Multi-Instance

... A statistical query will be a request for an approximation of the value of Pχ = Prx ∈ D r[χ( x о ,f( x о ))] = Pr EX(F,D r)[ χ = 1 ]. ... Here, the benefit of noise handling is less clear, as the classification error is only reduced by 2.8%, for η set to 15%, with an accuracy of 84.7%. ...

In this paper we upgrade linear logistic regression and boosting to multi-instance data, where each example consists of a labeled bag of instances. This is done by connecting predictions for individual instances to a bag-level probability estimate by simple averaging and maximizing the likelihood at the bag level—in other words, by assuming that all instances contribute equally and independently to a bag’s label. We present empirical results for artificial data generated according to the underlying generative model that we assume, and also show that the two algorithms produce competitive results on the Musk benchmark datasets.

Attribute-value based representations, standard in today's data mining systems, have a limited expressiveness. Inductive Logic Programming provides an interesting alternative, particularly for learning from structured examples whose parts, each with its own attributes, are related to each other by means of first-order predicates. Several subsets of first-order logic (FOL) with different expressive power have been proposed in Inductive Logic Programming (ILP). The challenge lies in the fact that the more expressive the subset of FOL the learner works with, the more critical the dimensionality of the learning task. The Datalog language is expressive enough to represent realistic learning problems when data is given directly in a relational database, making it a suitable tool for data mining. Consequently, it is important to elaborate techniques that will dynamically decrease the dimensionality of learning tasks expressed in Datalog, just as Feature Subset Selection (FSS) techniques do it in attribute-value learning. The idea of re-using these techniques in ILP runs immediately into a problem as ILP examples have variable size and do not share the same set of literals. We propose here the first paradigm that brings Feature Subset Selection to the level of ILP, in languages at least as expressive as Datalog. The main idea is to first perform a change of representation, which approximates the original relational problem by a multi-instance problem. The representation obtained as the result is suitable for FSS techniques which we adapted from attribute-value learning by taking into account some of the characteristics of the data due to the change of representation. We present the simple FSS proposed for the task, the requisite change of representation, and the entire method combining those two algorithms. The method acts as a filter, preprocessing the relational data, prior to the model building, which outputs relational examples with empirically relevant literals. We discuss experiments in which the method was successfully applied to two real-world domains.

Clustering is an essential data mining task with various types of applications. Traditional clustering algorithms are based on a vector space model representation. A relational database system often contains multi-relational information spread across multiple relations (tables). In order to cluster such data, one would require to restrict the analysis to a single representation, or to construct a feature space comprising all possible representations from the data stored in multiple tables. In this paper, we present a data summarization approach, borrowed from the Information Retrieval theory, to clustering in multi-relational environment. We find that the data summarization technique can be used here to capture the typical high volume of multiple instances and numerous forms of patterns. Our experiments demonstrate a technique to cluster data in a multi-relational environment and show the evaluation results on the mutagenesis dataset. In addition, the effect of varying the number of features considered in clustering on the classification performance is also evaluated.