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24
Topdown induction of clustering trees
 In 15th Int’l Conf. on Machine Learning
, 1998
"... An approach to clustering is presented that adapts the basic topdown induction of decision trees method towards clustering. To this aim, it employs the principles of instance based learning. The resulting methodology is implemented in the TIC (Top down Induction of Clustering trees) system for firs ..."
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Cited by 99 (22 self)
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An approach to clustering is presented that adapts the basic topdown induction of decision trees method towards clustering. To this aim, it employs the principles of instance based learning. The resulting methodology is implemented in the TIC (Top down Induction of Clustering trees) system for first order clustering. The TIC system employs the first order logical decision tree representation of the inductive logic programming system Tilde. Various experiments with TIC are presented, in both propositional and relational domains. 1
Distance Between Herbrand Interpretations: a measure for approximations to a target concept
, 1997
"... . We can use a metric to measure the di#erences between elements in a domain or subsets of that domain #i.e. concepts#. Which particular metric should be chosen, depends on the kind of di#erence wewant to measure. The well known Euclidean metric on # n and its generalizations are often used f ..."
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Cited by 38 (0 self)
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. We can use a metric to measure the di#erences between elements in a domain or subsets of that domain #i.e. concepts#. Which particular metric should be chosen, depends on the kind of di#erence wewant to measure. The well known Euclidean metric on # n and its generalizations are often used for this purpose, but such metrics are not always suitable for concepts where elements have some structure di#erent from real numbers. For example, in #Inductive# Logic Programming a concept is often expressed as an Herbrand interpretation of some #rstorder language. Every element in an Herbrand interpretation is a ground atom which has a tree structure. We start by de#ning a metric d on the set of expressions #ground atoms and ground terms#, motivated by the structure and complexity of the expressions and the symbols used therein. This metric induces the Hausdor # metric h on the set of all sets of ground atoms, which allows us to measure the distance between Herbrand interpretatio...
Relational DistanceBased Clustering
, 1998
"... Work on firstorder clustering has primarily been focused on the task of conceptual clustering, i.e., forming clusters with symbolic generalizations in the given representation language. By contrast, for propositional representations, experience has shown that simple algorithms based exclusively on ..."
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Cited by 32 (0 self)
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Work on firstorder clustering has primarily been focused on the task of conceptual clustering, i.e., forming clusters with symbolic generalizations in the given representation language. By contrast, for propositional representations, experience has shown that simple algorithms based exclusively on distance measures can often outperform their conceptbased counterparts. In this paper, we therefore build on recent advances in the area of #rstorder distance metrics and present RDBC, a bottomup agglomerative clustering algorithm for #rstorder representations that relies on distance information only and features a novel parameterfree pruning measure for selecting the #nal clustering from the cluster tree. The algorithm can empirically be shown to produce good clusterings #on the mutagenesis domain# that, when used for subsequent prediction tasks, improve on previous clustering results and approach the accuracies of dedicated predictive learners.
A Framework for Defining Distances Between FirstOrder Logic Objects
, 1998
"... this paper we develop a framework for distances between clauses and distances between models. The framework can be parametrised by a measure for the distance between atoms. It takes into account subterms common to distinct atoms of a set of atoms in the measurement of the distance between sets. More ..."
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Cited by 30 (3 self)
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this paper we develop a framework for distances between clauses and distances between models. The framework can be parametrised by a measure for the distance between atoms. It takes into account subterms common to distinct atoms of a set of atoms in the measurement of the distance between sets. Moreover, for a constant number of variables, the complexity of the distance computation is polynomially bounded by the size of the objects. Initial experiments show that the framework can be the basis of good clustering algorithms. The framework consists of three levels: At the first level one chooses a distance between atoms . The second level upgrades this distance to a distance between sets of atoms. We propose a framework that is a generalisation of three polynomial time computable similarity measures proposed by Eiter and Mannila, and an instance which is a real distance function, computable in polynomial time. We develop also a binary prototype function for sets of points. Prototype fun
Using Logical Decision Trees for Clustering
 In Proceedings of the 7th International Workshop on Inductive Logic Programming
, 1997
"... A novel first order clustering system, called C 0.5, is presented. It inherits its logical decision tree formalism from the TILDE system, but instead of using class information to guide the search, it employs the principles of instance based learning in order to perform clustering. Various experimen ..."
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Cited by 22 (2 self)
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A novel first order clustering system, called C 0.5, is presented. It inherits its logical decision tree formalism from the TILDE system, but instead of using class information to guide the search, it employs the principles of instance based learning in order to perform clustering. Various experiments are discussed, which show the promise of the approach. 1 Introduction A decision tree is usually seen as representing a theory for classification of examples. If the examples are positive and negative examples for one specific concept, then the tree defines these two concepts. One could also say, if there are k classes, that the tree defines k concepts. Another viewpoint is taken in Langley's Elements of Machine Learning [ Langley, 1996 ] . Langley sees decision tree induction as a special case of the induction of concept hierarchies. A concept is associated with each node of the tree, and as such the tree represents a kind of taxonomy, a hierarchy of many concepts. This is very similar...
Hierarchical MultiClassification
, 2002
"... The problem of hierarchical multiclassification is considered. ..."
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Cited by 22 (6 self)
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The problem of hierarchical multiclassification is considered.
Distance Measures Between Atoms
 In Proceedings of the CompulogNet Area Meeting on 'Computational Logic and Machine Learning
, 1998
"... Many learning systems, e.g. systems based on clustering and instance based learning systems, need a measure for the distance between objects. Adequate measures are available for attribute value learners. In recent years there is a growing interest in first order learners, however existing proposals ..."
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Cited by 15 (2 self)
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Many learning systems, e.g. systems based on clustering and instance based learning systems, need a measure for the distance between objects. Adequate measures are available for attribute value learners. In recent years there is a growing interest in first order learners, however existing proposals for distances between nonground atoms have some drawbacks. In this paper we develop a new measure for the distance between nonground atoms. 1 Introduction In learning systems based on clustering (e.g. C0.5 [3], KBG [1]) and in instance based learning (e.g. [9, ch.4], RIBL [6]), a measure of the distance between objects is an essential component. Good measures exist for distances between objects in an attribute value representation (see e.g. [9, ch. 4]). Recently there is a growing interest in using more expressive first order representations of objects and in upgrading propositional learning systems into first order learning systems (e.g. TILDE [2], ICL [5] and CLAUDIEN [4]). Some adhoc s...
Analogical prediction
 Proceedings of the 9th International Workshop on Inductive Logic Programming, volume 1634 of Lecture Notes in Artificial Intelligence
, 1999
"... Abstract. Inductive Logic Programming (ILP) involves constructing an hypothesis H on the basis of background knowledge B and training examples E. An independent test set is used to evaluate the accuracy of H. This paper concerns an alternative approach called Analogical Prediction (AP). AP takes B, ..."
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Cited by 9 (0 self)
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Abstract. Inductive Logic Programming (ILP) involves constructing an hypothesis H on the basis of background knowledge B and training examples E. An independent test set is used to evaluate the accuracy of H. This paper concerns an alternative approach called Analogical Prediction (AP). AP takes B, E and then for each test example 〈x, y 〉 forms an hypothesis Hx from B, E, x. Evaluation of AP is based on estimating the probability that Hx(x) = y for a randomly chosen 〈x, y〉. AP has been implemented within CProgol4.4. Experiments in the paper show that on English past tense data AP has significantly higher predictive accuracy on this data than both previously reported results and CProgol in inductive mode. However, on KRK illegal AP does not outperform CProgol in inductive mode. We conjecture that AP has advantages for domains in which a large proportion of the examples must be treated as exceptions with respect to the hypothesis vocabulary. The relationship of AP to analogy and instancebased learning is discussed. Limitations of the given implementation of AP are discussed and improvements suggested. 1
Bridging the gap between distance and generalisation: Symbolic learning in metric spaces
, 2008
"... Distancebased and generalisationbased methods are two families of artificial intelligence techniques that have been successfully used over a wide range of realworld problems. In the first case, general algorithms can be applied to any data representation by just changing the distance. The metric ..."
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Cited by 7 (4 self)
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Distancebased and generalisationbased methods are two families of artificial intelligence techniques that have been successfully used over a wide range of realworld problems. In the first case, general algorithms can be applied to any data representation by just changing the distance. The metric space sets the search and learning space, which is generally instanceoriented. In the second case, models can be obtained for a given pattern language, which can be comprehensible. The generalityordered space sets the search and learning space, which is generally modeloriented. However, the concepts of distance and generalisation clash in many different ways, especially when knowledge representation is complex (e.g. structured data). This work establishes a framework where these two fields can be integrated in a consistent way. We introduce the concept of distancebased generalisation, which connects all the generalised examples in such a way that all of them are reachable inside the generalisation by using straight paths in the metric space. This makes the metric space and the generalityordered space coherent (or even dual). Additionally, we also introduce a definition of minimal distancebased generalisation that can be seen as the first formulation of the Minimum Description Length (MDL)/Minimum Message Length (MML) principle in terms of a distance function. We instantiate and develop the framework for the most common data representations and distances, where we show that consistent instances can be found for numerical data, nominal data, sets, lists, tuples, graphs, firstorder atoms and clauses. As a result, general learning methods that integrate the best from distancebased and generalisationbased methods can be defined and adapted to any specific problem by appropriately choosing the distance, the pattern language and the generalisation operator.
Instance Based Function Learning
 In Proceedings of the Ninth International Workshop on Inductive Logic Programming, Lecture Notes in Arti Intelligence
, 1999
"... . The principles of instance based function learning are presented. In IBFL one is given a set of positive examples of a functional predicate. These examples are true ground facts that illustrate the input output behaviour of the predicate. The purpose is then to predict the output of the predic ..."
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Cited by 3 (1 self)
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. The principles of instance based function learning are presented. In IBFL one is given a set of positive examples of a functional predicate. These examples are true ground facts that illustrate the input output behaviour of the predicate. The purpose is then to predict the output of the predicate given a new input. Further assumptions are that there is no background theory and that the inputs and outputs of the predicate consist of structured terms. IBFL is a novel technique that addresses this problem and that combines ideas from instance based learning, first order distances and analogical or case based reasoning. We also argue that IBFL is especially useful when there is a need for handling complex and deeply nested terms. Though we present the technique in isolation, it might be more useful as a component of a larger system to deal e.g. with the logic, language and learning challenge. 1