Conceptual clustering using relational informatio

Work in conceptual clustering has focused on creating classes from objects with a fixed set of features, such as color or size. In this paper we describe a system which uses relations between the objects being clustered as well as features of the objects to form a hierarchy tree of classes. Unlike previous conceptual clustering systems, this algorithm can define new attributes. Using relational information the system is able to find object classifications not possible with conventional conceptual clustering methods

Towards an integrated discovery system

Previous research on machine discovery has focused on limited parts of the empirical discovery task. In this paper we describe IDS, an integrated system that addresses both qualitative and quantitative discovery. The program represents its knowledge in terms of qualitative schemas, which it discovers by interacting with a simulated physical environment. Once IDS has formulated a qualitative schema, it uses that schema to design experiments and to constrain the search for quantitative laws. We have carried out preliminary tests in the domain of heat phenomena. In this context the system has discovered both intrinsic properties, such as the melting point of substances, and numeric laws, such as the conservation of mass for objects going through a phase change

A framework for empirical discovery

Previous research in machine learning has viewed the process of empirical discovery as search through a space of 'theoretical' terms. In this paper, we propose a problem space for empirical discovery, specifying six complementary operators for defining new terms that ease the statement of empirical laws. The six types of terms include: numeric attributes (such as PV/T); intrinsic properties (such as mass); composite objects (such as pairs of colliding balls); classes of objects (such as acids and alkalis); composite relations (such as chemical reactions); and classes of relations (such as combustion/oxidation). We review existing machine discovery systems in light of this framework, examining which parts of the problem space were, covered by these systems. Finally, we outline an integrated discovery system (IDS) we are constructing that includes all six of the operators and which should be able to discover a broad range of empirical laws

A cautionary note on robust covariance plug-in methods

Many multivariate statistical methods rely heavily on the sample covariance matrix. It is well known though that the sample covariance matrix is highly non-robust. One popular alternative approach for "robustifying" the multivariate method is to simply replace the role of the covariance matrix with some robust scatter matrix. The aim of this paper is to point out that in some situations certain properties of the covariance matrix are needed for the corresponding robust "plug-in" method to be a valid approach, and that not all scatter matrices necessarily possess these important properties. In particular, the following three multivariate methods are discussed in this paper: independent components analysis, observational regression and graphical modeling. For each case, it is shown that using a symmetrized robust scatter matrix in place of the covariance matrix results in a proper robust multivariate method.Comment: 24 pages, 7 figure

Multivariate L1 Statistical Methods: The Package MNM

In the paper we present an R package MNM dedicated to multivariate data analysis based on the L_1 norm. The analysis proceeds very much as does a traditional multivariate analysis. The regular L_2 norm is just replaced by different L_1 norms, observation vectors are replaced by their (standardized and centered) spatial signs, spatial ranks, and spatial signed-ranks, and so on. The procedures are fairly efficient and robust, and no moment assumptions are needed for asymptotic approximations. The background theory is briefly explained in the multivariate linear regression model case, and the use of the package is illustrated with several examples using the R package MNM.

New Algorithms for MM-Estimation of Multivariate Scatter and Location

We present new algorithms for $M$-estimators of multivariate scatter and location and for symmetrized $M$-estimators of multivariate scatter. The new algorithms are considerably faster than currently used fixed-point and related algorithms. The main idea is to utilize a second order Taylor expansion of the target functional and to devise a partial Newton-Raphson procedure. In connection with symmetrized $M$-estimators we work with incomplete $U$-statistics to accelerate our procedures initially