Fuzzy Divisive Hierarchical Clustering Research Articles

Fuzzy Divisive Hierarchical Clustering of Solvents According to Their Experimentally and Theoretically Predicted Descriptors

The present study describes a simple procedure to separate into patterns of similarity a large group of solvents, 259 in total, presented by 15 specific descriptors (experimentally found and theoretically predicted physicochemical parameters). Solvent data is usually characterized by its high variability, different molecular symmetry, and spatial orientation. Methods of chemometrics can usefully be used to extract and explore accurately the information contained in such data. In this order, advanced fuzzy divisive hierarchical-clustering methods were efficiently applied in the present study of a large group of solvents using specific descriptors. The fuzzy divisive hierarchical associative-clustering algorithm provides not only a fuzzy partition of the solvents investigated, but also a fuzzy partition of descriptors considered. In this way, it is possible to identify the most specific descriptors (in terms of higher, smallest, or intermediate values) to each fuzzy partition (group) of solvents. Additionally, the partitioning performed could be interpreted with respect to the molecular symmetry. The chemometric approach used for this goal is fuzzy c-means method being a semi-supervised clustering procedure. The advantage of such a clustering process is the opportunity to achieve separation of the solvents into similarity patterns with a certain degree of membership of each solvent to a certain pattern, as well as to consider possible membership of the same object (solvent) in another cluster. Partitioning based on a hybrid approach of the theoretical molecular descriptors and experimentally obtained ones permits a more straightforward separation into groups of similarity and acceptable interpretation. It was shown that an important link between objects’ groups of similarity and similarity groups of variables is achieved. Ten classes of solvents are interpreted depending on their specific descriptors, as one of the classes includes a single object and could be interpreted as an outlier. Setting the results of this research into broader perspective, it has been shown that the fuzzy clustering approach provides a useful tool for partitioning by the variables related to the main physicochemical properties of the solvents. It gets possible to offer a simple guide for solvents recognition based on theoretically calculated or experimentally found descriptors related to the physicochemical properties of the solvents.

Finding specific peaks (markers) using fuzzy divisive hierarchical associative-clustering based on the chromatographic profiles of medicinal plant extracts obtained at various detection wavelengths.

Advanced chemometric methods, such as fuzzy c-means (FCM), a fuzzy divisive hierarchical clustering algorithm (FDHC), and fuzzy divisive hierarchical associative-clustering (FDHAC), which offer the excellent possibility to associate each fuzzy partition of samples with a fuzzy set of characteristics (features), have been successfully applied in this study. FDHAC, a method that utilizes specific regions of chromatographic fingerprints or specific peaks as a fuzzy set of characteristics, was effectively applied to the characterization and classification of medicinal plant extracts according to their antioxidant capacities, using their chromatographic profiles monitored at 242, 260, 280, 320, 340, and 380 nm via HPLC with a multistep isocratic and gradient elution system and diode array detection (HPLC-DAD). What is quite new is the partitioning of the chromatographic retention time ranges and peaks (markers) and their association with different plant extract samples with high, moderate or low antioxidant capacity. Furthermore, the degrees of membership of fingerprints (fuzzy markers) are highly relevant with respect to the (dis)similarity of samples because they indicate both the positions and degrees of association of chromatographic peaks from different classes or individual samples. The obtained results clearly demonstrate the efficiency and information power of these advanced fuzzy methods for medicinal plant characterization and authentication, and this study generates the premise for a new chemometrics approach with high-impact for use in analytical chemistry and other fields.

Fuzzy hierarchical cross-clustering of data from abandoned mine site contaminated with heavy metals

The characteristics of pore water and slate samples are critically analyzed using fuzzy hierarchical cross-clustering statistical techniques. The main aim of this study was to investigate the source of contamination near an abandoned uranium mine in Germany. The mining activities were abandoned in 1990 the site was closed, and the surrounding area was remediated. However, heavy metal contamination is still detectable in water, soil and plants today. Hence, investigating the source of the current contamination is an important task. In order to achieve the goal, results from chemical analysis of both pore water samples and leachates from slate samples were initially analyzed using hard (classical) hierarchical clustering algorithms that did not provide meaningful results. By using two fuzzy clustering algorithms, Fuzzy Divisive Hierarchical Clustering (FDHC) and Fuzzy Hierarchical Cross-Clustering (FHCC), a relationship between the leachate from Ordovician-Silurian slate samples (10 samples collected from the test site and the surrounding area) and pore water samples (53 samples collected from 3 locations within the test site at 3 depths over the course of 4 years) was identified. The leachate data formed a cluster which was statistically similar to the cluster formed by the pore water samples collected from two of three locations. In addition, the fuzzy cross-clustering approach allowed for the identification of the characteristics (qualitative and quantitative) responsible for the observed similarities between all the samples. We conclude that the fuzzy algorithms were a better tool for the analysis and interpretation of geological/hydrogeological data where the data sets have an inherent vagueness/uncertainty.

Important Developments in Romanian Propolis Research

The most important developments in propolis analysis and pharmacological properties are discussed. In order to help in the Romanian propolis standardization, different methodologies for chemical composition analysis (UV-VIS, HP-TLC, and HPLC-DAD) are reviewed using new approaches and software (fuzzy divisive hierarchical clustering approach and ChromQuest software) and compared with international studies made until now in propolis research. Practical applications of Romanian propolis in medicinal therapy and cosmetics are reviewed, and quality criteria for further standardization are proposed.

Ecosystem discrimination and fingerprinting of Romanian propolis by hierarchical fuzzy clustering and image analysis of TLC patterns

The fingerprinting capacity of thin layer chromatography (TLC) and image analysis in the case of propolis samples collected in different area in Romania has been investigated. Fuzzy divisive hierarchical clustering approach was used as a powerful tool of samples discrimination and fingerprinting according to the geographical origin and local flora. The fuzzy partition and patterns obtained by membership degrees plot were in a very good agreement with floral origin and geographic location of Romanian propolis samples, and clearly illustrate the fuzziness concerning their similarities and difference. The results obtained strongly support that TLC via image analysis can be successfully employed in the fingerprinting methodologies if they are combined with appropriate fuzzy clustering method. The method developed in this paper might be also extended in the authenticity and origin control of fruits, herbs or derived products.

Fuzzy divisive hierarchical clustering of soil data using Gustafson–Kessel algorithm

In this paper we discuss the clustering results of 304 soil samples based on the concentration of 13 chemical elements (Cd, Co, Cr, Cu, Eu, Fe, Mn, Ni, Pb, Sb, Se, Y, and Zn) determined according to a four-step sequential extraction procedure: acetic acid ( 1), hydroxyl ammonium chloride ( 2), hydrogen peroxide/ammonium acetate ( 3) and aqua regia ( 4). The use of a sequential extraction procedure is the only objective method to determine the present binding forms of metals in soils and sediments. The mobility of chemicals in the environment is of a large interest for scientists because their mobility in soils and sediments, for example, is strongly associated to their toxicity effects. Considering the enormous data flood and their complexity it appears evident that chemometric techniques are the most suitable methods of investigation and as a direct consequence fuzzy clustering could be one of the best solution. In this order we have applied different fuzzy clustering algorithms, namely hierarchical and horizontal fuzzy clustering including Gustafson–Kessel algorithm which may detect clusters of different geometrical shapes in a data set by introducing an adaptive distance norm for each cluster. The present assessment has shown that the Gustafson–Kessel algorithm is the superior and effective method for clustering soil samples. This conclusion has been also clearly supported by the values of some conventional cluster validity indices.

A Hierarchical Fuzzy Clustering-based System to Create User Profiles

The rapid development of the World Wide Web as a medium of commerce and information dissemination has generated a growing interest of web portal managers in systems able to identify user profiles from the web access logs. The interpretation of these profiles can help re-organize the web portal, e.g., by restructuring the site's content more efficiently, or even to build adaptive web portals, i.e., portals whose organization and presentation change depending on the specific visitor's needs. In this paper, we assume that the pages of the web portal have been prearranged in a number of different categories. We introduce a systematic approach to determine a hierarchy of user profiles from the history of users' accesses to the categories. First, we filter the access log by removing both occasional users and categories of poor interest. Then, we apply an Unsupervised Fuzzy Divisive Hierarchical Clustering (UFDHC) algorithm to cluster the users of the web portal into a hierarchy of fuzzy groups characterized by a set of common interests and each represented by a prototype, which defines the profile of the group typical member. To identify the profile a specific user belongs to, we propose a novel classification method which completely exploits the information contained in the hierarchy. To prove the effectiveness of our approach, we apply the UFDHC algorithm to access log data collected over a period of 15 days and use the classification method to associate a profile with the users defined by access log data collected during subsequent 60 days. Finally, we highlight the good characteristics of our system by comparing our results with the ones obtained by applying a profiling system based on a modified version of the fuzzy C-means.

A Fuzzy Hierarchical Classification System for Olfactory Signals

A fuzzy logic-based system to classify olfactory signals is presented. The odour samples are obtained from an electronic nose that contains conducting polymer sensors with partially overlapping sensitivities to odours. The sensor responses are represented by means of the coefficients of their Fast Fourier Transform (FFT). A feature reduction method is applied to reduce the feature space dimension. Then, an Unsupervised Fuzzy Divisive Hierarchical Clustering (UFDHC) method is used to establish the optimal number of clusters in the data set, as well as the optimal cluster structure. The output of UFDHC is a binary hierarchy of fuzzy classes that are adopted to build a supervised fuzzy hierarchical classifier. At each level of the hierarchy a separating hyperplane of the two corresponding fuzzy classes is determined. The hyperplane identifies two crisp decision regions, which will be refined at the next level of the hierarchy. In this way, we obtain a hierarchy of regions, which defines a crisp decision tree. Each region is, therefore, related to a specific expected output of the system. Two small-scale applications demonstrate the effectiveness and the good recognition performance of the proposed method.

A Fuzzy Divisive Hierarchical Clustering Algorithm for the Optimal Choice of Sets of Solvent Systems

Abstract This paper proposes a Fuzzy Divisive Hierarchical Clustering Algorithm (FDHC) for the optimal choice of sets of solvents systems in thin layer chromatography. This new approach described here is capable of finding the best system and the optimal combination of two or more TLC systems according to, for instance, the quality partition coefficient (QP). In this order an IBM-PC computer has been used to run the corresponding program written in Pascal.