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Öğe A comparison of different procedures for principal component analysis in the presence of outliers(Taylor & Francis Ltd, 2015) Alkan, B. Baris; Atakan, Cemal; Alkan, NesrinPrincipal component analysis (PCA) is a popular technique that is useful for dimensionality reduction but it is affected by the presence of outliers. The outlier sensitivity of classical PCA (CPCA) has caused the development of new approaches. Effects of using estimates obtained by expectation-maximization - EM and multiple imputation - MI instead of outliers were examined on the artificial and a real data set. Furthermore, robust PCA based on minimum covariance determinant (MCD), PCA based on estimates obtained by EM instead of outliers and PCA based on estimates obtained by MI instead of outliers were compared with the results of CPCA. In this study, we tried to show the effects of using estimates obtained by MI and EM instead of outliers, depending on the ratio of outliers in data set. Finally, when the ratio of outliers exceeds 20%, we suggest the use of estimates obtained by MI and EM instead of outliers as an alternative approach.Öğe Comparison of principal component analysis biplots based on different robust covariance matrix estimates(Springer, 2014) Alkan, B. Barış; Atakan, CemalGraphical approaches are widely used in the examination of multivariate data. The most popular of them is called Biplot. This technique provides an geometric approach that examined the relations between observations and variables in the principal components space with reduced-size. Principal component analysis (PCA) is obtained by covariance (or corelation) matrix. Therefore it is influenced by the presence of outliers. PCA biplot is used for visualization of PCA results. In this study, we compare the performances of PCA biplots based on different robust cavariance matrix estimates on the one real and the artificial data sets. Results indicate that Robust PCA biplot is preferred to instead of Classical PCA biplot in the presence of outliers. © Springer Science+Business Media Dordrecht 2014.Öğe DAYANIKLI LİNEER DİSKRİMİNANT ANALİZİ İÇİN YENİ BİR YAKLAŞIM(2018) Alkan, B Barış; Atakan, Cemal; Alkan, NesrinLineer diskriminant analizi, önceden bilinen p sayıda özelliğe sahip birimleri, doğadaki gerçek sınıflarına en doğru şekilde atamayı amaçlayan çok değişkenli istatistiksel bir yöntemdir. Burada hedef, birimleri gerçek sınıfına minimum hatayla atamaktır. Lineer Diskriminant Analizi (LDA), veri kümesinde diğer gözlemlerden farklı hareket eden ve aykırı gözlem olarak adlandırılan gözlemlerin varlığında dayanıklı bir yöntem değildir ve güvenilir sonuçlar vermeyebilir. Böyle durumlarda, klasik LDA’nın dayanıklı versiyonlarının kullanımının gerekliliği üzerine literatürde birçok çalışmaya rastlamak mümkündür. Bu çalışmada, jackknife yeniden örnekleme yaklaşımı, minimum kovaryans determinant (MKD) ve LDA yönteminin bir kombinasyonu ile LDA’nın yeni bir dayanıklı versiyonu elde edilmiştir. Önerilen bu yeni yaklaşım ile Croux ve Dehon (2001) tarafından önerilen (Yöntem-1), Hawkins ve McLachlan (1997) tarafından önerilen (Yöntem-2) yaklaşımların aykırı gözlem oranındaki değişimlere göre nasıl etkilendiği yapay veri uygulaması ve benzetim çalışması üzerinden değerlendirilmektedir. Elde edilen bulgular ışığında, önerilen yaklaşımın diğer iki yaklaşıma göre, veri kümesinde aykırı gözlemlerin varlığında performansının bazı durumlarda daha iyi, bazı durumlarda ise en az onlar kadar iyi olduğu görülmektedir.Öğe DAYANIKLI LINEER DISKRIMINANT ANALIZI IÇIN YENI BIR YAKLASIM(Erciyes Üniversitesi, 2018) Alkan, B.baris; Atakan, Cemal; Alkan, NesrinLineer diskriminant analizi, önceden bilinen p sayidaki özelliklerine göre birimleri, dogadaki gerçeksiniflarina en dogru sekilde atamayi amaçlayan çok degiskenli istatistiksel biryöntemdir. Burada hedef, birimleri gerçek sinifina minimum hatayla atamaktir.Lineer Diskriminant Analizi (LDA), veri kümesinde diger gözlemlerden farklihareket eden ve aykiri gözlem olarak adlandirilan gözlemlerin varligindadayanikli bir yöntem degildir ve güvenilir sonuçlar vermeyebilir. Böyledurumlarda, klasik LDA’nin dayanikli versiyonlarinin kullaniminin gerekliligiüzerine literatürde birçok çalismaya rastlamak mümkündür. Bu çalismada,jackknife yeniden örnekleme yaklasimi, minimum kovaryans determinant (MKD) veLDA yönteminin bir kombinasyonu ile LDA’nin yeni bir dayanikli versiyonu eldeedilmistir. Önerilen bu yeni yaklasimile Croux ve Dehon (2001) tarafindan önerilen (Yöntem-1), Hawkins ve McLachlan(1997) tarafindan önerilen (Yöntem-2) yaklasimlarin aykiri gözlem oranindaki degisimleregöre nasil etkilendigi yapay veri uygulamasi ve benzetim çalismasi üzerindendegerlendirilmektedir. Elde edilen bulgular isiginda, önerilen yaklasimin digeriki yaklasima göre, veri kümesinde aykiri gözlemlerin varliginda performansininbazi durumlarda daha iyi, bazi durumlarda ise en az onlar kadar iyi oldugugörülmektedir.Öğe Examination of relation between nutrient components and fruits: Biplot approach(Taylor & Francis Ltd, 2009) Atakan, Cemal; Alkan, Baris; Sahin, AfsinAdequate intake of fruits and vegetables as part of the daily diet may help prevent major diseases. Low fruit intake is a major risk factor for cancer, coronary heart disease and stroke. The World Health Organization recommends eating at least five portions of a variety of fruit, which is nearly 400 g/day. Essential nutrients, water, carbohydrates, oils and vitamins are needed in appropriate quantities in order to have a well-functioning body. In this study we try to carry out a food composition study to identify and determine the chemical nature of the organic and inorganic macro-nutrient and micro-nutrient properties of the main fruit types that affect human nature, by a biplot graphical approach. The biplot can be considered as multivariate equivalents of scatter plots that have been used for graphically analyzing bivariate data. Biplot approaches show a simultaneous display of fruits and nutrient components in low dimensions. In the present study, the theory of biplot and different types of biplot will be given and than an application of the biplot approach will be applied to the real data.Öğe Measuring inequalities in the distribution of health workers by bi-plot approach: The case of Turkey(Journal of Economics and Behavioral Studies, 2011) Alkan, B. Barış; Atakan, Cemal; Şahin, AfşinOptimal planning of the health workers is of vital importance for a country. Distribution of health workers among provinces in emerging markets is an important development criterion. In this study, biplot graphical approach is used to determine the distribution of health workers. The results of biplot analysis point out that the distribution of the healthcare staff in Turkey is unbalanced. The number of health workers should be planned and considered according to the desire, need, population, target and workload criteria. The new employment opportunities should be created and the workers should be encouraged to serve in low income regions by providing better conditions.Öğe Türkiye'de Yeni Tanımlı Sanayi Üretim Endeksi ve Alt Sanayi Gruplarındaki Büyümenin Biplot Yöntemi ile İncelenmesi(Journal of Yaşar University, 2010) Şahin, Afşin; Atakan, Cemal; Alkan, B. BarışBu çalışmada yeni tanımlı Sanayi Üretim Endeksi (2005=100)’nin ana sanayi grupları aralarındaki ilişki biplot tekniği ve yakınsama analizleriyle incelenmektedir. Kovaryans biplot grafiği ve yakınsama testi sonuçlarına göre imalat, toplam, dayanıksız, ara, dayanıklı ve sermaye malları üretimi endekslerindeki büyümeler arasında pozitif yönde bir ilişki olduğu tespit edilmiştir. Ancak ana sanayi grupları büyümeleri arasındaki korelasyonlar heterojen bir yapı göstermektedir.Öğe Use of biplot technique for the comparison of the missing value imputation methods(Inderscience Enterprises Ltd., 2015) Alkan, B. Baris; Alkan, Nesrin; Atakan, Cemal; Terzi, YukselThis study was performed to assess the effects of different imputation methods on the performance of a biplot technique. We selected the Fisher's iris data as our reference dataset. Some elements of the Iris data were deleted in different rates under missing at random (MAR) assumption to generate incomplete datasets which had 3.5%, 7%, %15, 20% missing value. Datasets with missing values were completed by four imputation methods [mean imputation, regression imputation, expectation maximisation (EM) algorithm, multiple imputation (MI)]. The new imputed datasets were analysed by biplot technique and their results were compared with original complete biplot of the data. The results of biplot analysis were similar in all the imputation methods when missing rate is low under MAR assumption. Even when the missing rate was greater than 10%, results of EM and MI methods were similar to real values and graphical representation of original data. For multivariate methods, we also propose filling in the missing value with the arithmetic mean of the imputed estimates which are obtained with multiple imputation. This paper also indicates that the use of biplot technique for the comparison of the missing value imputation methods provides a useful visual tool. © 2015 Inderscience Enterprises Ltd.Öğe Use of canonical variate analysis biplot in examination of choline content data of some foods(Taylor & Francis Ltd, 2011) Alkan, Baris; Atakan, CemalAdequate intake (AI) of choline as part of the daily diet can help prevent major diseases. Low choline intake is a major risk factor for liver and several neurological disorders. Extreme choline consumption may cause diseases such as hypotension, sweating, diarrhea, and fishy body odor. The AI of choline is 425 mg/day for adult women; higher for pregnant and lactating women. The AI for adult men is 550 mg/day. The total choline content of foods is calculated as the sum of free choline, glycerophosphocholine, phosphocholine, phosphatidylcholine and sphingomyelin. These are called the choline variables. Observed values of choline variables may be different in amounts of nutrients. So different food groups in terms of choline variables are useful to compare. The present paper shows the advantages of using canonical variate analysis biplot to optimally separate groups and explore the differentiality of choline variables amounts in foods.Öğe Visualizing Diagnostic of Multicollinearity: Tableplot and Biplot Methods(Pakistan Journal of Statistics, 2013) Alkan, B. Barış; Atakan, CemalIn this study we tried to bring out the importance of two methods used for visualizing multicollinearity diagnostics. The first method is called Tableplot (see Friendly and Kwan, 2009). Through this technique, multicollinearity diagnostics ideas are combined with a visualizing approach. The second method is called Biplot (see Gabriel, 1971; Gower and Hand, 1996). The biplot technique is used for demonstrating significant properties of multivariate data structure. Both of these approaches have been examined by one real and three artificial data. Results indicate that Biplot method is preferred to instead of Tableplot for too large condition indexes.
