Intelligent Data Analysis: An International Journal

This paper presents a taxonomy for Self-organizing Maps (SOMs) for temporal sequence processing. Four main application areas for SOMs with temporal processing have been identified. These are prediction, control, monitoring and data mining. Three main techniques have been used to model temporal relations in SOMs: 1) pre-processing or post-processing the data, but keeping the basic SOM algorithm; 2) modifying the activation and/or learning algorithm to take those temporal dependencies into account; 3) modifying the network topology, either by introducing feedback elements, or by using hierarchical SOMs. Each of these techniques is explained and discussed, and a more detailed taxonomy is proposed. Finally, a list of some of the existing and relevant papers in this area is presented, and the distinct approaches of SOMs for temporal sequence processing are classified into the proposed taxonomy. In order to handle complex domains, several of the adaptation forms are often combined.

A nearest-neighbor classifier compares an unclassified object to a set of pre-classified examples and assigns to it the class of the most similar of them (the object's nearest neighbor). In some applications, many pre-classified examples are available and comparing the object to each of them is expensive. This motivates studies of methods to remove redundant and noisy examples. Another strand of research seeks to remove irrelevant attributes that compromise classification accuracy. The paper suggests to use the genetic algorithm to address both issues simultaneously. Experiments indicate considerable reduction of the set of examples, and of the set of attributes, without impaired classification accuracy. The algorithm compares favorably with earlier solutions.

Clustering is the problem of identifying the distribution of patterns and intrinsic correlations in large data sets by partitioning the data points into similarity classes. The clustering problem has been widely studied in machine learning, databases, and statistics. This paper studies the problem of clustering high dimensional data. The paper proposes an algorithm called the CoFD algorithm, which is a non-distance based clustering algorithm for high dimensional spaces. Based on the Maximum Likelihood Principle, CoFD attempts to optimize its parameter settings to maximize the likelihood between data points and the model generated by the parameters. The distributed versions of the problem, called the D-CoFD algorithms, are also proposed. Experimental results on both synthetic and real data sets show the efficiency and effectiveness of CoFD and D-CoFD algorithms.

The application of neuro-fuzzy systems to domains involving prediction and classification of symbolic data requires a reconsideration and a careful definition of the concept of distance between patterns. Traditional distances are inadequate to provide information about the proximity between the symbolic patterns. This work proposes a new architecture of neurofuzzy systems, the Symbolic Adaptive Neuro Fuzzy Inference System (SANFIS) that utilizes effectively a statistically extracted distance measure. The learning approach is a hybrid one and consists of a sequence of steps some of which are essential and some are used in order to optimize further the performance. Initially, a Statistical Distance Metric space is computed from the information provided with the training set. The premise parameters are subsequently evaluated with a three-phase Instance Based Learning (IBL) scheme that estimates the input membership function centers and spreads and constructs the corresponding fuzzy rules. The first phase of this scheme explores heuristic approaches that can uncover information for the relative importance and the reliability of the examples. The second phase exploits this information and extracts an adequate subset of the training patterns for the construction of the fuzzy rules. The concept of fuzzy adaptive subsethood is used at the third phase, for the reduction of the number of the fuzzy sets used as input membership functions. The consequent parameters are estimated with an efficient linear least squares formulation. The obtained performances from the SANFIS trained with the hybrid learning methods are significantly better than the traditional nearest neighbour Instance Based Learning schemes and compares well with advanced neural designs. At the same time SANFIS provides an enhanced explanation ability with the construction of a few interpretable rules.

When mining a large database, the number of patterns discovered can easily exceed the capabilities of a human user to identify interesting results. To address this problem, various techniques have been suggested to reduce and/or order the patterns prior to presenting them to the user. In this paper, our focus is on ranking summaries generated from a single dataset, where attributes can be generalized in many different ways and to many levels of granularity according to taxonomic hierarchies. We theoretically and empirically evaluate twelve diversity measures used as heuristic measures of interestingness for ranking summaries generated from databases. The twelve diversity measures have previously been utilized in various disciplines, such as information theory, statistics, ecology, and economics. We describe five principles that any measure must satisfy to be considered useful for ranking summaries. Theoretical results show that the proposed principles define a partial order on the ranked summaries in most cases, and in some cases, define a total order. Theoretical results also show that seven of the twelve diversity measures satisfy all of the five principles. We empirically analyze the rank order of the summaries as determined by each of the twelve measures. These empirical results show that the measures tend to rank the less complex summaries as most interesting. Finally, we analyze the distribution of the index values generated by each of the twelve diversity measures. Empirical results, obtained using synthetic data, show that the distribution of index values generated tend to be highly skewed about the mean, median, and middle index values. Finally, we demonstrate a technique, based upon our principles, for visualizing the relative interestingness of summaries. The objective of this work is to gain some insight into the behaviour that can be expected from our principled approach in practice.