposition to those methods, this paper focuses on general pruning methods which can be successfully applied for arbitrary classification method. Simple but efficient wrapper method based on generalization of Hart's Condensed Nearest Neighbors rule is presented and impact of this method on classification quality is reported.}
}
@INBOOK{DuchMG11,
author = {Wlodzislaw Duch and Tomasz Maszczyk and Marek Grochowski},
pages = {317--358},
title = {Optimal Support Features for Meta-Learning},
publisher = {Springer},
year = {2011},
editor = {Norbrt Jankowski and W\l{}odzis\l{}aw Duch and Krzysztof Gr\k{a}bczewski},
volume = {358},
series = {Studies in Computational Intelligence},
booktitle = {Meta-learning in Computational Intelligence},
file = { http://www.fizyka.umk.pl/publications/kmk/11-Features-Meta.pdf},
abstract = {Meta-learning has many aspects, but its final goal is to discover in an automatic way many interesting models for a given data. Our early attempts in this area involved heterogeneous learning systems combined with a complexity-guided search for optimal models, performed within the framework of (dis)similarity based methods to discover ``knowledge granules''. This approach, inspired by neurocognitive mechanisms of information processing in the brain, is generalized here to learning based on parallel chains of transformations that extract useful information granules and use it as additional features. Various types of transformations that generate hidden features are analyzed and methods to generate them are discussed. They include restricted random projections, optimization of these features using projection pursuit methods, similarity-based and general kernel-based features, conditionally defined features, features derived from partial successes of various learning algorithms, and using the whole learning models as new features. In the enhanced feature space the goal of learning is to create image of the input data that can be directly handled by relatively simple decision processes. The focus is on hierarchical methods for generation of information, starting from new support features that are discovered by different types of data models created on similar tasks and successively building more complex features on the enhanced feature spaces. Resulting algorithms facilitate deep learning, and also enable understanding of structures present in the data by visualization of the results of data transformations and by creating logical, fuzzy and prototype-based rules based on new features. Relations to various machine-learning approaches, comparison of results, and neurocognitive inspirations for meta-learning are discussed. }
}
@ARTICLE{GrochowskiD09,
author = {Marek Grochowski and W\l{}odzis\l{}aw Duch},
title = {Constrained Learning Vector Quantization or Relaxed k-Separability},
journal = {Lecture Notes in Computer Science},
year = {2009},
volume = {5768},
pages = {151--160},
bibdate = {2009-09-21},
bibsource = {DBLP, http://dblp.uni-trier.de/db/conf/icann/icann2009-1.html#GrochowskiD09},
booktitle = {ICANN (1)},
editor = {Cesare Alippi and Marios M. Polycarpou and Christos Panayiotou and
Georgios Ellinas},
isbn = {978-3-642-04273-7},
owner = {marek},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
timestamp = {2011.10.18},
url = {http://dx.doi.org/10.1007/978-3-642-04274-4},
file = { http://www.fizyka.umk.pl/publications/kmk/09-LVQ-QPC.pdf},
abstract = {Neural networks and other sophisticated machine learning algorithms frequently miss simple solutions that can be discovered by a more constrained learning methods. Transition from a single neuron solving linearly separable problems, to multithreshold neuron solving k-separable problems, to neurons implementing prototypes solving q-separable problems, is investigated. Using Learning Vector Quantization (LVQ) approach this transition is presented as going from two prototypes defining a single hyperplane, to many co-linear prototypes defining parallel hyperplanes, to unconstrained prototypes defining Voronoi tessellation. For most datasets relaxing the co-linearity condition improves accuracy increasing complexity of the model, but for data with inherent logical structure LVQ algorithms with constraints significantly outperforms original LVQ and many other algorithms. }
}
@ARTICLE{GrochowskiD11,
author = {Marek Grochowski and W\l{}odzis\l{}aw Duch},
title = {Fast Projection Pursuit Based on Quality of Projected Clusters},
journal = {Lecture Notes in Computer Science},
year = {2011},
volume = {6594},
pages = {89-97},
booktitle = {ICANNGA (2)},
editor = {Andrej Dobnikar and Uros Lotric and Branko Ster},
publisher = {Springer},
file = {http://www.fizyka.umk.pl/publications/kmk/11-FastQPC.pdf},
abstract = {Projection pursuit index measuring quality of projected clusters (QPC) introduced recently optimizes projection directions by minimizing leave-one-out error searching for pure localized clusters. QPC index has been used in constructive neural networks to discover non-local clusters in high-dimensional multi-class data, reduce dimensionality, aggregate features, visualize and classify data. However, for n training instances such optimization requires O(n^2) calculations. Fast approximate version of QPC introduced here obtains results of similar quality with O(n) effort, as illustrated in a number of classification and data visualization problems. }
}
@INBOOK{GrochowskiD09a,
author = {Marek Grochowski and W\l{}odzis\l{}aw Duch},
pages = {49-70},
title = {Constructive Neural Network Algorithms that Solve Highly Non-Separable
Problems},
publisher = {Springer},
year = {2009},
editor = {Franco, Leonardo and David A. Elizondo and Jos{\'e} M. Jerez},
volume = {258},
series = {Studies in Computational Intelligence},
booktitle = {Constructive Neural Networks},
owner = {marek},
timestamp = {2011.10.18},
file = {http://www.phys.uni.torun.pl/publications/kmk/08-constr-book.pdf},
abstract = {Learning from data with complex non-local relations and multimodal class distribution is still very hard for standard classification algorithms. Even if an accurate solution is found the resulting model may be too complex for a given data and will not generalize well. New types of learning algorithms are needed to extend capabilities of machine learning systems to handle such data. Projection pursuit methods can avoid "curse of dimensionality" by discovering interesting structures in low-dimensional subspace. This paper introduces constructive neural architectures based on projection pursuit techniques that are able to discover simplest models of data with inherent highly complex logical structures. The key principle is to look for transformations that discover interesting structures, going beyond error functions and separability.}
}
@ARTICLE{GrochowskiD08a,
author = {Marek Grochowski and W\l{}odzis\l{}aw Duch},
title = {Projection Pursuit Constructive Neural Networks Based on Quality
of Projected Clusters},
journal = {Lecture Notes in Computer Science},
year = {2008},
volume = {5164},
pages = {754--762},
bibdate = {2008-09-01},
bibsource = {DBLP, http://dblp.uni-trier.de/db/conf/icann/icann2008-2.html#GrochowskiD08},
booktitle = {ICANN (2)},
editor = {Vera Kurkov{\'a} and Roman Neruda and Jan Koutn{\'i}k},
isbn = {978-3-540-87558-1},
owner = {marek},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
timestamp = {2011.10.18},
file = {http://www.fizyka.umk.pl/publications/kmk/08-PPNN.pdf},
url = {http://dx.doi.org/10.1007/978-3-540-87559-8_78},
abstract = {Linear projection pursuit index measuring quality of projected clusters (QPC) is used to discover non-local clusters in high-dimensional multiclass data, reduce dimensionality, select features, visualize and classify data. Constructive neural networks that optimize the QPC index are able to discover simplest models of complex data, solving problems that standard networks based on error minimization are not able to handle. Tests on problems with complex Boolean logic, and tests on real world datasets show high efficiency of this approach. }
}
@ARTICLE{GrochowskiD08,
author = {Marek Grochowski and W\l{}odzis\l{}aw Duch},
title = {A Comparison of Methods for Learning of Highly Non-separable Problems},
journal = {Lecture Notes in Computer Science},
year = {2008},
volume = {5097},
pages = {566--577},
bibdate = {2008-06-23},
bibsource = {DBLP, http://dblp.uni-trier.de/db/conf/icaisc/icaisc2008.html#GrochowskiD08},
booktitle = {ICAISC},
editor = {Leszek Rutkowski and Ryszard Tadeusiewicz and Lotfi A. Zadeh and
Jacek M. \.{Z}urada},
isbn = {978-3-540-69572-1},
owner = {marek},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
timestamp = {2011.10.18},
url = {http://dx.doi.org/10.1007/978-3-540-69731-2_55},
file = { http://www.fizyka.umk.pl/publications/kmk/08-ksepcomp.pdf },
abstract = { Learning in cases that are almost linearly separable is easy, but for highly non-separable problems all standard machine learning methods fail. Many strategies to build adaptive systems are based on the "divide-and-conquer" principle. Constructive neural network architectures with novel training methods allow to overcome some drawbacks of standard backpropagation MLP networks. They are able to handle complex multidimensional problems in reasonable time, creating models with small number of neurons. In this paper a comparison of our new constructive c3sep algorithm based on k-separability idea with several sequential constructive learning methods is reported. Tests have been performed on parity function, 3 artificial Monks problems, and a few benchmark problems. Simple and accurate solutions have been discovered using c3sep algorithm even in highly non-separable cases. }
}
@ARTICLE{GrochowskiD07,
author = {Marek Grochowski and W\l{}odzis\l{}aw Duch},
title = {Learning highly non-separable Boolean functions using Constructive
Feedforward Neural Network},
journal = {Lecture Notes in Computer Science},
year = {2007},
volume = {4668},
pages = {180--189},
editor = {Joaquim Marques de S{\'a} and Lu{\'i}s A. Alexandre and W\l{}odzis\l{}aw
Duch and Danilo P. Mandic},
isbn = {978-3-540-74689-8},
owner = {marek},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
timestamp = {2011.10.18},
file = { http://www.fizyka.umk.pl/publications/kmk/07-ksep.pdf},
url = {http://dx.doi.org/10.1007/978-3-540-74690-4_19},
abstract = {Learning problems with inherent non-separable Boolean logic is still a challenge that has not been addressed by neural or kernel classifiers. The k-separability concept introduced recently allows for characterization of complexity of non-separable learning problems. A simple constructive feedforward network that uses a modified form of the error function and a window-like functions to localize outputs after projections on a line has been tested on such problems with quite good results. The computational cost of training is low because most nodes and connections are fixed and only weights of one node are modified at each training step. Several examples of learning Boolean functions and results of classification tests on real-world multiclass datasets are presented.}
}
@ARTICLE{GrochowskiJ04,
author = {Marek Grochowski and Norbert Jankowski},
title = {Comparison of Instance Selection Algorithms~{II}. {R}esults and Comments},
journal = {Lecture Notes in Computer Science},
year = {2004},
volume = {3070},
pages = {580--585},
bibdate = {2004-06-04},
bibsource = {DBLP, http://dblp.uni-trier.de/db/conf/icaisc/icaisc2004.html#GrochowskiJ04},
booktitle = {ICAISC},
editor = {Leszek Rutkowski and J{\"o}rg H. Siekmann and Ryszard Tadeusiewicz
and Lotfi A. Zadeh},
isbn = {3-540-22123-9},
owner = {marek},
publisher = {Springer},
series = {Lecture Notes in Computer Science},
timestamp = {2011.10.18},
file = {http://www.phys.uni.torun.pl/publications/kmk/04-ProtComp2-MGNJ.pdf},
url = {http://springerlink.metapress.com/openurl.asp?genre=article&amp;issn=0302-9743&amp;volume=3070&amp;spage=580},
abstract = { This paper is an continuation of the accompanying paper with the same main title. The first paper reviewed instance selection algorithms, here results of empirical comparison and comments are presented. Several test were performed mostly on benchmark data sets from the machine learning repository at UCI. Instance selection algorithms were tested with neural networks and machine learning algorithms.}
}
@ARTICLE{GrudzinskiGD10,
author = {Karol Grudzi\'{n}ski and Marek Grochowski and W\l{}odzis\l{}aw Duch},
title = {Pruning Classification Rules with Reference Vector Selection Methods},
journal = {Lecture Notes in Computer Science},
year = {2010},
volume = {6113},
pages = {347-354},
bibsource = {DBLP, http://dblp.uni-trier.de},
booktitle = {ICAISC (1)},
editor = {Leszek Rutkowski and Rafal Scherer and Ryszard Tadeusiewicz and Lotfi
A. Zadeh and Jacek M. \.{Z}urada},
ee = {http://dx.doi.org/10.1007/978-3-642-13208-7},
isbn = {978-3-642-13207-0},
publisher = {Springer},
file = { http://www.fizyka.umk.pl/publications/kmk/10-EkP_Prunning-ICAISC.pdf },
abstract = {Attempts to extract logical rules from data often lead to large sets of classification rules that need to be pruned. Training two classifiers, the C4.5 decision tree and the Non-Nested Generalized Exemplars (NNGE) covering algorithm, on datasets that have been reduced earlier with the EkP instance compressor leads to statistically significantly lower number of derived rules with nonsignificant degradation of results. Similar results have been observed with other popular instance filters used for data pruning. Numerical experiments presented here illustrate that it is possible to extract more interesting and simpler sets of rules from filtered datasets. This enables a better understanding of knowledge structures when data is explored using algorithms that tend to induce a large number of classification rules.}
}
@ARTICLE{JankowskiG05,
author = {Norbert Jankowski and Marek Grochowski},
title = {Instances Selection Algorithms in the Conjunction with {LVQ}},
year = {2005},
pages = {703--708},
bibdate = {2005-10-17},
bibsource = {DBLP, http://dblp.uni-trier.de/db/conf/aia/aia2005.html#JankowskiG05},
booktitle = {Artificial Intelligence and Applications},
editor = {M. H. Hamza},
isbn = {0-88986-459-4},
owner = {marek},
publisher = {IASTED/ACTA Press},
timestamp = {2011.10.18},
file = {http://www.phys.uni.torun.pl/~norbert/publications/05-aia-NJMG.pdf},
abstract = { This paper can be seen from two sides. From the first side as the answer of the question: how to initialize the Learning Vectors Quantization algorithm. And from second side it can be seen as the method of improving of instances selection algorithms. In the article we propose to use a conjunction of the LVQ and some of instances selection algorithms because it simplify the LVQ initialization and provide to better prototypes set. Moreover prepared experiments clearly show that such combinations of methods provide to higher classification accuracy on the unseen data. The results were computed and averaged for several benchmarks. }
}
@ARTICLE{JankowskiG04,
author = {Norbert Jankowski and Marek Grochowski},
title = {Comparison of Instances Seletion Algorithms~{I}. {A}lgorithms Survey},
journal = {Lecture Notes in Computer Science},
year = {2004},
volume = {3070},
pages = {598--603},
editor = {Leszek Rutkowski and J{\"o}rg H. Siekmann and Ryszard Tadeusiewicz
and Lotfi A. Zadeh},
owner = {marek},
publisher = {Springer},
timestamp = {2011.10.18},
file = {http://www.is.umk.pl/~norbert/publications/04-zakopane-NJMG.pdf},
url = {http://springerlink.metapress.com/openurl.asp?genre=article&amp;issn=0302-9743&amp;volume=3070&amp;spage=598},
abstract = {Several methods were proposed to reduce the number of instances (vectors) in the learning set. Some of them extract only bad vectors while others try to remove as many instances as possible without significant degradation of the reduced dataset for learning. Several strategies to shrink training sets are compared here using different neural and machine learning classification algorithms. In part II (the accompanying paper) results on benchmarks databases have been presented.}
}
@INBOOK{MaszczykGD10,
author = {Tomasz Maszczyk and Marek Grochowski and W\l{}odzis\l{}aw Duch},
pages = {467--484},
title = {Discovering Data Structures Using Meta-learning, Visualization and
Constructive Neural Networks},
publisher = {Springer},
year = {2010},
editor = {Jacek Koronacki and Zbigniew W. Ra\'{s} and S\l{}awomir T. Wierzcho\'{n} and
Janusz Kacprzyk},
volume = {263},
series = {Studies in Computational Intelligence},
bibdate = {2009-12-01},
bibsource = {DBLP, http://dblp.uni-trier.de/db/series/sci/sci263.html#MaszczykGD10},
booktitle = {Advances in Machine Learning II},
isbn = {978-3-642-05178-4},
owner = {marek},
timestamp = {2011.10.18},
url = {http://dx.doi.org/10.1007/978-3-642-05179-1},
file = {http://www.fizyka.umk.pl/publications/kmk/08-Discovering-data.pdf},
abstract = {Visualization methods are used to discover simplest data transformations implemented by constructive neural networks, revealing hidden data structures. In this way meta-learning, based on search for simplest models in the space of all data transformations, is facilitated. }
}
@PHDTHESIS{GrochowskiM12,
author = {Marek Grochowski},
title = {Projection pursuit neural networks (in polish)},
year = {2012},
school = {Instytut Podstaw Informatyki PAN},
owner = {marek},
file = {http://www.fizyka.umk.pl/~grochu/data/articles/PhD-MG-PPNN.pdf},
abstract = { Learning complex multidimensional classification problems with inherent logic structure, non-local relations, and multi-modal class distributions is still a great challenge where standard machine learning methods fail. On the other hand, without appropriate strategies for model complexity selection, even simple solutions may be easily missed . Therefore, there is a strong need for the development of new machine learning algorithms capable of handling such highly non-separable problems leading to the simplest possible solution (with respect to number of parameters and speed of learning).

Complex classification problems can be simplified by proper transformations of the input space. This work focuses on projection pursuit methods which are able to discover important structures in multidimensional data, and which can reduce the dimensionality of the problem to a space defined by only few interesting projections. Then, searching for optimal discrimination rule in the transformed space is much more likely to succeed.

In this thesis the projection pursuit method is used for training of a constructive neural networks applied to classification task of complex non-separable data. Constructive architectures, by exploring the space of possible solutions, starting from the simplest model and proceeding to more complex and sophisticated structures, are able to fit model complexity to given data. An important part of this work is to characterize classification problems due to their complexity, especially for data with inherent logic. New projection indices have been proposed in this work and comparison with similar methods have been presented. }