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Fractal Based Information Processing and Recognition

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Computing and Artificial Intelligence".

Deadline for manuscript submissions: closed (30 June 2018) | Viewed by 41218

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Special Issue Editors

Prof. Dr. Shuai Liu

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Guest Editor

College of Computer Science, Inner Mongolia University, Hohhot 010010, China
Interests: fractal; computer vision; information recognition
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Carlo Cattani

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Engineering School (DEIM), University of Tuscia, Largo dell'Università, 01100 Viterbo, Italy
Interests: wavelets; fractals; fractional and stochastic equations; numerical and computational methods; mathematical physics; nonlinear systems; artificial intelligence
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Yudong Zhang

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Guest Editor

Informatics Building School of Informatics, University of Leicester, Leicester LE1 7RH, UK
Interests: deep learning; artificial intelligence; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Since Mandelbrot integrated and provided fractal theory, it was soon applied as a characteristic of complex information, and used in many research domains. Today, fractal theory is widely used in combination with dynamical system, chaos, and fractional dimensions.

Except for the theory of fractals, fractal-based applications have also been successfully applied in the analysis of complex natural or engineering phenomenon, especially in empirical description of information with complex structures. For example, a great deal of thermodynamic information can be analyzed using fractal-based methods. Moreover, the biological information of many species can be discovered using fractal analysis. In addition, fractal-based information analysis and processing can be used in information encoding, compression, recognition, extraction, and so on. In fact, fractal compression can compress information with a very high compression ratio, which is higher than classical compression methods by several times, or even more. Fractal-based classification and recognition and recognition method are also used in bioinformatics, geology, and other domains of natural science.

Since fractal-based methods have started to occupy a central place in information processing and recognition domains today, this Special Issue aims to provide an opportunity for researchers to publish their fractal-based studies in information processing and recognition. All accepted papers must have original research results, as well as excellent engineering applications.

Prof. Dr. Carlo Cattani
Prof. Dr. Shuai Liu
Prof. Dr. Yudong Zhang
Guest Editors

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Keywords

Fractal
Fractal Information Processing
Fractal Recognition
Fractal Classification
Fractal Encoding

Published Papers (10 papers)

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Editorial

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4 pages, 156 KiB

Open AccessEditorial

Introduction of Fractal Based Information Processing and Recognition

by Shuai Liu, Carlo Cattani and Yudong Zhang

Appl. Sci. 2019, 9(7), 1297; https://doi.org/10.3390/app9071297 - 28 Mar 2019

Viewed by 1837

Abstract

Fractal characteristic, one typical nonlinear characteristic, is applied as a key characteristic in complex information processing and used in many research domains [...] Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

Research

Jump to: Editorial

17 pages, 3283 KiB

Open AccessArticle

Hybrid Models Combining Technical and Fractal Analysis with ANN for Short-Term Prediction of Close Values on the Warsaw Stock Exchange

by Michał Paluch and Lidia Jackowska-Strumiłło

Appl. Sci. 2018, 8(12), 2473; https://doi.org/10.3390/app8122473 - 03 Dec 2018

Cited by 9 | Viewed by 3554

Abstract

This paper presents new methods and models for forecasting stock prices and computing hybrid models, combining analytical and neural approaches. First, technical and fractal analyses are conducted and selected stock market indices calculated, such as moving averages and oscillators. Next, on the basis of these indices, an artificial neural network (ANN) provides predictions one day ahead of the closing prices of the assets. New technical analysis indicators using fractal modeling are also proposed. Three kinds of hybrid model with different degrees of fractal analysis were considered. The new hybrid modeling approach was compared to previous ANN-based prediction methods. The results showed that the hybrid model with fractal analysis outperforms other models and is more robust over longer periods of time. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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14 pages, 4178 KiB

Open AccessArticle

Different Soil Particle-Size Classification Systems for Calculating Volume Fractal Dimension—A Case Study of Pinus sylvestris var. Mongolica in Mu Us Sandy Land, China

by Jifeng Deng, Chengzhong Ma and Hongzhou Yu

Appl. Sci. 2018, 8(10), 1872; https://doi.org/10.3390/app8101872 - 10 Oct 2018

Cited by 16 | Viewed by 3596

Abstract

Characterizing changes in the soil particle-size distributions (PSD) are a major issue in environmental research because it has a great impact on soil properties, soil management, and desertification. To date, the use of soil volume fractal dimension (D) is a feasible approach to describe PSD, and its calculation is mainly dependent on subdivisions of clay, silt, sand fractions as well as different soil particle-size classification (PSC) systems. But few studies have developed appropriate research works on how PSC systems affect the calculations of D. Therefore, in this study, topsoil (0–5 cm) across nine forest density gradients of Pinus sylvestris var. mongolica plantations (MPPs) ranging from 900–2700 trees ha^–1 were selected in the Mu Us sandy land, China. The D of soil was calculated by measuring soil PSD through fractal model and laser diffraction technique. The experimental results showed that: (1) The predominant PSD was distributed within the sand classification followed by clay and silt particle contents, which were far less prevalent in the study area. The general order of D values (Ds) was USDA (1993) > ISO14688 (2002) > ISSS (1929) > Katschinski (1957) > China (1987) > Blott & Pye (2012) PSC systems. (2) Ds were significantly positively related to the contents of clay and silt, and Ds were significantly negatively to the sand content. Ds were susceptible to the MPPs establishment and forest densities. (3) Ds of six PSC systems were significantly positive correlated, which indicated that they not only have difference, but also have close connection. (4) According to the fractal model and descriptions of soil fractions under different PSC systems, refining scales of clay and sand fractions could increase Ds, while the refining scale of silt fraction could decrease Ds. From the conclusions above, it is highly recommended that USDA (1993) and Blott & Pye (2012) PSC systems be used as reliable and practical PSC systems for describing and calculating D of soil PSD. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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10 pages, 1968 KiB

Open AccessArticle

GARLM: Greedy Autocorrelation Retrieval Levenberg–Marquardt Algorithm for Improving Sparse Phase Retrieval

by Zhuolei Xiao, Yerong Zhang, Kaixuan Zhang, Dongxu Zhao and Guan Gui

Appl. Sci. 2018, 8(10), 1797; https://doi.org/10.3390/app8101797 - 01 Oct 2018

Cited by 4 | Viewed by 2803

Abstract

The goal of phase retrieval is to recover an unknown signal from the random measurements consisting of the magnitude of its Fourier transform. Due to the loss of the phase information, phase retrieval is considered as an ill-posed problem. Conventional greedy algorithms, e.g., greedy spare phase retrieval (GESPAR), were developed to solve this problem by using prior knowledge of the unknown signal. However, due to the defect of the Gauss–Newton method in the local convergence problem, especially when the residual is large, it is very difficult to use this method in GESPAR to efficiently solve the non-convex optimization problem. In order to improve the performance of the greedy algorithm, we propose an improved phase retrieval algorithm, which is called the greedy autocorrelation retrieval Levenberg–Marquardt (GARLM) algorithm. Specifically, the proposed GARLM algorithm is a local search iterative algorithm to recover the sparse signal from its Fourier transform magnitude. The proposed algorithm is preferred to existing greedy methods of phase retrieval, since at each iteration the problem of minimizing the objective function over a given support is solved by using the improved Levenberg–Marquardt (ILM) method and matrix transform. A local search procedure such as the 2-opt method is then invoked to get the optimal estimation. Simulation results are given to show that the proposed algorithm performs better than the conventional GESPAR algorithm. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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15 pages, 2440 KiB

Open AccessArticle

Signal Pattern Recognition Based on Fractal Features and Machine Learning

by Chang-Ting Shi

Appl. Sci. 2018, 8(8), 1327; https://doi.org/10.3390/app8081327 - 08 Aug 2018

Cited by 48 | Viewed by 7543

Abstract

As a typical pattern recognition method, communication signal modulation involves many complicated factors. Fractal theory can be used for signal modulation feature extraction and recognition because of its good ability to express complex information. In this paper, we conduct a systematic research study by using the fractal dimension as the feature of modulation signals. Box fractal dimension, Katz fractal dimension, Higuchi fractal dimension, Petrosian fractal dimension, and Sevcik fractal dimension are extracted from eight different modulation signals for signal pattern recognition. Meanwhile, the anti-noise function, box-diagram, and running time are used to evaluate the noise robustness, separability, and computational complexity of five different fractal features. Finally, Bback-Propagation (BP) neural network, grey relation analysis, random forest, and K-nearest neighbor are proposed to classify the different modulation signals based on these fractal features. The confusion matrices and recognition results are provided in the experimental section. They indicate that random forest had a better recognition performance, which could reach 96% in 10 dB. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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13 pages, 2216 KiB

Open AccessArticle

Fractal Behavior of Particle Size Distribution in the Rare Earth Tailings Crushing Process under High Stress Condition

by Wen Zhong, Fucai Yue and Armando Ciancio

Appl. Sci. 2018, 8(7), 1058; https://doi.org/10.3390/app8071058 - 28 Jun 2018

Cited by 15 | Viewed by 2935

Abstract

To disclose the fractal transformation mechanism of the size distribution of rare earth tailing particles, this paper utilizes the side confined uniaxial compression test to study the evolution rule of the particle size distribution of the rare earth tailing and the particle breakage features under the high stress condition. The fractal behavior of the particle size distribution in the crushing process is studied based on the fractal model and the particle size distribution. The experimental results show that, under the high stress condition, the particle size distribution tends towards fractal distribution due to the particle breakage of the rare earth tailing. The crushing process is closely related to the breakage amount of the particles and can be described with the increased fractal dimension. Although the initial distribution and particle size of the rare earth tailings are different, the measured data of the particle size distribution with the fractal dimension greater than 2.2 shows fairly strict self-similarity, and this value can be taken as the lower limit value of the fractal dimension when the particle size distribution tends towards fractal distribution. When the particle size distribution becomes a fractal distribution due to the particle breakage, the ratio between the volumetric strain and the relative breakage rate remains constant and is slightly affected by the initial distribution uniformity and particle size. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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Graphical abstract

13 pages, 6502 KiB

Open AccessArticle

Synchronization of Chemical Synaptic Coupling of the Chay Neuron System under Time Delay

by Kaijun Wu, Dicong Wang, Chao Yu and Jose Tenreiro Machado

Appl. Sci. 2018, 8(6), 927; https://doi.org/10.3390/app8060927 - 04 Jun 2018

Cited by 12 | Viewed by 3821

Abstract

This paper studies the chemical synaptic coupling of Chay neurons and the effect of adding time delay on their synchronization behavior. The results indicate that coupling strength stimuli can affect the discharge activity and the synchronization behavior. In the absence of coupling strength, the Chay neurons have chaotic discharge behavior and the system is in a nonsynchronous state. When a certain coupling strength is added, the neurons change from chaotic discharge to ordered periodic discharge, and the system state changes from asynchronous to synchronous. On the other hand, a time lag can alter the coupled system from synchronous to asynchronous. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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Graphical abstract

16 pages, 4088 KiB

Open AccessArticle

An Automated Segmentation Method for Lung Parenchyma Image Sequences Based on Fractal Geometry and Convex Hull Algorithm

by Xiaojiao Xiao, Juanjuan Zhao, Yan Qiang, Hua Wang, Yingze Xiao, Xiaolong Zhang and Yudong Zhang

Appl. Sci. 2018, 8(5), 832; https://doi.org/10.3390/app8050832 - 21 May 2018

Cited by 15 | Viewed by 4236

Abstract

Statistically solitary pulmonary nodules are about 6% to 17% of juxtapleural nodules. The accurate segmentation of lung parenchyma sequences of juxtapleural nodules is the basis of subsequent pulmonary nodule segmentation and detection. In order to solve the problem of incomplete segmentation of the juxtapleural nodules and segmentation inefficiency, this paper proposes an automated framework to combine the threshold iteration method to segment the lung parenchyma images and the fractal geometry method to detect the depression boundary. The framework includes an improved convex hull repair to complete the accurate segmentation of the lung parenchyma. The evaluation results confirm that the proposed method can segment juxtapleural lung parenchymal images accurately and efficiently. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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15 pages, 656 KiB

Open AccessArticle

TRSDL: Tag-Aware Recommender System Based on Deep Learning–Intelligent Computing Systems

by Nan Liang, Hai-Tao Zheng, Jin-Yuan Chen, Arun Kumar Sangaiah and Cong-Zhi Zhao

Appl. Sci. 2018, 8(5), 799; https://doi.org/10.3390/app8050799 - 16 May 2018

Cited by 36 | Viewed by 4872

Abstract

In recommender systems (RS), many models are designed to predict ratings of items for the target user. To improve the performance for rating prediction, some studies have introduced tags into recommender systems. Tags benefit RS considerably, however, they are also redundant and ambiguous. In this paper, we propose a hybrid deep learning model TRSDL (tag-aware recommender system based on deep learning) to improve the performance of tag-aware recommender systems (TRS). First, TRSDL uses pre-trained word embeddings to represent user-defined tags, and constructs item and user profiles based on the items’ tags set and users’ tagging behaviors. Then, it utilizes deep neural networks (DNNs) and recurrent neural networks (RNNs) to extract the latent features of items and users, respectively. Finally, it predicts ratings from these latent features. The model not only addresses tag limitations and takes advantage of semantic tag information but also learns more advanced implicit features via deep structures. We evaluated our proposed approach and several baselines on MovieLens-20 m, and the experimental results demonstrate that TRSDL significantly outperforms all the baselines (including the state-of-the-art models BiasedMF and I-AutoRec). In addition, we also explore the impacts of network depth and type on model performance. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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15 pages, 3482 KiB

Open AccessArticle

Extraction of Coal and Gangue Geometric Features with Multifractal Detrending Fluctuation Analysis

by Kai Liu, Xi Zhang and YangQuan Chen

Appl. Sci. 2018, 8(3), 463; https://doi.org/10.3390/app8030463 - 17 Mar 2018

Cited by 34 | Viewed by 4788

Abstract

The separation of coal and gangue is an important process of the coal preparation technology. The conventional way of manual selection and separation of gangue from the raw coal can be replaced by computer vision technology. In the literature, research on image recognition and classification of coal and gangue is mainly based on the grayscale and texture features of the coal and gangue. However, there are few studies on characteristics of coal and gangue from the perspective of their outline differences. Therefore, the multifractal detrended fluctuation analysis (MFDFA) method is introduced in this paper to extract the geometric features of coal and gangue. Firstly, the outline curves of coal and gangue in polar coordinates are detected and achieved along the centroid, thereby the multifractal characteristics of the series are analyzed and compared. Subsequently, the modified local singular spectrum widths

Δ h

of the outline curve series are extracted as the characteristic variables of the coal and gangue for pattern recognition. Finally, the extracted geometric features by MFDFA combined with the grayscale and texture features of the images are compared with other methods, indicating that the recognition rate of coal gangue images can be increased by introducing the geometric features. Full article

(This article belongs to the Special Issue Fractal Based Information Processing and Recognition)

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