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Yayın Cryptanalysis of Fridrich's chaotic image encryption(World Scientific Publishing, 2010-05) Solak, Ercan; Çokal, Cahit; Yıldız, Olcay Taner; Bıyıkoğlu, TürkerWe cryptanalyze Fridrich's chaotic image encryption algorithm. We show that the algebraic weaknesses of the algorithm make it vulnerable against chosen-ciphertext attacks. We propose an attack that reveals the secret permutation that is used to shuffle the pixels of a round input. We demonstrate the effectiveness of our attack with examples and simulation results. We also show that our proposed attack can be generalized to other well-known chaotic image encryption algorithms.Yayın Parallel univariate decision trees(Elsevier B.V., 2007-05-01) Yıldız, Olcay Taner; Dikmen, OnurUnivariate decision tree algorithms are widely used in data mining because (i) they are easy to learn (ii) when trained they can be expressed in rule based manner. In several applications mainly including data mining, the dataset to be learned is very large. In those cases it is highly desirable to construct univariate decision trees in reasonable time. This may be accomplished by parallelizing univariate decision tree algorithms. In this paper, we first present two different univariate decision tree algorithms C4.5 and univariate linear discriminant tree. We show how to parallelize these algorithms in three ways: (i) feature based; (ii) node based; (iii) data based manners. Experimental results show that performance of the parallelizations highly depend on the dataset and the node based parallelization demonstrate good speedups.Yayın On the feature extraction in discrete space(Elsevier Sci Ltd, 2014-05) Yıldız, Olcay TanerIn many pattern recognition applications, feature space expansion is a key step for improving the performance of the classifier. In this paper, we (i) expand the discrete feature space by generating all orderings of values of k discrete attributes exhaustively, (ii) modify the well-known decision tree and rule induction classifiers (ID3, Quilan, 1986 [1] and Ripper, Cohen, 1995 [2]) using these orderings as the new attributes. Our simulation results on 15 datasets from UCI repository [3] show that the novel classifiers perform better than the proper ones in terms of error rate and complexity.Yayın Incremental construction of classifier and discriminant ensembles(Elsevier Science Inc, 2009-04-15) Ulaş, Aydın; Semerci, Murat; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemWe discuss approaches to incrementally construct an ensemble. The first constructs an ensemble of classifiers choosing a subset from a larger set, and the second constructs an ensemble of discriminants, where a classifier is used for some classes only. We investigate criteria including accuracy, significant improvement, diversity, correlation, and the role of search direction. For discriminant ensembles, we test subset selection and trees. Fusion is by voting or by a linear model. Using 14 classifiers on 38 data sets. incremental search finds small, accurate ensembles in polynomial time. The discriminant ensemble uses a subset of discriminants and is simpler, interpretable, and accurate. We see that an incremental ensemble has higher accuracy than bagging and random subspace method; and it has a comparable accuracy to AdaBoost. but fewer classifiers.Yayın Tree Ensembles on the induced discrete space(Institute of Electrical and Electronics Engineers Inc., 2016-05) Yıldız, Olcay TanerDecision trees are widely used predictive models in machine learning. Recently, K-tree is proposed, where the original discrete feature space is expanded by generating all orderings of values of k discrete attributes and these orderings are used as the new attributes in decision tree induction. Although K-tree performs significantly better than the proper one, their exponential time complexity can prohibit their use. In this brief, we propose K-forest, an extension of random forest, where a subset of features is selected randomly from the induced discrete space. Simulation results on 17 data sets show that the novel ensemble classifier has significantly lower error rate compared with the random forest based on the original feature space.Yayın Cost-conscious comparison of supervised learning algorithms over multiple data sets(Elsevier Sci Ltd, 2012-04) Ulaş, Aydın; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemIn the literature, there exist statistical tests to compare supervised learning algorithms on multiple data sets in terms of accuracy but they do not always generate an ordering. We propose Multi(2)Test, a generalization of our previous work, for ordering multiple learning algorithms on multiple data sets from "best" to "worst" where our goodness measure is composed of a prior cost term additional to generalization error. Our simulations show that Multi2Test generates orderings using pairwise tests on error and different types of cost using time and space complexity of the learning algorithms.Yayın Eigenclassifiers for combining correlated classifiers(Elsevier Science Inc, 2012-03-15) Ulaş, Aydın; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemIn practice, classifiers in an ensemble are not independent. This paper is the continuation of our previous work on ensemble subset selection [A. Ulas, M. Semerci, O.T. Yildiz, E. Alpaydin, Incremental construction of classifier and discriminant ensembles, Information Sciences, 179 (9) (2009) 1298-1318] and has two parts: first, we investigate the effect of four factors on correlation: (i) algorithms used for training, (ii) hyperparameters of the algorithms, (iii) resampled training sets, (iv) input feature subsets. Simulations using 14 classifiers on 38 data sets indicate that hyperparameters and overlapping training sets have higher effect on positive correlation than features and algorithms. Second, we propose postprocessing before fusing using principal component analysis (PCA) to form uncorrelated eigenclassifiers from a set of correlated experts. Combining the information from all classifiers may be better than subset selection where some base classifiers are pruned before combination, because using all allows redundancy.Yayın Mapping classifiers and datasets(Pergamon-Elsevier Science Ltd, 2011-04) Yıldız, Olcay TanerGiven the posterior probability estimates of 14 classifiers on 38 datasets, we plot two-dimensional maps of classifiers and datasets using principal component analysis (PCA) and Isomap. The similarity between classifiers indicate correlation (or diversity) between them and can be used in deciding whether to include both in an ensemble. Similarly, datasets which are too similar need not both be used in a general comparison experiment. The results show that (i) most of the datasets (approximately two third) we used are similar to each other, (ii) multilayer perceptrons and k-nearest neighbor variants are more similar to each other than support vector machine and decision tree variants. (iii) the number of classes and the sample size has an effect on similarity.Yayın Model selection in omnivariate decision trees using Structural Risk Minimization(Elsevier Science Inc, 2011-12-01) Yıldız, Olcay TanerAs opposed to trees that use a single type of decision node, an omnivariate decision tree contains nodes of different types. We propose to use Structural Risk Minimization (SRM) to choose between node types in omnivariate decision tree construction to match the complexity of a node to the complexity of the data reaching that node. In order to apply SRM for model selection, one needs the VC-dimension of the candidate models. In this paper, we first derive the VC-dimension of the univariate model, and estimate the VC-dimension of all three models (univariate, linear multivariate or quadratic multivariate) experimentally. Second, we compare SRM with other model selection techniques including Akaike's Information Criterion (AIC), Bayesian Information Criterion (BIC) and cross-validation (CV) on standard datasets from the UCI and Delve repositories. We see that SRM induces omnivariate trees that have a small percentage of multivariate nodes close to the root and they generalize more or at least as accurately as those constructed using other model selection techniques.Yayın Quadratic programming for class ordering in rule induction(Elsevier Science BV, 2015-03-01) Yıldız, Olcay TanerSeparate-and-conquer type rule induction algorithms such as Ripper, solve a K>2 class problem by converting it into a sequence of K - 1 two-class problems. As a usual heuristic, the classes are fed into the algorithm in the order of increasing prior probabilities. Although the heuristic works well in practice, there is much room for improvement. In this paper, we propose a novel approach to improve this heuristic. The approach transforms the ordering search problem into a quadratic optimization problem and uses the solution of the optimization problem to extract the optimal ordering. We compared new Ripper (guided by the ordering found with our approach) with original Ripper (guided by the heuristic ordering) on 27 datasets. Simulation results show that our approach produces rulesets that are significantly better than those produced by the original Ripper.
