Retinal Vessel Segmentation Using the 2-D Morlet Wavelet and Supervised Classification

We present a method for automated segmentation of the vasculature in retinal images. The method produces segmentations by classifying each image pixel as vessel or non-vessel, based on the pixel's feature vector. Feature vectors are composed of the pixel's intensity and continuous two-dimensional Morlet wavelet transform responses taken at multiple scales. The Morlet wavelet is capable of tuning to specific frequencies, thus allowing noise filtering and vessel enhancement in a single step. We use a Bayesian classifier with class-conditional probability density functions (likelihoods) described as Gaussian mixtures, yielding a fast classification, while being able to model complex decision surfaces and compare its performance with the linear minimum squared error classifier. The probability distributions are estimated based on a training set of labeled pixels obtained from manual segmentations. The method's performance is evaluated on publicly available DRIVE and STARE databases of manually labeled non-mydriatic images. On the DRIVE database, it achieves an area under the receiver operating characteristic (ROC) curve of 0.9598, being slightly superior than that presented by the method of Staal et al.Comment: 9 pages, 7 figures and 1 table. Accepted for publication in IEEE Trans Med Imag; added copyright notic

In vivo morphometric and mechanical characterization of trabecular bone from high resolution magnetic resonance imaging

La osteoporosis es una enfermedad ósea que se manifiesta con una menor densidad ósea y el deterioro de la arquitectura del hueso esponjoso. Ambos factores aumentan la fragilidad ósea y el riesgo de sufrir fracturas óseas, especialmente en mujeres, donde existe una alta prevalencia. El diagnóstico actual de la osteoporosis se basa en la cuantificación de la densidad mineral ósea (DMO) mediante la técnica de absorciometría dual de rayos X (DXA). Sin embargo, la DMO no puede considerarse de manera aislada para la evaluación del riesgo de fractura o los efectos terapéuticos. Existen otros factores, tales como la disposición microestructural de las trabéculas y sus características que es necesario tener en cuenta para determinar la calidad del hueso y evaluar de manera más directa el riesgo de fractura. Los avances técnicos de las modalidades de imagen médica, como la tomografía computarizada multidetector (MDCT), la tomografía computarizada periférica cuantitativa (HR-pQCT) y la resonancia magnética (RM) han permitido la adquisición in vivo con resoluciones espaciales elevadas. La estructura del hueso trabecular puede observarse con un buen detalle empleando estas técnicas. En particular, el uso de los equipos de RM de 3 Teslas (T) ha permitido la adquisición con resoluciones espaciales muy altas. Además, el buen contraste entre hueso y médula que proporcionan las imágenes de RM, así como la utilización de radiaciones no ionizantes sitúan a la RM como una técnica muy adecuada para la caracterización in vivo de hueso trabecular en la enfermedad de la osteoporosis. En la presente tesis se proponen nuevos desarrollos metodológicos para la caracterización morfométrica y mecánica del hueso trabecular en tres dimensiones (3D) y se aplican a adquisiciones de RM de 3T con alta resolución espacial. El análisis morfométrico está compuesto por diferentes algoritmos diseñados para cuantificar la morfología, la complejidad, la topología y los parámetros de anisotropía del tejido trabecular. En cuanto a la caracterización mecánica, se desarrollaron nuevos métodos que permiten la simulación automatizada de la estructura del hueso trabecular en condiciones de compresión y el cálculo del módulo de elasticidad. La metodología desarrollada se ha aplicado a una población de sujetos sanos con el fin de obtener los valores de normalidad del hueso esponjoso. Los algoritmos se han aplicado también a una población de pacientes con osteoporosis con el fin de cuantificar las variaciones de los parámetros en la enfermedad y evaluar las diferencias con los resultados obtenidos en un grupo de sujetos sanos con edad similar.Los desarrollos metodológicos propuestos y las aplicaciones clínicas proporcionan resultados satisfactorios, presentando los parámetros una alta sensibilidad a variaciones de la estructura trabecular principalmente influenciadas por el sexo y el estado de enfermedad. Por otra parte, los métodos presentan elevada reproducibilidad y precisión en la cuantificación de los valores morfométricos y mecánicos. Estos resultados refuerzan el uso de los parámetros presentados como posibles biomarcadores de imagen en la enfermedad de la osteoporosis.Alberich Bayarri, Á. (2010). In vivo morphometric and mechanical characterization of trabecular bone from high resolution magnetic resonance imaging [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8981Palanci

Fractal dimension: analyzing its potential as a neuroimaging biomarker for brain tumor diagnosis using machine learning

Purpose: The main purpose of this study was to comprehensively investigate the potential of fractal dimension (FD) measures in discriminating brain gliomas into low-grade glioma (LGG) and high-grade glioma (HGG) by examining tumor constituents and non-tumorous gray matter (GM) and white matter (WM) regions.Methods: Retrospective magnetic resonance imaging (MRI) data of 42 glioma patients (LGG, n = 27 and HGG, n = 15) were used in this study. Using MRI, we calculated different FD measures based on the general structure, boundary, and skeleton aspects of the tumorous and non-tumorous brain GM and WM regions. Texture features, namely, angular second moment, contrast, inverse difference moment, correlation, and entropy, were also measured in the tumorous and non-tumorous regions. The efficacy of FD features was assessed by comparing them with texture features. Statistical inference and machine learning approaches were used on the aforementioned measures to distinguish LGG and HGG patients.Results: FD measures from tumorous and non-tumorous regions were able to distinguish LGG and HGG patients. Among the 15 different FD measures, the general structure FD values of enhanced tumor regions yielded high accuracy (93%), sensitivity (97%), specificity (98%), and area under the receiver operating characteristic curve (AUC) score (98%). Non-tumorous GM skeleton FD values also yielded good accuracy (83.3%), sensitivity (100%), specificity (60%), and AUC score (80%) in classifying the tumor grades. These measures were also found to be significantly (p < 0.05) different between LGG and HGG patients. On the other hand, among the 25 texture features, enhanced tumor region features, namely, contrast, correlation, and entropy, revealed significant differences between LGG and HGG. In machine learning, the enhanced tumor region texture features yielded high accuracy, sensitivity, specificity, and AUC score.Conclusion: A comparison between texture and FD features revealed that FD analysis on different aspects of the tumorous and non-tumorous components not only distinguished LGG and HGG patients with high statistical significance and classification accuracy but also provided better insights into glioma grade classification. Therefore, FD features can serve as potential neuroimaging biomarkers for glioma

Advanced Guided Whale Optimization Algorithm for Feature Selection in BlazePose Action Recognition

The BlazePose, which models human body skeletons as spatiotemporal graphs, has achieved fantastic performance in skeleton-based action identification. Skeleton extraction from photos for mobile devices has been made possible by the BlazePose system. A Spatial-Temporal Graph Convolutional Network (STGCN) can then forecast the actions. The Spatial-Temporal Graph Convolutional Network (STGCN) can be improved by simply replacing the skeleton input data with a different set of joints that provide more information about the activity of interest. On the other hand, existing approaches require the user to manually set the graph’s topology and then fix it across all input layers and samples. This research shows how to use the Statistical Fractal Search (SFS)-Guided whale optimization algorithm (GWOA). To get the best solution for the GWOA, we adopt the SFS diffusion algorithm, which uses the random walk with a Gaussian distribution method common to growing systems. Continuous values are transformed into binary to apply to the feature-selection problem in conjunction with the BlazePose skeletal topology and stochastic fractal search to construct a novel implementation of the BlazePose topology for action recognition. In our experiments, we employed the Kinetics and the NTU-RGB+D datasets. The achieved actiona accuracy in the X-View is 93.14% and in the X-Sub is 96.74%. In addition, the proposed model performs better in numerous statistical tests such as the Analysis of Variance (ANOVA), Wilcoxon signed-rank test, histogram, and times analysis

An investigation with fractial geometry analysis of time series

Thesis (Master)--Izmir Institute of Technology, Materials Science and Engineering, Izmir, 2005Includes bibliographical references (leaves: 83-84)Text in English; Abstract: Turkish and Englishxiii,94 leavesIn this thesis, three kinds of fractal dimensions, correlation dimension, Hausdorff dimension and box-counting dimension were used to examine time series. To demonstrate the universality of the method, ECG (Electrocardiogram) time series were chosen. The ECG signals consisted of ECGs of three persons in four states for two applications. States are normal, walk, rapid walk and run. These three people are selected from the same age, and height group to minimize variations. First application was made for approximately 1000 samples of size of ECG signals and the second for the whole of the measured ECG signals. Fractal dimension measurements under different conditions were carried out to find out whether these dimensions could discriminate the states under question. A total of 24 ECG signals were measured to determine their corresponding fractal dimensions through the above-mentioned methods. It was expected that fractal dimension values would indicate the states related to the different activities of the persons. Results show that no direct link was found connecting a certain dimension to a certain activity in a consistent manner. Furthermore, no congruence was also found among the three dimensions that were employed. According to these results, it can be stated that fractal dimension values on their own may not be sufficient to identify distinct cases hidden in time series. Time series analysis may be facilitated when additional tools and methods are utilized as well as fractal dimensions at detecting telltale signs in signals of different states

네트워크 프랙탈 성질에 기반한 금융시장 예측 및 거래전략

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2020. 8. 장우진.Extensive academic research was performed for the financial market as it is closely connected to practical economy. Research in traditional financial economics resulted in economic indicators and the econometrics was instrumental for quantitative research in financial market. However, it proved to be difficult to predict the market behavior as it is a result of complex interaction among many agents with their own agenda. An effective tool to predict a change in market would be beneficial for policy makers and market participants to assist them with rational and consistent decision making. On the other hand, inconsistent prediction would lead to a suboptimal and inconsistent market activity which sometimes result in sudden collapse in the market as it did in 2008 Financial crisis and 1997 Asian financial crisis. The purpose of this dissertation is to develop approach based on econophysics and machine learning to systematically analyze the financial market. The main focus of this dissertation involves the network structure of stock market. To predict the change in market behavior, it is critical to understand the relationship or correlation among the market participants beforehand, and complex network analysis is one of the most prominent methods for such study. The fractal theory was employed as the primary approach to analyze the network structure of financial market. The empirical study shows that the network of financial market exhibits fractal properties. Also, analysis of fractal dimension and network topology led to two key discoveries. First, the fractal dimension and the Strong effective repulsion between distinct network nodes known as the hub are closely related. Second, the fractal dimension reveals the shortcut of network structure. Through further analysis, these two properties were proved to be useful for risk management in financial market. Three fractal measures were proposed to specify network structure for ease of implementation in future studies. In the second step, the fractal measures were implemented in a financial market to assess its ability to predict the market movement. Recently, studies were conducted to determine if a new measure or index improves the prediction accuracy for financial time series. These studies are advantageous for future studies as it proposes new indices for other implementation and further analysis rather than studying the precision of their own method. In this paper, machine learning algorithms were employed to assess the predictive properties of fractal measures. Empirical experiments were performed to predict direction of market movement, which is effectively a classification task, and prediction for returns, a regression task. The studies concludes that the fractal measure proposed were effective in prediction for long-term stock returns of more than three months period. Finally, a model to improve trading strategy based on learning-to-rank algorithm and the fractal measures was introduced. Previous studies are often based on the modern portfolio theory(MPT), but it is insufficient for real-world application as it doesnt provide any implication for rebalancing period of portfolio. The optimal rebalancing model proposed in this study allows its application with traditional portfolio methods. The experiments were carried out in two steps. The model learns to predict the better time period to perform rebalancing between two time periods in the future, followed by the empirical simulation to apply the model in real world trading scenario. Two traditional portfolio methods, equal weighted and maximized Sharpe ratio, were taken for experiment. The result affirms that the optimal rebalancing model was able to capture the better time period of rebalancing portfolio. In addition, the model outperformed a simple rebalancing method of fixed time period. When the fractal measures were employed as an input variable, the model performance was further improved. The primary contribution achieved through this model is that it allows application and expansion into all traditional portfolio models. Also, the fractal measures observed in the network structure grants insight regarding the market behavior and empirically proved that the measure provides benefit in prediction for the real-world stock market.금융시장에 대한 연구는 전반적인 경제 활동과 밀접한 연관성이 있기 때문에, 다양한 학계의 지식들과 연계되어 광범위하게 연구되고 있다. 전통적인 경제학 이론을 바탕으로 여러가지 경제 지표들이 개발되었고, 계량경제학의 발전으로 이를 정량적으로 분석하는 연구가 진행되었다. 하지만, 서로 다른 특징을 갖는 시장참여자들의 행위로 이루어진 금융시장의 복잡한 특성 때문에, 기존의 경제학 기반의 방법론들만으로 금융시장의 변화를 정밀하게 예측하기에는 한계가 있었다. 만약 금융시장의 변화를 효율적으로 예측 할 수 있다면, 국가 정책이나 기업들 및 시장 참여자들은 합리적인 의사결정을 통해서 건전한 금융 활동을 할 수 있을 것이다. 반면에 이러한 금융시장의 변화를 효율적으로 예측하지 못해 비이상적인 금융 활동이 지속된다면, 최악의 경우에는 글로벌 금융 위기와 같은 대규모 시장 붕괴 현상이 발생할 수 있을 것이아. 따라서 본 학위논문에서는 경제물리학과 머신러닝을 융합하여 체계적으로 금융시장 분석을 진행하고자 한다. 본 학위논문에서는 금융시장의 다양한 섹터 중에서 주식시장 네트워크 구조를 분석하는데 초점을 맞춘다. 미래의 주식시장의 변화를 올바르게 예측하기 위해서는 주식시장 구성원들간의 관계 파악이 선행되어야 하는데, 이에 대표적인 분석 방법이 복잡계 네트워크 분석(Complex network analysis)이기 때문이다. 본 연구에서는 주식시장 네트워크 구조를 분석하는 여러 방법론들 중 프랙탈 이론(Fractal theory)의 도입을 제안한다. 실험 결과 주식시장 네트워크의 구조는 프랙탈 특성을 가짐을 밝혀냈다. 또한, 측정된 프랙탈 차원(Fractal dimension)과 네트워크의 토폴로지(Topology)와의 관계를 살펴본 결과 두 가지 주요한 주식시장 네트워크의 구조적인 특징을 발견할 수 있었다. 첫번째는, 프랙탈 차원과 소위 허브(Hub)라고 불리우는 네트워크 상에서 연결이 많이된 노드들간의 강한 반발(Strong effective repulsion) 현상과 연관성이 있다는 점이다. 두번째는, 프랙탈 차원으로 네트워크의 지름길(Shortcut) 구조를 관찰할 수 있었다. 또한 이 두 가지 네트워크의 구조적인 특성은 주식시장의 위험 관리(Risk management) 관점에서 유용하게 쓰일 수 있음을 분석했다. 그리고, 위 특성들을 다른 연구들에 쉽게 적용 가능하도록 네트워크 구조를 표현하는 3가지 프랙탈 지표(Fractal measures)들을 제안한다. 다음 단계로 주식시장에서 측정한 프랙탈 지표가 미래에 주가 지수의 예측력 향상에 도움이 되는지를 검증했다. 최근 다양한 분야에서 새롭게 발견한 지표들이 금융 시계열 데이터에 대하여 예측력 향상에 도움이 되는지를 검증하는 연구들이 진행되고있다. 이러한 연구들은 발견한 지표들 만을 사용하여 정밀한 예측을 하는 목적이 아닌, 발견한 지표들이 예측력 향상에 도움이 된다는 점을 밝혀내는데 주 목적이 있다. 이렇게 예측력 향상이 있는것이 밝혀진 지표들은 다른 연구나 산업에 쉽게 적용할 수 있는 장점이 있다. 본 학위논문에서는 몇 가지 머신러닝 알고리즘을 활용하여 측정한 프랙탈 지표가 미래의 주가 지수의 예측력 향상에 도움이 되는지를 검증했다. 검증 실험은 가장 단순한 미래 주가 지수의 방향 분류(Classification) 부터, 주가 지수 수익률의 예측(Prediction) 까지 이루어진다. 그 결과 제안한 프랙탈 지표들은 약 3개월 이후의 장기 미래의 주가 지수에 대해 일관성있는 예측력 향상 효과가 있음을 밝혀냈다. 마지막으로 제안한 프랙탈 지표들과 Learning-to-rank 알고리즘을 활용하여 기존의 주식시장에 연구되었던 거래 전략(Trading strategy)의 성능을 개선할 수 있는 모델을 제안한다. 기존의 주식시장에서 연구된 거래 전략들 중 큰 비율을 차지하는 연구들은 현대 포트폴리오 이론(Modern portfolio theory)에 기반한 포트폴리오 구성 방법에 대한 연구들이다. 하지만, 실제 투자에 적용하기 위해서는 포트폴리오를 구성하는 방법론 뿐 만 아니라, 언제 포트폴리오를 재구성해야 하는지를 판단하는것 또한 중요한 의사결정 요소이다. 본 학위논문에서 제안하는 모델은 기존에 연구된 방법론들에 유연하게 접목하여 활용할 수 있는 최적 리밸런싱 시점 판단 모델(Optimal rebalancing model)이다. 실험은 두단계로 진행된다. 먼저, 제안한 모델로 학습 데이터 내의 서로 다른 두 시점 중 미래의 더 나은 성능을 보이는 리밸런싱 지점을 예측할수 있는지를 학습한다. 그후에, 학습된 모델들 중 좋은 성능을 갖는 파라미터를 선택하고, 시뮬레이션 분석을 통해서 실제 거래전략에 적용 가능성을 평가한다. 실험에서 사용된 기존의 포트폴리오 구성 방법론은, 관련 연구들에서 가장 대표적인 벤치마크로 활용되는 자산 균등 분배 포트폴리오 방식과 샤프 비율(Sharpe ratio) 최대화 포트폴리오 방식이다. 실험결과 두 방식 모두에서 본 연구에서 제안한 최적 리밸런싱 시점 판단 모델이 더 나은 포트폴리오 구성 시점을 구해냈다. 또한 시뮬레이션 결과 일정주기로 리밸런싱하는 동일한 포트폴리오 구성방식보다 더 나은 성능을 보였다. 특히 입력 변수로 프랙탈 지표들을 추가했을 때 가장 좋은 성능을 보임을 관찰했다. 본 모델은 연구된 기존의 모든 포트폴리오 구성 방법론들에 적용할 수 있는 확장성의 관점에서 중요한 기여가 있다. 그리고 프랙탈 지표를 통해서 관찰되는 네트워크의 구조적 특징들이 미래 시장을 판단하는데 도움이 됨을 보임으로써, 제안한 프랙탈 지표들이 실제 주식시장에 적용 가능한 실용적인 특성을 나타냄도 검증했다.Chapter 1 Introduction 1 1.1 Research Motivation and Purpose 1 1.2 Organization of the Research 5 Chapter 2 Literature Review 7 2.1 Complex Network 7 2.2 Market Prediction with Machine Learning 8 2.3 Trading Strategies 11 Chapter 3 Fractal Structure in Stock Market 13 3.1 Network Fractality 13 3.1.1 Threshold Network 13 3.1.2 Fractal Dimension 15 3.1.3 Fractal Measures 17 3.2 Fractal Analysis on Stock Market 21 3.2.1 Data Description 21 3.2.2 Fractality of S&P500 Network 25 3.2.3 Network Topology and Fractal Measures 27 3.3 Summary and Discussion 43 Chapter 4 Stock Market Prediction with Fractality 45 4.1 Classification of Stock Market 45 4.1.1 Classification Model 45 4.1.2 Classification Results 50 4.2 Fractal Measures and Predictive Power 55 4.2.1 Prediction of Stock Market Return 55 4.2.2 Parameter Analysis 59 4.2.3 Predictive Power Results 60 4.3 Summary and Discussion 66 Chapter 5 Trading Strategy with Optimal Rebalancing Model 69 5.1 Optimal Rebalancing Model 69 5.1.1 Portfolio Selection Method 69 5.1.2 Learning-to-rank algorithm 71 5.1.3 Proposed Modeling Method 73 5.1.4 Model Results 77 5.2 Simulation Analysis 84 5.2.1 Simulation Structure 84 5.2.2 Simulation Results 88 5.3 Summary and Discussion 101 Chapter 6 Conclusion 103 6.1 Conclusions 103 6.2 Future Works 106 Bibliography 107 국문초록 117Docto