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Yayın Calculating the VC-dimension of decision trees(IEEE, 2009) Aslan, Özlem; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemWe propose an exhaustive search algorithm that calculates the VC-dimension of univariate decision trees with binary features. The VC-dimension of the univariate decision tree with binary features depends on (i) the VC-dimension values of the left and right subtrees, (ii) the number of inputs, and (iii) the number of nodes in the tree. From a training set of example trees whose VC-dimensions are calculated by exhaustive search, we fit a general regressor to estimate the VC-dimension of any binary tree. These VC-dimension estimates are then used to get VC-generalization bounds for complexity control using SRM in decision trees, i.e., pruning. Our simulation results shows that SRM-pruning using the estimated VC-dimensions finds trees that are as accurate as those pruned using cross-validation.Yayın Univariate margin tree(Springer, 2010) Yıldız, Olcay TanerIn many pattern recognition applications, first decision trees are used due to their simplicity and easily interpretable nature. In this paper, we propose a new decision tree learning algorithm called univariate margin tree, where for each continuous attribute, the best split is found using convex optimization. Our simulation results on 47 datasets show that the novel margin tree classifier performs at least as good as C4.5 and LDT with a similar time complexity. For two class datasets it generates smaller trees than C4.5 and LDT without sacrificing from accuracy, and generates significantly more accurate trees than C4.5 and LDT for multiclass datasets with one-vs-rest methodology.Yayın Incremental construction of rule ensembles using classifiers produced by different class orderings(IEEE, 2016) Yıldız, Olcay Taner; Ulaş, AydınIn this paper, we discuss a novel approach to incrementally construct a rule ensemble. The approach constructs an ensemble from a dynamically generated set of rule classifiers. Each classifier in this set is trained by using a different class ordering. We investigate criteria including accuracy, ensemble size, and the role of starting point in the search. Fusion is done by averaging. Using 22 data sets, floating search finds small, accurate ensembles in polynomial time.Yayın Soft decision trees(IEEE, 2012) İrsoy, Ozan; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemWe discuss a novel decision tree architecture with soft decisions at the internal nodes where we choose both children with probabilities given by a sigmoid gating function. Our algorithm is incremental where new nodes are added when needed and parameters are learned using gradient-descent. We visualize the soft tree fit on a toy data set and then compare it with the canonical, hard decision tree over ten regression and classification data sets. Our proposed model has significantly higher accuracy using fewer nodes.Yayın Vikipedi ve Vikisözlük'ten Hypernym çıkarma(IEEE, 2017-06-27) Şaşmaz, Emre; Ehsani, Razieh; Yıldız, Olcay TanerDoğal dil işleme alanında kullanılan önemli yapılardan bir tanesi WordNet gibi büyük ölçekli sözlüklerdir. WordNet; eşanlamlı, zıt anlamlı gibi anlamsal ilişkileri de içeren kapsamlı bir sözlüktür. Bu bildiride, WordNet’in önemli bir parçası olan Hypernym-Hyponym ilişkisini çıkarmaya çalıştık. Bu amaca ulaşmak için, Vikipedi, Türkçe Sözlük ve Vikisözlük kaynaklarını kullandık. Sonlu Durum Makinelerinden ürettiğimiz kurallarla Hypernym-Hyponym ilişkilerini çıkardık.Yayın VC-dimension of rule sets(IEEE Computer Soc, 2014-12-04) Yıldız, Olcay TanerIn this paper, we give and prove lower bounds of the VC-dimension of the rule set hypothesis class where the input features are binary or continuous. The VC-dimension of the rule set depends on the VC-dimension values of its rules and the number of inputs.Yayın İngilizce-Türkçe istatistiksel makine çevirisinde biçimbilim kullanımı(IEEE, 2012-04-18) Görgün, Onur; Yıldız, Olcay TanerBu çalışmada, İngilizce-Türkçe dil ikilisi için biçimbilimsel çözümleme yardımı ile SIU dermecesi üzerinde istatistiksel makine çevirisi denemeleri yapılmıştır. Kelime biçimlerinin baz alındığı çeviri denemeleri İngilizce-Türkçe dil ikilisi gibi biçimbilimsel ve çekimsel olarak birbirinden uzak diller için düşük performans göstermektedir. Bu durumda, çeviri temel birimi olarak kelime formlarının yerine alt-sözcüksel temsiller kullanmak, makine çevirisi performansını önemli ölçüde arttırmaktadır.Yayın Budding trees(IEEE Computer Soc, 2014-08-24) İrsoy, Ozan; Yıldız, Olcay Taner; Alpaydın, Ahmet İbrahim EthemWe propose a new decision tree model, named the budding tree, where a node can be both a leaf and an internal decision node. Each bud node starts as a leaf node, can then grow children, but then later on, if necessary, its children can be pruned. This contrasts with traditional tree construction algorithms that only grows the tree during the training phase, and prunes it in a separate pruning phase. We use a soft tree architecture and show that the tree and its parameters can be trained using gradient-descent. Our experimental results on regression, binary classification, and multi-class classification data sets indicate that our newly proposed model has better performance than traditional trees in terms of accuracy while inducing trees of comparable size.Yayın Multivariate statistical tests for comparing classification algorithms(Springer, Berlin, Heidelberg, 2011) Yıldız, Olcay Taner; Aslan, Özlem; Alpaydın, Ahmet İbrahim EthemThe misclassification error which is usually used in tests to compare classification algorithms, does not make a distinction between the sources of error, namely, false positives and false negatives. Instead of summing these in a single number, we propose to collect multivariate statistics and use multivariate tests on them. Information retrieval uses the measures of precision and recall, and signal detection uses true positive rate (tpr) and false positive rate (fpr) and a multivariate test can also use such two values instead of combining them in a single value, such as error or average precision. For example, we can have bivariate tests for (precision, recall) or (tpr, fpr). We propose to use the pairwise test based on Hotelling's multivariate T test to compare two algorithms or multivariate analysis of variance (MANOVA) to compare L > 2 algorithms. In our experiments, we show that the multivariate tests have higher power than the univariate error test, that is, they can detect differences that the error test cannot, and we also discuss how the decisions made by different multivariate tests differ, to be able to point out where to use which. We also show how multivariate or univariate pairwise tests can be used as post-hoc tests after MANOVA to find cliques of algorithms, or order them along separate dimensions.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.
