Interval data clustering using self-organizing maps based on adaptive Mahalanobis distances

The clustering of high-dimensional data presents a critical computational problem. Therefore, it is convenient to arrange the cluster centres on a grid with a small dimensional space that reduces computational cost and can be easily visualized. Moreover, in real applications there is no sharp boundary between classes, real datasets are naturally defined in a fuzzy context. Therefore, fuzzy clustering fits better for complex real datasets to determine the best distribution. Self-organizing map (SOM) technique is appropriate for clustering and vector quantization of high-dimensional data. In this paper we present a new fuzzy learning approach called FMIG (fuzzy multilevel interior growing self-organizing maps). The proposed algorithm is a fuzzy version of MIGSOM (multilevel interior growing self-organizing maps). The main contribution of FMIG is to define a fuzzy process of data mapping and to take into account the fuzzy aspect of high-dimensional real datasets. This new algorithm is able to auto-organize the map accordingly to the fuzzy training property of the nodes. In the second step, the introduced scheme for FMIG is clustered by means of fuzzy C-means (FCM) to discover the interior class distribution of the learned data. The validation of FCM partitions is directed by applying six validity indexes. Superiority of the new method is demonstrated by comparing it with crisp MIGSOM, GSOM (growing SOM) and FKCN (fuzzy Kohonen clustering network) techniques. Thus, our new method shows improvement in term of quantization error, topology preservation and clustering ability.

Unsupervised knowledge discovery using Self Organising Maps (SOM) has been successfully used in obtaining unbiased and visualisable results. A Growing (or Dynamic) Self Organising Maps (GSOM) is an extended version of the original SOM with adaptive map size and controllable spread. In experiments a GSOM usually has considerably higher topographic error than SOM with similar quantisation error. This can be undesirable in cases where, topology preservation is important, therefore in this paper the authors proposed an algorithm to assist the growing of the dynamic self-organising map in achieving better topographic quality whilst maintaining or even improving level of quantisation error. Results have shown improvement of topographic error when comparing to GSOM, and have better topology preservation than non-topologically optimised SOM with similar map size.

We have been working on the application of Machining Learning in Metabolomics, Drug-Drug Interaction Discovery and Human Gait Recognition [1-5], profiling large data sets. Extraction of vital information about 1) plant metabolomics that can improve the environment and food quality, 2) in vitro neuronal network behavior patterns for various drugs that can be used to characterize drugs for brain deceases and 3) human gait patterns that can reveal various diseases were among these applications. We have demonstrated with considerable success in using unsupervised clustering techniques to analyze genetic and metabolomic data. This includes analysis of drought resistance in wheat [4] and microbial metagenomes [5].We introduced two methods: Near Unsupervised Learning (NUL) and Sub-sample Error Graphs (SEGs) [5] to analyze large amount of data. Self Organizing Map (SOM), which is one of the widely used Unsupervised Neural Networks, has been used as a data-mining tool due to its ability to map high dimensional data into a two dimensional feature map, which is expected to be topology preserving allowing users to visually identify clusters by their topological relationships in terms of their proximity on the map. The Growing Self Organizing Maps (GSOM) further allows the map size to be determined by the algorithm, which relies upon a user set parameter called Spread Factor (SF) [6]. The wide availability of GPUs for affordable prices allows faster comparison of various SOMs with different maps sizes taking away some of the advantages GSOM claimed. Further development of GSOM into a Dynamic SOM Tree exploits the possibility of varying SF to obtain multiple GSOMs from a small number of compact clusters to a large number of sparse clusters [7]. NUL methods can be applied on GSOM using a small number of labels that should be available for every class. This is however not realistic in some applications where the number of classes cannot be explicitly known. We propose a new method call Deep Near Unsupervised Learning (D-NUL), where Dynamic SOM tree is used instead of GSOM and the number of classes are not assumed to be known. The implementation of Dynamic SOM tree methods with varying SF on GPUs will make the computation with D-NUL possible for many problems in big data analytics.

Clustering methods aims to organize a set of items into clusters such that items within a given cluster have a high degree of similarity, while items belonging to different clusters have a high degree of dissimilarity. The self-organizing map (SOM) introduced by Kohonen is an unsupervised competitive learning neural network method which has both clustering and visualization properties, using a neighborhood lateral interaction function to discover the topological structure hidden in the data set. In this paper, we introduce a batch self-organizing map algorithm based on adaptive distances. Experimental results obtained in real benchmark datasets show the effectiveness of our approach in comparison with traditional batch self-organizing map algorithms.

The Self-Organizing Maps have been widely used as multidimensional unsupervised classifiers. The aim of this paper is to develop a self-organizing map for interval data. Due to the increasing use of such data in Data Mining, many clustering methods for interval data have been proposed this last decade. In this paper, we propose an algorithm to train the self-organizing map for interval data. We use the Hausdorff distance to compare two vectors of intervals. In order to show the usefulness of our approach, we apply the self-organizing map on real interval data issued from meteorological stations in China.

We have proposed neural-network based visualization approach, called sequence-based SOM (self-organizing map) that visualizes transition of dynamic clusters by introducing the sequencing weight function onto the neuron topology. This approach mitigates the problems with a sliding window-based method. In this paper, we confirmed the properties of the proposed method via artificial data sets, and a real news articles data set by showing the topicspsila derivation and diversification/convergence. Visualization of cluster transition aids in the comprehension of such phenomena which come useful in various domains such as fault diagnosis and medical check-up, among others.

The Self-Organizing Map (SOM) is a popular unsupervised neural network able to provide effective clustering and data visualization for multidimensional input spaces. Fast Learning SOM (FLSOM) adopts a learning algorithm that improves the performance of the standard SOM with respect to the convergence time in the training phase. In this paper we show that FLSOM also improves the quality of the map by providing better clustering quality and topology preservation of multidimensional input data. Several tests have been carried out on different multidimensional datasets, which demonstrate the superiority of the algorithm in comparison with the original SOM.

The self-organizing map (SOM) is an efficient tool for visualizing high-dimensional data as it performs a topology-presenting projection of the input space on a low-dimensional grid. To utilize the information provided by the SOM and obtain an approximation of the data structure, a separate data projection method is usually needed. However, most of the SOM projection methods are computationally expensive when the size of the data set becomes large. In this paper, we present an intuitive and effective SOM projection method with comparatively low computational complexity for the purpose of cluster visualization. This method maps data vectors on the output space based on their responses to different prototype vectors. High-resolution maps can be obtained with a relatively small network size. The proposed method is demonstrated using both an artificial and a real world data set.

Problem statement: High leverage points are extreme outliers in the X-direction. In regression analysis, the detection of these leverage points becomes important due to their arbitrary large effects on the estimations as well as multicollinearity problems. Mahalanobis Distance (MD) has been used as a diagnostic tool for identification of outliers in multivariate analysis where it finds the distance between normal and abnormal groups of the data. Since the computation of MD relies on non-robust classical estimations, the classical MD can hardly detect outliers accurately. As an alternative, Robust MD (RMD) methods such as Minimum Covariance Determinant (MCD) and Minimum Volume Ellipsoid (MVE) estimators had been used to identify the existence of high leverage points in the data set. However, these methods tended to swamp some low leverage points even though they can identify high leverage points correctly. Since, the detection of leverage points is one of the most important issues in regression analysis, it is imperative to introduce a novel detection method of high leverage points. Approach: In this study, we proposed a relatively new two-step method for detection of high leverage points by utilizing the RMD (MVE) and RMD (MCD) in the first step to identify the suspected outlier points. Then, in the second step the MD was used based on the mean and covariance of the clean data set. We called this method two-step Robust Diagnostic Mahalanobis Distance (RDMDTS) which could identify high leverage points correctly and also swamps less low leverage points. Results: The merit of the newly proposed method was investigated extensively by real data sets and Monte Carlo Simulations study. The results of this study indicated that, for small sample sizes, the best detection method is (RDMDTS) (MVE)-mad while there was not much difference between (RDMDTS) (MVE)-mad and (RDMDTS) (MCD)-mad for large sample sizes. Conclusion/Recommendations: In order to swamp less low leverage as high leverage point, the proposed robust diagnostic methods, (RDMDTS) (MVE)-mad and (RDMDTS) (MCD)-mad were recommended.

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.

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.

Determining the structure of data without prior knowledge of the number of clusters or any information about their composition is a problem of interest in many fields, such as image analysis, astrophysics, biology, etc. Partitioning a set of n patterns in a p-dimensional feature space must be done such that those in a given cluster are more similar to each other than the rest. As there are approximately Kn/K! possible ways of partitioning the patterns among K clusters, finding the best solution is very hard when n is large. The search space is increased when we have no a priori number of partitions. Although the self-organizing feature map (SOM) can be used to visualize clusters, the automation of knowledge discovery by SOM is a difficult task. This paper proposes region-based image processing methods to post-processing the U-matrix obtained after the unsupervised learning performed by SOM. Mathematical morphology is applied to identify regions of neurons that are similar. The number of regions and their labels are automatically found and they are related to the number of clusters in a multivariate data set. New data can be classified by labeling it according to the best match neuron. Simulations using data sets drawn from finite mixtures of p-variate normal densities are presented as well as related advantages and drawbacks of the method.

Self organized mapping of data clusters to neuron groups

The influence of the missing values in the classification of incomplete pattern mainly depends on the context. In this paper, we present a fast classification method for incomplete pattern based on the fusion of belief functions where the missing values are selectively (adaptively) estimated. At first, it is assumed that the missing information is not crucial for the classification, and the object (incomplete pattern) is classified based only on the available attribute values. However, if the object cannot be clearly classified, it implies that the missing values play an important role to obtain an accurate classification. In this case, the missing values will be imputed based on the K-nearest neighbor (K-NN) and self-organizing map (SOM) techniques, and the edited pattern with the imputation is then classified. The (original or edited) pattern is respectively classified according to each training class, and the classification results represented by basic belief assignments (BBA's) are fused with proper combination rules for making the credal classification. The object is allowed to belong with different masses of belief to the specific classes and meta-classes (i.e. disjunctions of several single classes). This credal classification captures well the uncertainty and imprecision of classification, and reduces effectively the rate of misclassifications thanks to the introduction of meta-classes. The effectiveness of the proposed method with respect to other classical methods is demonstrated based on several experiments using artificial and real data sets.

In the case of two small toy data sets, we found out that subsampling has a much weaker behavior in the finding of the true number of clusters K than bootstrapping (Mucha and Bartel, Soft bootstrapping in cluster analysis and its comparison with other resampling methods. In: M. Spiliopoulou, L. Schmidt-Thieme, R. Janning (eds.) Data analysis, machine learning and knowledge discovery. Springer, Cham, 2014). In contradiction, Möller and Dörte (Intell Data Anal 10:139–162, 2006) pointed out that “subsampling … clearly outperformed the bootstrapping technique in the detection of correct clustering consensus results.” Obviously, there is a need for further investigations. Therefore here we compare these two resampling techniques based on real and artificial data sets by means of different indices: ARI or Jaccard. We consider hierarchical cluster analysis methods because they find all partitions into K = 2, 3, … clusters in one run only, and, moreover, these results are (usually) unique (Spaeth, Cluster analysis algorithms for data reduction and classification of objects. Ellis Horwood, Chichester, 1982). The methods are tested on two synthetic data sets and two real data sets. Obviously, bootstrapping is better than subsampling in finding the true number of clusters.