M. Alper Tunga

An approximation method to model multivariate interpolation problems: Indexing HDMR

Dealing with univariate or bivariate data sets instead of a multivariate data set is an important concern in interpolation problems and computer-based applications. This paper presents a new data partitioning method that partitions the given multivariate data set into univariate and bivariate data sets and constructs an approximate analytical structure that interpolates function values at arbitrarily distributed points of the given grid. A number of numerical implementations are also given to show the performance of this new method.

Emotion Recognition with Eigen Features of Frequency Band Activities Embedded in Induced Brain Oscillations Mediated by Affective Pictures

In this study, singular spectrum analysis (SSA) has been used for the first time in order to extract emotional features from well-defined electroencephalography (EEG) frequency band activities (BAs) so-called delta (0.5-4 Hz), theta (4-8 Hz), alpha (8-16 Hz), beta (16-32 Hz), gamma (32-64 Hz). These five BAs were estimated by applying sixth-level multi-resolution wavelet decomposition (MRWD) with Daubechies wavelets (db-8) to single channel nonaveraged emotional EEG oscillations of 6 s for each scalp location over 16 recording sites (Fp1, Fp2, F3, F4, F7, F8, C3, C4, P3, P4, T3, T4, T5, T6, O1, O2). Every trial was mediated by different emotional stimuli which were selected from international affective picture system (IAPS) to induce emotional states such as pleasant (P), neutral (N), and unpleasant (UP). Largest principal components (PCs) of BAs were considered as emotional features and data mining approaches were used for the first time in order to classify both three different (P, N, UP) and two contrasting (P and UP) emotional states for 30 healthy controls. Emotional features extracted from gamma BAs (GBAs) for 16 recording sites provided the high classification accuracies of 87.1% and 100% for classification of three emotional states and two contrasting emotional states, respectively. In conclusion, we found the followings: (1) Eigenspectra of high frequency BAs in EEG are highly sensitive to emotional hemispheric activations, (2) emotional states are mostly mediated by GBA, (3) pleasant pictures induce the higher cortical activation in contrast to unpleasant pictures, (4) contrasting emotions induce opposite cortical activations, (5) cognitive activities are necessary for an emotion to occur.

A novel method for multivariate data modelling: Piecewise Generalized EMPR

A multivariate data modelling problem consists of a number of nodes with associated function values. Increase in multivariance urges us to use divide-and-conquer algorithms in modelling process of these problems. High dimensional model representation based methods can partition a given multivariate data set into less-variate data sets and have the ability of building a model through these partitioned data sets. Generalized HDMR (GHDMR) is one of these methods and it is known that it works well for dominantly and purely additive natures. Piecewise Generalized HDMR is an alternative method and was developed to increase the efficiency of GHDMR but the performance of the method for modelling multiplicative natures is still not sufficient and acceptable. This work aims to develop a new piecewise method based on enhanced multivariance product representation which works well for representing multiplicative natures.

Computational complexity investigations for high dimensional model representation algorithms used in multivariate interpolation problems

In multivariate interpolation problems, increase in both the number of independent variables of the sought function and the number of nodes appearing in the data set cause computational and mathematical difficulties. It may be a better way to deal with less variate partitioned data sets instead of an N-dimensional data set in a multivariate interpolation problem. New algorithms such as High Dimensional Model Representation (HDMR), Generalized HDMR, Factorized HDMR, Hybrid HDMR are developed or rearranged for these types of problems. Up to now, the efficiency of the methods in mathematical sense were discussed in several papers. In this work, the efficiency of these methods in computational sense will be discussed. This investigation will be done by using several numerical implementations.

Mutual Information Analysis of Sleep EEG in Detecting Psycho-Physiological Insomnia

The primary goal of this study is to state the clear changes in functional brain connectivity during all night sleep in psycho-physiological insomnia (PPI). The secondary goal is to investigate the usefulness of Mutual Information (MI) analysis in estimating cortical sleep EEG arousals for detection of PPI. For these purposes, healthy controls and patients were compared to each other with respect to both linear (Pearson correlation coefficient and coherence) and nonlinear quantifiers (MI) in addition to phase locking quantification for six sleep stages (stage.1–4, rem, wake) by means of interhemispheric dependency between two central sleep EEG derivations. In test, each connectivity estimation calculated for each couple of epoches (C3-A2 and C4-A1) was identified by the vector norm of estimation. Then, patients and controls were classified by using 10 different types of data mining classifiers for five error criteria such as accuracy, root mean squared error, sensitivity, specificity and precision. High performance in a classification through a measure will validate high contribution of that measure to detecting PPI. The MI was found to be the best method in detecting PPI. In particular, the patients had lower MI, higher PCC for all sleep stages. In other words, the lower sleep EEG synchronization suffering from PPI was observed. These results probably stand for the loss of neurons that then contribute to less complex dynamical processing within the neural networks in sleep disorders an the functional central brain connectivity is nonlinear during night sleep. In conclusion, the level of cortical hemispheric connectivity is strongly associated with sleep disorder. Thus, cortical communication quantified in all existence sleep stages might be a potential marker for sleep disorder induced by PPI.

Generalized Enhanced Multivariance Product Representation for Data Partitioning: Constancy Level

Enhanced Multivariance Product Representation (EMPR) method is used to represent multivariate functions in terms of less‐variate structures. The EMPR method extends the HDMR expansion by inserting some additional support functions to increase the quality of the approximants obtained for dominantly or purely multiplicative analytical structures. This work aims to develop the generalized form of the EMPR method to be used in multivariate data partitioning approaches. For this purpose, the Generalized HDMR philosophy is taken into consideration to construct the details of the Generalized EMPR at constancy level as the introductory steps and encouraging results are obtained in data partitioning problems by using our new method. In addition, to examine this performance, a number of numerical implementations with concluding remarks are given at the end of this paper.

A polynomial based algorithm for detection of embolism

The Transcranial Doppler ultrasound can be used to detect asymptomatic circulating cerebral emboli. Emboli indicate particles that can plug the arterial system. Asymptomatic emboli signals help to discover critical stroke events by taking the embolus activities into consideration. Cerebral emboli detection is searched deeply in the literature. But none of them proposed a polynomial method to generalize the solution of the emboli detection. High Dimensional Model Representation (HDMR) philosophy is an effective way of generating an analytical model for a given multivariate data modeling problem, that is, HDMR can be used in constructing a general polynomial model for detecting embolism. In this study, emboli related data set was collected from

Dosage planning for type 2 diabetes mellitus patients using Indexing HDMR

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