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An algorithm for rank estimation and subspace tracking
(Taylor & Francis Ltd, 2009) Erbay, Hasan; Aba, K.
This article presents an URV-based matrix decomposition, the truncated URV decomposition, and an updating algorithm for it. The complexity of the updating is [image omitted] for an m-by- n matrix of rank r. The theoretical and numerical results presented shows that the decomposition can be a good alternative to the singular value decomposition.
Alternate Low-Rank Matrix Approximation in Latent Semantic Analysis
(Hindawi Ltd, 2019) Horasan, Fahrettin; Erbay, Hasan; Varcin, Fatih; Deniz, Emre
The latent semantic analysis (LSA) is a mathematical/statistical way of discovering hidden concepts between terms and documents or within a document collection (i.e., a large corpus of text). Each document of the corpus and terms are expressed as a vector with elements corresponding to these concepts to form a term-document matrix. Then, the LSA uses a low-rank approximation to the term-document matrix in order to remove irrelevant information, to extract more important relations, and to reduce the computational time. The irrelevant information is called as noise and does not have a noteworthy effect on the meaning of the document collection. This is an essential step in the LSA. The singular value decomposition (SVD) has been the main tool obtaining the low-rank approximation in the LSA. Since the document collection is dynamic (i.e., the term-document matrix is subject to repeated updates), we need to renew the approximation. This can be done via recomputing the SVD or updating the SVD. However, the computational time of recomputing or updating the SVD of the term-document matrix is very high when adding new terms and/or documents to preexisting document collection. Therefore, this issue opened the door of using other matrix decompositions for the LSA as ULV- and URV-based decompositions. This study shows that the truncated ULV decomposition (TULVD) is a good alternative to the SVD in the LSA modeling.
An alternative algorithm for a sliding window ULV decomposition
(Springer Wien, 2006) Erbay, Hasan; Barlow, J.
The ULV decomposition (ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition (SVD). The ULVD can be modified much faster than the SVD. When modifiying the ULVD, the accurate computation of the subspaces is required in certain time varying applications in signal processing. In this paper, we present an updating algorithm which is suitable for large scaled matrices of low rank and as effective as alternatives. The algorithm runs in O(n(2)) time.
An alternative algorithm for the refinement of ULV decompositions
(Siam Publications, 2005) Barlow, Jesse L.; Erbay, Hasan; Slapnicar, Ivan
The ULV decomposition ( ULVD) is an important member of a class of rank-revealing two-sided orthogonal decompositions used to approximate the singular value decomposition ( SVD). It is useful in applications of the SVD such as principal components where we are interested in approximating a matrix by one of lower rank. It can be updated and downdated much more quickly than an SVD. In many instances, the ULVD must be refined to improve the approximation it gives for the important right singular subspaces or to improve the matrix approximation. Present algorithms to perform this refinement require O( mn) operations if the rank of the matrix is k, where k is very close to 0 or n, but these algorithms require O( mn(2)) operations otherwise. Presented here is an alternative refinement algorithm that requires O( mn) operations no matter what the rank is. Our tests show that this new refinement algorithm produces similar improvement in matrix approximation and in the subspaces. We also propose slight improvements on the error bounds on subspaces and singular values computed by the ULVD.
Approximating by Szsz-Type operators
(Vsp Bv-C/O Brill Acad Publ, 2005) Aral, Ali; Erbay, Hasan
We introduce a new Szasz-Type operators depending on weighted functions. We analyze approximation results of these operators on weighted space. Our numerical results are consistent with our theory.
Block classical Gram-Schmidt-based block updating in low-rank matrix approximation
(Scientific Technical Research Council Turkey-Tubitak, 2018) Erbay, Hasan; Varcin, Fatih; Horasan, Fahrettin; Bicer, Cenker
Low-rank matrix approximations have recently gained broad popularity in scientific computing areas. They are used to extract correlations and remove noise from matrix-structured data with limited loss of information. Truncated singular value decomposition (SVD) is the main tool for computing low-rank approximation. However, in applications such as latent semantic indexing where document collections are dynamic over time, i.e. the term document matrix is subject to repeated updates, SVD becomes prohibitive due to the high computational expense. Alternative decompositions have been proposed for these applications such as low-rank ULV/URV decompositions and truncated ULV decomposition. Herein, we propose a BLAS-3 compatible block updating truncated ULV decomposition algorithm based on the block classical Gram-Schmidt process. The simulation results presented show that the block update algorithm is promising.
A Comparative Study On Segmentation And Classification In Breast Mri Imaging
(Inst Integrative Omics & Applied Biotechnology, 2018) Yurttakal, Ahmet Hasim; Erbay, Hasan; Ikizceli, Tiirkan; Karacavus, Seyhan; Cinarer, Gokalp
Background: Breast cancer is the type of cancer that develops from cells in the breast tissue. The breast cancer is leading cancer in women. One in every eight to nine women has breast cancer at some point during their lifetime. Computer-Aided Diagnosis (CAD) Technology is getting more important to assist radiologists not only to detect breast cancer tumor but also to interpret lesioned regions. The CAD, as a second reader in the clinic, improves the classification of malignant and benign lesions. On the other hand, Magnetic Resonance Imaging (MRI) is a highly recommended test for detecting and monitoring breast cancer tumors and interpreting lesioned regions since it has an excellent capability for soft tissue imaging. In MRI image analysis, the segmentation images are important objective because accurate measurement of the delineation of the regions of interest (ROI) is critical for the breast cancer diagnosis and treatment. Herein, by using MRI scans, we propose a semi-automated CAD system prototype to assist radiologists in detecting breast cancer tumors and interpreting lesioned regions. The prototype, first, pre-processes the raw selected suspicious region to reduce the noises and to reveal the structure. Later, using Expectation Maximization (EM), the prototype segments the pre-processed region. After that, we use the Discrete Wavelet Transform (DWT) for providing efficient multi-resolution sub and decomposition of signals. Then Random Forest Algorithm is used for feature selection. Finally, Naive Bayes, Linear Discriminant Analysis and C4.5 Decision Tree Algorithms are used to classify the features of the ROI in the diagnosis analysis. We tested the prototype CAD on 105 patients, among them, 53 are benign and 52 malign. 80% of the images are allocated for training and 20% of images reserved for testing. The CAD classified 20 patients correctly in case of 5 fold cross-validation. Only one patient is misclassified. The computer-aided diagnosis system with the C4.5 has accuracy 95.24%. Furthermore, C4.5 classifies the breast cancer tumors better than Naive Bayes and Linear Discriminant Analysis. We tested the prototype CAD on 105 patients, among them, 53 are benign and 52 malign. The computer-aided diagnosis system with the C4.5 has accuracy 95.24%. Furthermore, C4.5 classifies the breast cancer tumors better than Naive Bayes and Linear Discriminant Analysis.
Comparison of the Proficiency Level of the Course Materials (Animations, Videos, Simulations, E-Books) Used In Distance Education
(Elsevier Science Bv, 2014) Kor, Hakan; Aksoy, Hamit; Erbay, Hasan
Activities in the field of distance education have shown a significant improvement in the world and Turkey in parallel with the technology. Activities in this field started through newspapers and letters and they were improved by using printed material, radio, television and internet. Recently, as well as the use of computer and internet have become widespread in the world, web-based distance education systems have been used more than the other teaching tools. In Turkey, departments of distance education attached to the Council of Higher Education were opened in large number and they are still continued to be opened. In this paper, in terms of quality and interactivity it is aimed to evaluate the course materials used by the institutions of distance education. Through the surveys applied to the institutions of distance education determined by choosing from the different regions of Turkey, it was aimed to find out the faults and defects of the course materials in terms of quality and interactivity. By sharing the obtained outputs with related institutions, formation of more efficient distance learning materials will be possible. (C) 2014 The Authors. Published by Elsevier Ltd.
Comparison of Two-Parameter Bernstein Operator and Bernstein-Durrmeyer Variants
(Springer Singapore Pte Ltd, 2018) Aral, Ali; Erbay, Hasan
The quantum calculus and the post-quantum calculus have recently gained broad popularity in computational science and engineering due to their applications to diverse areas such as solution of differential equations, approximation theory and computer-aided geometric design. Herein, we consider two parameters but two different modified Bernstein-Durrmeyer operators along with two-parameter Bernstein operator. We obtain estimates to the differences between the Bernstein operator and each modified Bernstein-Durrmeyer operator using classical modulus of continuity. In addition, similar estimates are obtained for Chebyshev functional of these operators. Main purpose of using two-parameter operators is to allow us more flexible approximations compared to their classical versions, namely depending on values of parameters, the approximation can be speeded up. Numerical results presented approves the theoretical results.
Context-dependent model for spam detection on social networks
(SPRINGER INTERNATIONAL PUBLISHING AG, 2020) Ghanem, Razan; Erbay, Hasan
Social media platforms are getting an important communication medium in our daily life, and their increasing popularity makes them an ideal platform for spammers to spread spam messages, known as spam problems. Moreover, messages on social media are vague and messy, so a good representation of the text may be the first step to address spam problem. While traditional weighting methods suffer from both high dimensionality and high sparsity problems, traditional word embedding methods suffer from context independence and out of vocabulary problems. To overcome these problems, in this study, we propose a novel architecture based on a context-dependent representation of text using the BERT model. The model was tested using the Twitter dataset, and experimental results show that the proposed method outperforms traditional weighting methods, traditional word embedding based methods as well as the existing state of the art methods used to detect spam on the twitter platform.
Correction to: Novel authorship verification model for social media accounts compromised by a human (Multimedia Tools and Applications, (2021), 80, 9, (13575-13591), 10.1007/s11042-020-10361-2)
(Springer, 2021) Alterkavı, Suleyman; Erbay, Hasan
The author name “Suleyman Alterkavı” was incorrectly presented in the original publication. The original article has been corrected. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
Crop pest classification with a genetic algorithm-based weighted ensemble of deep convolutional neural networks
(ELSEVIER SCI LTD, 2020) Ayan, Enes; Erbay, Hasan; Varcin, Fatih
Insects are among the important causes of significant losses in crops such as rice, wheat, corn, soybeans, sugarcane, chickpeas, potatoes. Identification of insect species in the early period is crucial so that the necessary precautions can be taken to keep losses at a low level. However, accurate identification of various types of crop insects is a challenging task for the farmers due to the similarities among insect species and also their lack of knowledge. To address this problem, computerized methods, especially based on Convolutional Neural Networks (CNNs), can be employed. CNNs have been used successfully in many image classification problems due to their ability to learn data-dependent features automatically from the data. Throughout the study, seven different pre-trained CNN models (VGG-16, VGG-19, ResNet-50, Inception-V3, Xception, MobileNet, SqueezeNet) were modified and re-trained using appropriate transfer learning and finetuning strategies on publicly available D0 dataset with 40 classes. Later, the top three best performing CNN models, Inception-V3, Xception, and MobileNet, were ensembled via sum of maximum probabilities strategy to increase the classification performance, the model was named SMPEnsemble. After that, these models were ensembled using weighted voting. The weights were determined by the genetic algorithm that takes the success rate and predictive stability of three CNN models into account, the model was named GAEnsemble. GAEnsemble achieved the highest classification accuracy of 98.81% for D0 dataset. For the sake of robustness ensembled model, without changing the initial best performing CNN models on D0, the process was repeated by using two more datasets such that SMALL dataset with 10 classes and IP102 dataset with 102 classes. The accuracy values for GAEnsemble are 95.15% for SMALL dataset and 67.13% for IP102. In terms of performance metrics, GAEnsemble is competitive compared to the literature for each of these three datasets.
Design and Analysis of a Novel Authorship Verification Framework for Hijacked Social Media Accounts Compromised by a Human
(Wiley-Hindawi, 2021) Alterkavi, Suleyman; Erbay, Hasan
Compromising the online social network account of a genuine user, by imitating the user's writing trait for malicious purposes, is a standard method. Then, when it happens, the fast and accurate detection of intruders is an essential step to control the damage. In other words, an efficient authorship verification model is a binary classification for the investigation of the text, whether it is written by a genuine user or not. Herein, a novel authorship verification framework for hijacked social media accounts, compromised by a human, is proposed. Significant textual features are derived from a Twitter-based dataset. They are composed of 16124 tweets with 280 characters crawled and manually annotated with the authorship information. XGBoost algorithm is then used to highlight the significance of each textual feature in the dataset. Furthermore, the ELECTRE approach is utilized for feature selection, and the rank exponent weight method is applied for feature weighting. The reduced dataset is evaluated with many classifiers, and the achieved result of the F-score is 94.4%.
Detection of breast cancer via deep convolution neural networks using MRI images
(SPRINGER, 2020) Yurttakal, Ahmet Hasim; Erbay, Hasan; Ikizceli, Turkan; Karacavus, Seyhan
Breast cancer is the type of cancer that develops from cells in the breast tissue. It is the leading cancer in women. Early detection of the breast cancer tumor is crucial in the treatment process. Mammography is a valuable tool for identifying breast cancer in the early phase before physical symptoms develop. To reduce false-negative diagnosis in mammography, a biopsy is recommended for lesions with greater than a 2% chance of having suspected malignant tumors and, among them, less than 30 percent are found to have malignancy. To decrease unnecessary biopsies, recently, Magnetic Resonance Imaging (MRI) has also been used to diagnose breast cancer. MRI is the highly recommended test for detecting and monitoring breast cancer tumors and interpreting lesioned regions since it has an excellent capability for soft tissue imaging. However, it requires an experienced radiologist and time-consuming process. On the other hand, convolutional neural networks (CNNs) have demonstrated better performance in image classification compared to feature-based methods and show promising performance in medical imaging. Herein, CNN was employed to characterize lesions as malignant or benign tumors using MRI images. Using only pixel information, a multi-layer CNN architecture with online data augmentation was designed. Later, the CNN architecture was trained and tested. The accuracy of the network is 98.33% and the error rate 0.0167. The sensitivity of the network is 1.0 whereas specificity is 0.9688. The precision is 0.9655.
Detection of hand osteoarthritis from hand radiographs using convolutional neural networks with transfer learning
(TUBITAK SCIENTIFIC & TECHNICAL RESEARCH COUNCIL TURKEY, 2020) Ureten, Kemal; Erbay, Hasan; Maras, Hadi Hakan
Osteoarthritis is the most common type of arthritis. Hand osteoarthritis leads to specific structural changes in the joints, such as asymmetric joint space narrowing and osteophytes (bone spurs). Conventional radiography has traditionally been the primary method of visualizing these structural changes and diagnosing osteoarthritis. We aimed to develop a computerized method that is capable of determining the structural changes seen in radiography of the hand and to assist practitioners in interpreting radiographic changes and diagnosing the disease. In this retrospective study, transfer-learning-based convolutional neural networks were trained on a randomly selected dataset containing 332 radiography images of hands from an original set of 420 and were validated with the remaining 88. Multilayer convolutional neural network models were designed based on a transfer learning method using pretrained AlexNet, GoogLeNet, and VGG-19 networks. The accuracies of the models were 93.2% for AlexNet, 94.3% for GoogLeNet, and 96.6% for VGG-19. The sensitivities of these models were 0.9167 for AlexNet, 0.9184 for GoogLeNet, and 0.9574 for VGG-19, while the specificity values were 0.9500, 0.9744, and 0.9756, respectively. The performance metrics, including accuracy, sensitivity, specificity, and precision, of our newly developed automated diagnosis methods are promising in the diagnosis of hand osteoarthritis. Our computer-aided detection systems may help physicians in interpreting hand radiography images, diagnosing osteoarthritis, and saving time.
Detection of rheumatoid arthritis from hand radiographs using a convolutional neural network
(SPRINGER LONDON LTD, 2020) Ureten, Kemal; Erbay, Hasan; Maras, Hadi Hakan
Introduction Plain hand radiographs are the first-line and most commonly used imaging methods for diagnosis or differential diagnosis of rheumatoid arthritis (RA) and for monitoring disease activity. In this study, we used plain hand radiographs and tried to develop an automated diagnostic method using the convolutional neural networks to help physicians while diagnosing rheumatoid arthritis. Methods A convolutional neural network (CNN) is a deep learning method based on a multilayer neural network structure. The network was trained on a dataset containing 135 radiographs of the right hands, of which 61 were normal and 74 RA, and tested it on 45 radiographs, of which 20 were normal and 25 RA. Results The accuracy of the network was 73.33% and the error rate 0.0167. The sensitivity of the network was 0.6818; the specificity was 0.7826 and the precision 0.7500. Conclusion Using only pixel information on hand radiographs, a multi-layer CNN architecture with online data augmentation was designed. The performance metrics such as accuracy, error rate, sensitivity, specificity, and precision state shows that the network is promising in diagnosing rheumatoid arthritis.
Determination of the severity level of yellow rust disease in wheat by using convolutional neural networks
(Springer, 2021) Hayit, Tolga; Erbay, Hasan; Varcin, Fatih; Hayit, Fatma; Akci, Nilufer
Yellow rust disease caused by Puccinia striiformis f. sp. tritici, a pathogen in wheat, results in significant losses in wheat production worldwide due to its high destructive property. On the other side, yellow rust can be taken under control by growing resistant cultivars, by the application of fungicides, and by the use of appropriate cultural practices. Thus, it is crucial to detect the disease at an early stage. The current study offers to use computerized models in determining the infection type of yellow rust disease in wheat. Herein, a deep convolutional neural networks-based model, named Yellow-Rust-Xception, was proposed. The model inputs the wheat leaf image and classifies it as no disease, resistant, moderately resistant, moderately susceptible, or susceptible according to the rust severity, i.e. percentage. The convolutional neural networks, a state-of-art approach, have layered structures those inspired by the human brain and able to learn discriminative features from data automatically; thus networks performance match and even surpass humans in task-specific applications, a newly developed dataset containing yellow rust-infected wheat leaf images, was used to train, validate, and test Yellow-Rust-Xception, in result, the test accuracy was 91%. Thus, Yellow-Rust-Xception can be used in determining wheat yellow rust and its severity level.
Diagnosing breast cancer tumors using stacked ensemble model
(Ios Press, 2022) Yurttakal, Ahmet Hasim; Erbay, Hasan; Ikizceli, Turkan; Karacavus, Seyhan; Bicer, Cenker
Breast cancer is the most common cancer that progresses from cells in the breast tissue among women. Early-stage detection could reduce death rates significantly, and the detection-stage determines the treatment process. Mammography is utilized to discover breast cancer at an early stage prior to any physical sign. However, mammography might return false-negative, in which case, if it is suspected that lesions might have cancer of chance greater than two percent, a biopsy is recommended. About 30 percent of biopsies result in malignancy that means the rate of unnecessary biopsies is high. So to reduce unnecessary biopsies, recently, due to its excellent capability in soft tissue imaging, Dynamic Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) has been utilized to detect breast cancer. Nowadays, DCE-MRI is a highly recommended method not only to identify breast cancer but also to monitor its development, and to interpret tumorous regions. However, in addition to being a time-consuming process, the accuracy depends on radiologists' experience. Radiomic data, on the other hand, are used in medical imaging and have the potential to extract disease characteristics that can not be seen by the naked eye. Radiomics are hard-coded features and provide crucial information about the disease where it is imaged. Conversely, deep learning methods like convolutional neural networks(CNNs) learn features automatically from the dataset. Especially in medical imaging, CNNs' performance is better than compared to hard-coded features-based methods. However, combining the power of these two types of features increases accuracy significantly, which is especially critical in medicine. Herein, a stacked ensemble of gradient boosting and deep learning models were developed to classify breast tumors using DCE-MRI images. The model makes use of radiomics acquired from pixel information in breast DCE-MRI images. Prior to train the model, radiomics had been applied to the factor analysis to refine the feature set and eliminate unuseful features. The performance metrics, as well as the comparisons to some well-known machine learning methods, state the ensemble model outperforms its counterparts. The ensembled model's accuracy is 94.87% and its AUC value is 0.9728. The recall and precision are 1.0 and 0.9130, respectively, whereas F1-score is 0.9545.
Discrimination of malignant and benign breast masses using computer-aided diagnosis from dynamic contrast-enhanced magnetic resonance imaging
(Galenos, 2021) Ikizceli, Turkan; Karacavus, Seyhan; Erbay, Hasan; Yurttakal, Ahmet
Aim: To reduce operator dependency and achieve greater accuracy, the computer-aided diagnosis (CAD) systems are becoming a useful tool for detecting noninvasively and determining tissue characterization in medical images. We aimed to suggest a CAD system in discriminating between benign and malignant breast masses. Methods: The dataset was composed of 105 randomly breast magnetic resonance imaging (MRI) including biopsy-proven breast lesions (53 malignant, 52 benign). The expectation-maximization (EM) algorithm was used for image segmentation. 2D-discrete wavelet transform was applied to each region of interests (ROIs). After that, intensity-based statistical and texture matrix-based features were extracted from each of the 105 ROIs. Random Forest algorithm was used for feature selection. The final set of features, by random selection base, splatted into two sets as 80% training set (84 MRI) and 20% test set (21 MRI). Three classification algorithms are such that decision tree (DT, C4.5), naive bayes (NB), and linear discriminant analysis (LDA) were used. The accuracy rates of algorithms were compared. Results: C4.5 algorithm classified 20 patients correctly with a success rate of 95.24%. Only one patient was misclassified. The NB classified 19 patients correctly with a success rate of 90.48%. The LDA Algorithm classified 18 patients correctly with a success rate of 85.71%. Conclusion: The CAD equipped with the EM segmentation and C4.5 DT classification was successfully distinguished benign and malignant breast tumor on MRI. © 2021 by The Medical Bulletin of İstanbul Haseki Training and Research Hospital The Medical Bulletin of Haseki published by Galenos Yayınevi.
An efficient algorithm for rank and subspace tracking
(Pergamon-Elsevier Science Ltd, 2006) Erbay, Hasan
Traditionally, the singular value decomposition (SVD) has been used in rank and subspace tracking methods. However, the SVD is computationally costly, especially when the problem is recursive in nature and the size of the matrix is large. The truncated ULV decomposition (TULV) is an alternative to the SVD. It provides a good approximation to subspaces for the data matrix and can be modified quickly to reflect changes in the data. It also reveals the rank of the matrix. This paper presents a TULV updating algorithm. The algorithm is most efficient when the matrix is of low rank. Numerical results are presented that illustrate the accuracy of the algorithm. (c) 2006 Elsevier Ltd. All rights reserved.

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