An overview of reconstructability analysis

Abstract

This paper is an overview of reconstructability analysis (RA), an approach to discrete multivariate modeling developed in the systems community. RA includes settheoretic modeling of relations and infonnation-theoretic modeling of frequency and probability distributions. It thus encompasses both statistical and non-statistical problems. It overlaps with logic design and machine learning in engineering and with log-linear modeling in the social. sciences. Its generality gives it considerable potential for knowledge representation and data mining. I. INTRODUCTION This paper is an overview of reconstructability analysis (RA), a discrete multivariate modeling methodology developed in the systems literature; an earlier version of this tutorial is (Zwick 2001). RA derives from Ashby (1964), and was developed by Broekstra, Cavallo, Cellier, Conant, Jones, Klir, Krippendorff, and others (Klir 1986, 1996). RA resembles and partially overlaps log-linear (LL) statistical methods used in the social sciences (Bishop et al 1978; Knoke & Burke 1980). RA also resembles and overlaps methods used in logic design and machine learning (LDL) in electrical and computer engineering (e.g., Perkowski 1997). Applications of RA, like those of LL and LDL modeling, are diverse, including time-series analysis, classification, decomposition, compression, pattern recognition, prediction, control, and decision analysis. RA involves the set-theoretic modeling ofrelations and mappings and the information-theoretic modeling of probability/frequency distributions. Its different uses can be categorized using the dimensions of variable, system, data, problem, and method-types shown in Table I. These will ' now be briefly discussed. Section II explains RA in more detail. Section JlJ gives examples, Section IV discusses software, and Section V offers a concluding discussion. 2. System-type: directed vs. neutral To relate RA to a familiar LDL problem, consider the task of decomposing a logic function Z=g(A, B, C), where variables are either binary or multivalued. In RA tenninology this is a directed system, since inputs and outputs ("independent variables" and "dependent variables")

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“…An account of its origin [18] and compact summaries [19], [20] are also available. In RA, a probability or frequency distribution or a set-theoretic relation is decomposed into component distributions or relations [21].…”

“…The earliest program was developed by Zwick and Hosseini [33]; reviews of RA methodology [19], [20], a list of recent RA papers, an OCCAM manual [34] and a description of OCCAM architecture [35] are available.…”

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“…Our dominant state analysis borrows ideas from structural modeling or reconstructability analysis in system theory ( [6]- [8]) as well as more recent graphical models in statistical learning theory [9]. The intuition behind our dominant state analysis is described below.…”

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“…Reconstructability analysis (RA) derives from [4], and was developed by Broekstra, Cavallo, Cellier, Conant, Jones, Klir, Krippendorff, and others; an extensive bibliography is available in [5], and a compact summary of RA may be found in [6] and [7]. RA resembles log-linear methods [8], used widely in the social sciences [9], and where RA and log-linear methodologies overlap they are equivalent [10].…”