Cluster Validity Index to Determine the Optimal Number Clusters of Fuzzy Clustering for Classify Customer Buying Behavior

One of the strategies in order to compete in Batik  MSMEs  is to look at the characteristics of the customer. To make it easier to see the characteristics of  customer buying behavior, it is necessary to classify customers based on similarity of characteristics using fuzzy clustering. One of the parameters that must be determined at the beginning of the fuzzy clustering method is the number of clusters. Increasing the number of clusters does not guarantee the best performance, but the right number of clusters greatly affects the performance of fuzzy clustering. So to get optimal number cluster, we can measured the result of clustering in each number cluster using the cluster validity index. From several types of cluster validity index,  NPC give the best value. Optimal number cluster that obtained by the validity index is 2 and this number cluster give classify result with small variance valu

A novel fuzzy clustering approach to regionalise watersheds with an automatic determination of optimal number of clusters

One of the most important problems faced in hydrology is the estimation of flood magnitudes and frequencies in ungauged basins. Hydrological regionalisation is used to transfer information from gauged watersheds to ungauged watersheds. However, to obtain reliable results, the watersheds involved must have a similar hydrological behaviour. In this study, two different clustering approaches are used and compared to identify the hydrologically homogeneous regions. Fuzzy C-Means algorithm (FCM), which is widely used for regionalisation studies, needs the calculation of cluster validity indices in order to determine the optimal number of clusters. Fuzzy Minimals algorithm (FM), which presents an advantage compared with others fuzzy clustering algorithms, does not need to know a priori the number of clusters, so cluster validity indices are not used. Regional homogeneity test based on L-moments approach is used to check homogeneity of regions identified by both cluster analysis approaches. The validation of the FM algorithm in deriving homogeneous regions for flood frequency analysis is illustrated through its application to data from the watersheds in Alto Genil (South Spain). According to the results, FM algorithm is recommended for identifying the hydrologically homogeneous regions for regional frequency analysis.Ingeniería, Industria y Construcció

Fuzzy clustering and fuzzy c-means partition cluster analysis and validation studies on a subset of citescore dataset

A hard partition clustering algorithm assigns equally distant points to one of the clusters, where each datum has the probability to appear in simultaneous assignment to further clusters. The fuzzy cluster analysis assigns membership coefficients of data points which are equidistant between two clusters so the information directs have a place toward in excess of one cluster in the meantime. For a subset of CiteScore dataset, fuzzy clustering (fanny) and fuzzy c-means (fcm) algorithms were implemented to study the data points that lie equally distant from each other. Before analysis, clusterability of the dataset was evaluated with Hopkins statistic which resulted in 0.4371, a value < 0.5, indicating that the data is highly clusterable. The optimal clusters were determined using NbClust package, where it is evidenced that 9 various indices proposed 3 cluster solutions as best clusters. Further, appropriate value of fuzziness parameter m was evaluated to determine the distribution of membership values with variation in m from 1 to 2. Coefficient of variation (CV), also known as relative variability was evaluated to study the spread of data. The time complexity of fuzzy clustering (fanny) and fuzzy c-means algorithms were evaluated by keeping data points constant and varying number of clusters

Pomegranate MR image analysis using fuzzy clustering algorithms

In this paper, the process of the pomegranate magnetic resonance (MR) images was studied.  Its internal structure is composed of tissue and seeds, which indicate the dependency between the maturity and internal quality.  The latter properties are important in pomegranate’s sorting and cannot be measured manually.  In this paper, an automatic algorithm was proposed to segment the internal structure of pomegranates.  Since the intensities of the calyx and stem of the pomegranate MR image are closely related to that of the soft tissue, their corresponding pixels are therefore labeled in the same class of the internal soft tissues.  In order to solve this problem, the exact shape of the pomegranate is first extracted from the background of the image using active contour models (ACMs).  Then, the stem and calyx are removed using morphological filters.  We have also proposed an improved version of the fuzzy c-means algorithm (FCM), the spatial FCM (SFCM), for segmentation of MR images of pomegranate.  SFCM is realized by incorporating the spatial neighborhood information into the standard FCM and modifying the membership weighting of each cluster.  SFCM employs spatial information of adjacent pixels leading to an improvement of the results.  It thus outperforms other techniques like FCM, even in the presence of Gaussian, salt and pepper, and speckle noises. Keywords: MRI, pomegranate, image segmentation, spatial fuzzy c-means, morphological filter&nbsp

라이다 점군자료를 이용한 암반 불연속면 특성검출 자동화 연구

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 에너지시스템공학부, 2020. 8. 전석원.The technique for determining rock mass quality and its stability is an important issue often encountered in many engineering projects including open pit and underground mines, slopes, tunnels, dams and others. Hand-mapping has been widely used as a conventional way to collect information of rock mass and determine the rock mass class. Then, a quick, safe and objective way for assessment of rock mass quality is desired to maximize the efficiency and economic benefits of the task as well as to provide essential feedback for the design, construction and operation of engineering projects. In this study, a light detection and ranging (LiDAR) technique, which can acquire 3D point cloud information quickly and accurately, was used to compensate for the shortcomings of field geological hand-mapping methods (scan line survey, window mapping survey, etc.). The geological strength index (GSI) was assessed by quantifying the characteristics of rock discontinuity using the point cloud data obtained from LiDAR scan on rock slopes. A circular window was adopted to visually represent the distribution of rock mass quality in a target rock mass. Prior to rock discontinuity characterization using LiDAR, the most important step is to extract the discontinuities from the point cloud. Thus, a triangulated irregular network was constructed using the ball-pivoting algorithm. Then, a patch was extracted by defining a set of triangular elements that satisfies the angle condition between adjacent triangular elements as a patch. Patch detection performance according to the different conditions of angle and point interval was confirmed to be independently applicable to the density of different point clouds, based on the specification or measurement location and distance of the LIDAR equipment. Optimal conditions were applied for determining the orientation of the joint, smoothness, waviness, joint spacing, and block volume. The results showed a good agreement among these factors, and thus, could be applied to two sites for comparison of measurements by the LiDAR process and hand-mapping. Consequently, similar GSI values were obtained, confirming the applicability of GSI rock classification using LiDAR. After a GSI calculation employing an overlapping circular window, a technique for determining the GSI distribution was presented using the contour plot shown in the point cloud for the target. This study aims to develop an automated algorithm that can minimize the the human bias and risk associated with field work, to quickly calculate the GSI with less manpower, and to be applied to sites requiring rapid rock engineering decisions. Another consideration is the reduction of labor and time consumed in hand-mapping. Such advantages can be maximized especially in huge survey areas or areas inaccessible targets.1. Introduction 1 1.1. Motivation 1 1.2. Research scope and contents 4 2. Background 5 2.1. Engineering rock mass classification 5 2.2. Acquisition of spatial data using LiDAR 16 3. Assessment of rock mass classification index using LiDAR 22 3.1. Joint orientation 22 3.1.1. Patch extraction method 22 3.1.2. Joint set clustering 26 3.2. Smoothness 32 3.2.1. Roughness parameter 32 3.2.2. Regression equation for roughness calculation 38 3.3. Waviness 53 3.4. Spacing 55 3.5. Block volume 59 3.6. Assessment of GSI 61 4. Application and validation 71 4.1. Mountain Gwanak (Site 1) 71 4.1.1. Field overview and LiDAR scanning at Site 1 71 4.1.2. Rock mass characterization using LiDAR at Site 1 74 4.1.3. Assessment of GSI at Site 1 115 4.2. Bangudae site (Site 2) 122 4.2.1. Field overview and LiDAR scanning at Site 2 123 4.2.2. Rock mass characterization using LiDAR at Site 2 127 4.2.3. Assessment of GSI at Site 2 163 4.3. Summary 174 5. Conclusions 178 References 181 국 문 초 록 191Docto

Rockfall threatening cumae archeological site fruition (Phlegraean fields park—naples)

Natural hazards threaten many archaeological sites in the world; therefore, susceptibility analysis is essential to reduce their impacts and support site fruition by visitors. In this paper, rockfall susceptibility analysis of the western slope of the Cumae Mount in the Cumae Archaeological Site (Phlegraean Fields, Naples), already affected by rockfall events, is described as support to a management plan for fruition and site conservation. Being the first Greek settlement in southern Italy, the site has great historical importance and offers unique historical elements such as the Cumaean Sibyl’s Cave. The analysis began with a 3D modeling of the slope through digital terrestrial photogrammetry, which forms a basis for a geomechanical analysis. Digital discontinuity measurements and cluster analysis provide data for kinematic analysis, which pointed out the planar, wedge and toppling failure potential. Subsequently, a propagation-based susceptibility analysis was completed into a GIS environment: it shows that most of the western sector of the site is susceptible to rockfall, including the access course, a segment of the Cumana Railroad and its local station. The work highlights the need for specific mitigation measures to increase visitor safety and the efficacy of filed-based digital reconstruction to support susceptibility analysis in rockfall prone areas

Texture-Based Image Segmentation

Segmentace obrazu je důležitým krokem zpracování obrazu a textura je jednou z obrazových informací, na jejichž základě lze segmentaci provádět. K popisu textury slouží texturní příznaky, přičemž existuje mnoho způsobů, jak je získat. Zde budou k reprezentaci textury využity Local Binary Patterns neboli LBP. Texturním příznakem u LBP není její hodnota, ale histogram četnosti výskytu v určité oblasti. Hlavním cílem této práce je porovnání vhodnosti několika variant extrakce texturních příznaků pomocí LBP a metod jejich následného shlukování za účelem segmentace obrazu. Ke shlukování texturních příznaků bude použita metoda Fuzzy C-Means.Image segmentation is an important step in image processing. A traditional way how to segment an image is a texture-based segmentation that uses texture features to describe image texture. In this work, Local Binary Patterns (LBP) are used for image texture representation. Texture feature is a histogram of occurences of LBP codes in a small image window. The work also aims to comparison of results of various modifications of Local Binary Patterns and their usability in the image segmentation which is done by unsupervised clustering of texture features. The Fuzzy C-Means algorithm is finally used for the clustering in this work.

Performance Evaluation of Cluster Validity Indices (CVIs) on Multi/Hyperspectral Remote Sensing Datasets

The number of clusters (i.e., the number of classes) for unsupervised classification has been recognized as an important part of remote sensing image clustering analysis. The number of classes is usually determined by cluster validity indices (CVIs). Although many CVIs have been proposed, few studies have compared and evaluated their effectiveness on remote sensing datasets. In this paper, the performance of 16 representative and commonly-used CVIs was comprehensively tested by applying the fuzzy c-means (FCM) algorithm to cluster nine types of remote sensing datasets, including multispectral (QuickBird, Landsat TM, Landsat ETM+, FLC1, and GaoFen-1) and hyperspectral datasets (Hyperion, HYDICE, ROSIS, and AVIRIS). The preliminary experimental results showed that most CVIs, including the commonly used DBI (Davies-Bouldin index) and XBI (Xie-Beni index), were not suitable for remote sensing images (especially for hyperspectral images) due to significant between-cluster overlaps; the only effective index for both multispectral and hyperspectral data sets was the WSJ index (WSJI). Such important conclusions can serve as a guideline for future remote sensing image clustering applications

Application of fuzzy c-means clustering for analysis of chemical ionization mass spectra: insights into the gas-phase chemistry of NO3-initiated oxidation of isoprene

Oxidation of volatile organic compounds (VOCs) can lead to the formation of secondary organic aerosol, a significant component of atmospheric fine particles, which can affect air quality, human health, and climate change. However, current understanding of the formation mechanism of SOA is still incomplete, which is not only due to the complexity of the chemistry, but also relates to analytical challenges in SOA precursor detection and quantification. Recent instrumental advances, especially the developments of high-resolution time-of-flight chemical ionization mass spectrometry (CIMS), greatly enhanced the capability to detect low- and extremely low-volatility organic molecules (L/ELVOCs). Although detection and characterization of low volatility vapors largely improved our understanding of SOA formation, analyzing and interpreting complex mass spectrometric data remains a challenging task. This necessitates the use of dimension-reduction techniques to simplify mass spectrometric data with the purpose of extracting chemical and kinetic information of the investigated system. Here we present an approach by using fuzzy c-means clustering (FCM) to analyze CIMS data from chamber experiments aiming to investigate the gas-phase chemistry of nitrate radical initiated oxidation of isoprene. The performance of FCM was evaluated and validated. By applying FCM various oxidation products were classified into different groups according to their chemical and kinetic properties, and the common patterns of their time series were identified, which gave insights into the chemistry of the system investigated. The chemical properties are characterized by elemental ratios and average carbon oxidation state, and the kinetic behaviors are parameterized with generation number and effective rate coefficient (describing the average reactivity of a species) by using the gamma kinetic parameterization model. In addition, the fuzziness of FCM algorithm provides a possibility to separate isomers or different chemical processes species are involved in, which could be useful for mechanism development. Overall FCM is a well applicable technique to simplify complex mass spectrometric data, and the chemical and kinetic properties derived from clustering can be utilized to understand the reaction system of interest.</p