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Abstract-Model trees are an extension of regression trees that associate leaves with multiple regression models. In this paper, a method for the data-driven construction of model trees is presented, namely, the Stepwise Model Tree Induction (SMOTI) method. Its main characteristic is the induction of trees with two types of nodes: regression nodes, which perform only straight-line regression, and splitting nodes, which partition the feature space. The multiple linear model associated with each leaf is then built stepwise by combining straight-line regressions reported along the path from the root to the leaf. In this way, internal regression nodes contribute to the definition of multiple models and have a "global" effect, while straight-line regressions at leaves have only "local" effects. Experimental results on artificially generated data sets show that SMOTI outperforms two model tree induction systems, M5' and RETIS, in accuracy. Results on benchmark data sets used for studies on both regression and model trees show that SMOTI performs better than RETIS in accuracy, while it is not possible to draw statistically significant conclusions on the comparison with M5'. Model trees induced by SMOTI are generally simple and easily interpretable and their analysis often reveals interesting patterns.

Abstract. In this paper we propose an extension of the naïve Bayes classification method to the multi-relational setting. In this setting, training data are stored in several tables related by foreign key constraints and each example is represented by a set of related tuples rather than a single row as in the classical data mining setting. This work is characterized by three aspects. First, an integrated approach in the computation of the posterior probabilities for each class that make use of first order classification rules. Second, the applicability to both discrete and continuous attributes by means a supervised discretization. Third, the consideration of knowledge on the data model embedded in the database schema during the generation of classification rules. The proposed method has been implemented in the new system Mr-SBC, which is tightly integrated with a relational DBMS. Testing has been performed on two datasets and four benchmark tasks. Results on predictive accuracy and efficiency are in favour of Mr-SBC for the most complex tasks.

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Abstract. Spatial associative classification takes advantage of employing association rules for spatial classification purposes. In this work, we investigate spatial associative classification in multi-relational data mining setting to deal with spatial objects having different properties, which are modeled by as many data tables (relations) as the number of spatial object types (layers). Spatial classification is based on two alternative approaches: a propositional approach and a structural approach. The propositional approach uses spatial association rules to construct an attribute-value representation (propositionalisation) of spatial data and performs spatial classification according to well-known propositional classification methods. Since the attribute-value representation should capture relational properties of spatial data, multi-relational association rules are used in propositionalisation step. The structural approach resorts to an extension of naïve Bayes classifiers to multi-relational data where the classification is driven by multi-relational association rules modelling regularities in spatial data. In both cases the spatial associative classification is performed at different levels of granularity and takes advantage from domain knowledge expressed in form of hierarchies and rules. Experiments on realworld geo-referenced census data analysis show the advantage of the structural approach over the propositional one.

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