K-Means and Related Clustering Methods

Extending the Kohonen self-organizing map networks for clustering analysis

Clustering is a group of unsupervised statistical techniques commonly used in many disciplines. Considering their applications to fish abundance data, many technical details need to be considered to ensure reasonable interpretation. However, the reliability and stability of the clustering methods have rarely been studied in the contexts of fisheries. This study presents an intensive evaluation of three common clustering methods, including hierarchical clustering (HC), K-means (KM), and expectation-maximization (EM) methods, based on fish community surveys in the coastal waters of Shandong, China. We evaluated the performances of these three methods considering different numbers of clusters, data size, and data transformation approaches, focusing on the consistency validation using the index of average proportion of non-overlap (APN). The results indicate that the three methods tend to be inconsistent in the optimal number of clusters. EM showed relatively better performances to avoid unbalanced classification, whereas HC and KM provided more stable clustering results. Data transformation including scaling, square-root, and log-transformation had substantial influences on the clustering results, especially for KM. Moreover, transformation also influenced clustering stability, wherein scaling tended to provide a stable solution at the same number of clusters. The APN values indicated improved stability with increasing data size, and the effect leveled off over 70 samples in general and most quickly in EM. We conclude that the best clustering method can be chosen depending on the aim of the study and the number of clusters. In general, KM is relatively robust in our tests. We also provide recommendations for future application of clustering analyses. This study is helpful to ensure the credibility of the application and interpretation of clustering methods.

With the increase of marine industry in the Beibu Gulf, data clustering has become an important task of intelligent ocean. Partition clustering methods are suitable for marine data. However, traditional K-means algorithm is not suitable for large scale data. Focusing on the characteristics of oceanic big data, we propose a clustering method based on incremental K-means (IKM) algorithm. First, a vector model is adopted to represent data sets, and the calculation model for mean values and centres is used to initialise arbitrary numbers of data points. Second, the input data vectors are iteratively calculated in an incremental vector form. Finally, by applying incremental vector and distance model, the large-scale data are clustered according to convergence condition. Experiments show that the algorithm can increase the clustering efficiency, reduce time and space complexity, and lower the missing data rate.

QuestionCan a Kohonen's self‐organizing map, which is robust to non‐linear relationships between variables and their non‐normal distributions, be effective in patterning the data on plant communities investigated with the classical Braun‐Blanquet phytosociological method based on the ordinal scale? Does the application of the self‐organizing map make it possible to obtain new information from the analysed plant communities when compared to the Braun–Blanquet method alone?LocationThe Babsk nature reserve, Central Poland.MethodsThe analysed data were derived from two separate series of phytosociological studies on plant communities dating from periods 31 yr apart (1960 and 1991). The data consisted of 24 quantitative sampling lists of plant species (=phytosociological releves). The releves were analysed by the application of a Kohonen's self‐organizing map and the indicator value (IndVal).ResultsThe transformations from Querco roboris–Pinetum to Tilio cordatae–Carpinetum betuli in the vegetation in the Babsk nature reserve over 31 yr were determined precisely. Valuable new data were also obtained on: (1) significant associations of individual plant species with the previous and recent phytocoenoses, i.e. diagnostic groups of plant species for each phytocoenosis; (2) abiotic conditions (determined retrospectively in the two study periods on the basis of ecological indicators for vascular plants); and (3) the concordance of phytocoenoses with the biotope.ConclusionsThe Kohonen's self‐organizing map method and the IndVal made it possible to efficiently identify abiotic and biotic patterns for plant communities on the basis of the data expressed in the conventional Braun‐Blanquet scale.

Coordinate Descent Optimized Trace Difference Model for Joint Clustering and Feature Extraction

Describes a series of experiments on using Kohonen self-organizing maps and hybrid systems for continuous speech recognition. Experiments with different nonlinear transformations on the signal before using a neural network has been done and results compared. The hybrid system developed by the authors combines self-organizing feature maps with dynamic time warping. The experiments suggest that the combination has better performance than either of the two methods applied individually. >

Artificial neural network analysis of noisy visual field data in glaucoma

There is a growing need for a method to analyze massive gene expression data obtained from DNA microarrays. We introduce a method of combining a self-organizing map (SOM) and a k-means clustering for analyzing and categorizing the gene expression data. The SOM is an unsupervised neural network learning algorithm and forms a mapping the high-dimensional data to two-dimensional space. However, it is difficult to find clustering boundaries from results of the SOM. On the other hand, the k-means clustering can partition the data into the clusters under the assumption of the known number of clusters. In order to understand easily the results of SOM, we apply the k-means clustering to finding the clustering boundaries from results of SOM. We have applied the proposed method to the published data of yeast gene expression and show that the method is effective for categorizing the data.

Kohonen's self-organizing map (SOM), which performs topology-preserving transformation from a high dimensional data vector space to a low-dimensional map space, provides a powerful tool for data analysis, classification and visualization in many application fields. Despite its power, SOM can only deal with vectorized data, although many expansions have been proposed for various data-type cases. This study aims to develop a novel generalization of SOM called modular network SOM (mnSOM), which enables users to deal with general data classes in a consistent manner. mnSOM has an array structure consisting of function modules that are trainable neural networks, e.g. multi-layer perceptrons (MLPs), instead of the vector units of the conventional SOM family. In the case of MLP-modules, mnSOM learns a group of systems or functions in terms of the input-output relationships, and at the same time, mnSOM generates a feature map that shows distances between the learned systems. Thus, mnSOM with MLP modules is an SOM in function space rather than in vector space. From this point of view, the conventional SOM of Kohonen's can be regarded as a special case of mnSOM, the modules consisting of fixed-value bias units. In this paper, mnSOM with MLP modules is described along with some application examples.

Identification of lithofacies using Kohonen self-organizing maps

With an onset of social network amount of data is increasing day by day. In order to analyze the data and extract useful information, the data mining technology can be used. Clustering is one of the popular method of data mining. Clustering can be used for visualizing and analyzing of data. We are discussing Kohonen SOM. We are using neural networks, as a data mining tool which provides statistical observation and layout from big data-sets. We determine how Self-Organizing Kohonen Maps, can be efficiently used for data mining purposes. The Self Organizing Map (SOM) unsupervised learning is an effective computational tool in data mining processes. Self-Organizing Maps (SOMs) used to visualize social network dataset. We used Self-Organizing Map for clustering and analyzing high-dimensional and complex social network datasets. This paper also visualizes SOM neighbor connection, SOM neighbor weight distance, SOM weight position. We perform self organizing map algorithm for social network dataset in matlab.

Rough set theory provides an alternative way of representing sets whose exact boundary cannot be described due to incomplete information. Rough sets have been widely used for classification and can be equally beneficial in clustering. The clusters in practical data mining do not necessarily have crisp boundaries. An object may belong to more than one cluster. This paper describes modifications of clustering based on Genetic Algorithms, K-means algorithm, and Kohonen Self-Organizing Maps (SOM). These modifications make it possible to represent clusters as rough sets. Rough clusters are shown to be useful for representing groups of highway sections, Web users, and supermarket customers. The rough clusters are also compared with conventional and fuzzy clusters.

Due to its cruciality, water requires a high care to its physicochemical and microbiological properties to ensure the quality of several utilizations. The particles it carries are likely to be ingested, breathed, or come into contact with the skin. For the classification of the quality of surface water in the Moulouya River (NE, Morocco), this study presents many unsupervised classification methods. The overall quality of surface water in the Moulouya River in northeast Morocco was assessed using nine physicochemical parameters (pH, T°C, EC, O2-diss, NH4+, NO3-, SO42-, PO43-, and biological oxygen demand after 5 days (BOD5)) from March to August 2014. Over a 600-kilometer stretch, twenty-two sites were examined, from the river's source in the High Atlas to its mouth in the Mediterranean. During the first stage, three quality classes (excellent, good and poor) were defined by the calculation of the water quality index (WQI) and water quality evaluation system (QES-Water). In the second stage, the K-means algorithm, the fuzzy C-means algorithm and the self-organizing maps (SOM) of Kohonen were applied to the nine physicochemical parameters used as input variables for the model. The classification method used is capable of projecting high-dimensional data into a lower dimension, typically 2D. This nonlinear projection can be useful in classes’ analysis and their discovery. In terms of performance, the SOM classification showed very close results compared to the K-means and the fuzzy C-means algorithms, with only an insignificant difference across the three models, with SOM maps having a slight advantage.

Spiking Self-organizing Maps for Classification Problem

It is objective and practical for an electric machinery and apparatus test to computerize its diagnosis process with fault location identification. It is possible to recognize a fault location from measured voltage and current information by using a Kohonen's self-organizing map (SOM) which only needs a learning process of relation between the locations and their voltage and current characteristics. Diagnosis methods for some types of apparatus are proposed by using the SOM. First a diagnosis method for a three-phase PWM inverter which may have a switch fault is proposed. Twelve types of switch fault patterns are analyzed for its DC and harmonic components which are used as input data for their diagnosis map. The method is also applied to a multi-level, for example, three-level inverter. Secondly a diagnosis method of a linear induction motor which may have a turn or a turn-to-turn fault is proposed. Diagonal impedance for all fault cases under considerations are used for the SOM learning process and they are checked for their fault detections. Finally a diagnosis method for an induction machine which may have a turn fault is proposed. An impedance, which is a small slip-dependent term and expresses the degree of motor asymmetry, is computed from two sets of applied input voltages and currents and used as SOM input data. A simple mathematical model of an induction motor with the reference frame transformation is investigated. The above application examples are all validated for its simulated results by developed Matlab programs.