Publikacje

Prace doktorskie (1)

• Marek Grochowski (2012) Sztuczne sieci neuronowe oparte na metodach wyszukiwania interesuj±cych projekcji. PDF bibtex

  • Abstract Rozwiązywanie złożonych problemów klasyfikacyjnych, gdzie mamy do czynienia z wielowymiarowymi danymi o strukturze logicznej, posiadającymi nielokalne relacje i wielomodalne rozkłady, jest wciąż bardzo dużym wyzwaniem, z którym często nie radzą sobie powszechnie stosowane maszyny uczące. Z drugiej strony, bez odpowiednich strategii doboru złożoności modelu, łatwo przeoczyć nawet proste rozwiązanie problemu, jeżeli takie istnieje. Uzasadnione wydaje się więc poszukiwanie nowych typów maszyn uczących o możliwościach adaptacyjnych obejmujących wysoce nieseparowalne problemy i generujących możliwie najprostsze rozwiązania (ze względu na ilość parametrów jak i szybkość ich znajdowania). Złożony problem klasyfikacyjny można uprościć przy pomocy odpowiednich transformacji danych wejściowych. Analizowane w pracy metody wyszukiwania interesujących projekcji (ang. Projection Pursuit) pozwalają wykrywać istotne struktury w wielowymiarowych danych, redukując problem do przestrzeni określonej przez kilka interesujących rzutów. Budowanie modelu dyskryminacyjnego w takiej przestrzeni ma wówczas większe szanse powodzenia. W pracy przeanalizowano wykorzystanie metod poszukiwania interesujących projekcji do uczenia konstruktywistycznych sieci neuronowych w zastosowaniu do klasyfikacji złożonych i trudno separowanych danych. Architektury konstruktywistyczne, eksplorujące przestrzeń rozwiązań, poczynając od najprostszego modelu, w kierunku coraz bardziej złożonych i wyrafinowanych struktur, dopasowują złożoność modelu do trudności zadania. Ważną częścią pracy jest próba charakteryzacji problemów klasyfikacyjnych ze względu na ich złożoność, ze szczególnym uwzględnieniem danych o strukturze logicznej. Zaprezentowano w niej nowe indeksy projekcyjne, ich wykorzystanie do treningu konstruktywistycznych sieci oraz przedstawiono porównanie ich możliwości z podobnymi istniejącymi algorytmami i powszechnie stosowanymi metodami.

Rozdziały w książkach (3)

• Marek Grochowski, Włodzisław Duch (2009) Constructive Neural Network Algorithms that Solve Highly Non-Separable Problems. In Constructive Neural Networks. pp. 49-70. Springer. PDF bibtex

  @INBOOK{GrochowskiD09a,
      author = {Marek Grochowski and Włodzisław 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{é} 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.} 
    }

  • 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.

• Tomasz Maszczyk, Marek Grochowski, Włodzisław Duch (2010) Discovering Data Structures Using Meta-learning, Visualization and Constructive Neural Networks. In Advances in Machine Learning II. pp. 467-484. Springer. PDF web bibtex

  @INBOOK{MaszczykGD10,
      author = {Tomasz Maszczyk and Marek Grochowski and Włodzisław 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. Raś and Sławomir T. Wierzchoń 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. } 
     }

  • 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.

• Wlodzislaw Duch, Tomasz Maszczyk, Marek Grochowski (2011) Optimal Support Features for Meta-Learning. In Meta-learning in Computational Intelligence. pp. 317-358. Springer. PDF bibtex

  • 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.

Artykuły (10)

• Marek Grochowski, Norbert Jankowski (2004) Comparison of Instance Selection Algorithms {II}. {R}esults and Comments. In ICAISC. Lecture Notes in Computer Science 3070 pp. 580-585. Springer. PDF web bibtex

  @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{ö}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&issn=0302-9743&volume=3070&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.}
    }

  • 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.

• Norbert Jankowski, Marek Grochowski (2004) Comparison of Instances Seletion Algorithms {I}. {A}lgorithms Survey. Lecture Notes in Computer Science 3070 pp. 598-603. Springer. PDF web bibtex

  @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{ö}rg H. Siekmann and Ryszard Tadeusiewicz
    	and Lotfi A. Zadeh},
      owner = {marek},
      publisher = {Springer},
      timestamp = {2011.10.18},
      file = {http://www.fizyka.umk.pl/publications/kmk/04-ProtComp1-NJMG.pdf},
      url = {http://springerlink.metapress.com/openurl.asp?genre=article&issn=0302-9743&volume=3070&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.}
    }

  • 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.

• Norbert Jankowski, Marek Grochowski (2005) Instances Selection Algorithms in the Conjunction with {LVQ}. In Artificial Intelligence and Applications. pp. 703-708. IASTED/ACTA Press. PDF bibtex

  @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. }
    }

  • 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.

• Marek Grochowski, Włodzisław Duch (2007) Learning highly non-separable Boolean functions using Constructive Feedforward Neural Network. Lecture Notes in Computer Science 4668 pp. 180-189. Springer. PDF web bibtex

  @ARTICLE{GrochowskiD07,
      author = {Marek Grochowski and Włodzisław 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{á} and Lu{í}s A. Alexandre and Włodzisław
    	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.}
    }

  • 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.

• Marek Grochowski, Włodzisław Duch (2008) Projection Pursuit Constructive Neural Networks Based on Quality of Projected Clusters. In ICANN (2). Lecture Notes in Computer Science 5164 pp. 754-762. Springer. PDF web bibtex

  @ARTICLE{GrochowskiD08a,
      author = {Marek Grochowski and Włodzisław 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{á} and Roman Neruda and Jan Koutn{í}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. }
    }

  • 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.

• Marek Grochowski, Włodzisław Duch (2008) A Comparison of Methods for Learning of Highly Non-separable Problems. In ICAISC. Lecture Notes in Computer Science 5097 pp. 566-577. Springer. PDF web bibtex

  @ARTICLE{GrochowskiD08,
      author = {Marek Grochowski and Włodzisław 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. Żurada},
      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.  }
    }

  • 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.

• Marek Grochowski, Włodzisław Duch (2009) Constrained Learning Vector Quantization or Relaxed k-Separability. In ICANN (1). Lecture Notes in Computer Science 5768 pp. 151-160. Springer. PDF web bibtex

  @ARTICLE{GrochowskiD09,
      author = {Marek Grochowski and Włodzisław 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. }
    }

  • 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.

• Karol Grudziński, Marek Grochowski, Włodzisław Duch (2010) Pruning Classification Rules with Reference Vector Selection Methods. In ICAISC (1). Lecture Notes in Computer Science 6113 pp. 347-354. Springer. PDF bibtex

  @ARTICLE{GrudzinskiGD10,
      author = {Karol Grudziński and Marek Grochowski and Włodzisław 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. Żurada},
      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.}
    }

  • 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.

• Marek Grochowski, Włodzisław Duch (2011) Fast Projection Pursuit Based on Quality of Projected Clusters. In ICANNGA (2). Lecture Notes in Computer Science 6594 pp. 89-97. Springer. PDF bibtex

  @ARTICLE{GrochowskiD11,
      author = {Marek Grochowski and Włodzisław 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.  }
      }

  • 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.

• Marek Grochowski (2012) Simple Incremental Instance Selection Wrapper for Classification. In ICAISC (2). Lecture Notes in Computer Science 7268 pp. 64-72. Springer. PDF bibtex

  @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. Żurada},
      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.}
    }

  • 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.

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