An overview of reconstructability analysis <s> Problem-type: Reconstruction vs. identification <s> 1: Introduction.- 1.1. Systems Science.- 1.2. Systems Problem Solving.- 1.3. Hierarchy of Epistemological Levels of Systems.- 1.4. The Role of Mathematics.- 1.5. The Role of Computer Technology.- 1.6. Architecture of Systems Problem Solving.- Notes.- 2: Source and Data Systems.- 2.1. Objects and Object Systems.- 2.2. Variables and Supports.- 2.3. Methodological Distinctions.- 2.4. Discrete Versus Continuous.- 2.5. Image Systems and Source Systems.- 2.6. Data Systems.- Notes.- Exercises.- 3: Generative Systems.- 3.1. Empirical Investigation.- 3.2. Behavior Systems.- 3.3. Methodological Distinctions.- 3.4. From Data Systems to Behavior Systems.- 3.5. Measures of Uncertainty.- 3.6. Search for Admissible Behavior Systems.- 3.7. State-Transition Systems.- 3.8. Generative Systems.- 3.9. Simplification of Generative Systems.- 3.10. Systems Inquiry and Systems Design.- Notes.- Exercises.- 4: Structure Systems.- 4.1. Wholes and Parts.- 4.2. Systems, Subsystems, Supersystems.- 4.3. Structure Source Systems and Structure Data Systems.- 4.4. Structure Behavior Systems.- 4.5. Problems of Systems Design.- 4.6. Identification Problem.- 4.7. Reconstruction Problem.- 4.8. Reconstructability Analysis.- 4.9. Simulation Experiments.- 4.10. Inductive Reasoning.- 4.11. Inconsistent Structure Systems.- Notes.- Exercises.- 5: Metasystems.- 5.1. Change versus Invariance.- 5.2. Primary and Secondary Systems Traits.- 5.3. Metasystems.- 5.4. Metasystems versus Structure Systems.- 5.5. Multilevel Metasystems.- 5.6. Identification of Change.- Notes.- Exercises.- 6: Complexity.- 6.1. Complexity in Systems Problem Solving.- 6.2. Three Ranges of Complexity.- 6.3. Measures of Systems Complexity.- 6.4. Bremermann's Limit.- 6.5. Computational Complexity.- 6.6. Complexity Within GSPS.- Notes.- Exercises.- 7: Goal-Oriented Systems.- 7.1. Primitive, Basic, and Supplementary Concepts.- 7.2. Goal and Performance.- 7.3. Goal-Oriented Systems.- 7.4. Structure Systems as Paradigms of Goal-Oriented Behavior Systems.- 7.5. Design of Goal-Oriented Systems.- 7.6. Adaptive Systems.- 7.7. Autopoietic Systems.- Notes.- Exercises.- 8: Systems Similarity.- 8.1. Similarity.- 8.2. Similarity and Models of Systems.- 8.3. Models of Source Systems.- 8.4. Models of Data Systems.- 8.5. Models of Generative Systems.- 8.6. Models of Structure Systems.- 8.7. Models of Metasystems.- Notes.- Exercises.- 9: GSPS: Architecture, USE, Evolution.- 9.1. Epistemological Hierarchy of Systems: Formal Definition.- 9.2. Methodological Distinctions: A Summary.- 9.3. Problem Requirements.- 9.4. Systems Problems.- 9.5. GSPS Conceptual Framework: Formal Definition.- 9.6. Overview of GSPS Architecture.- 9.7. GSPS Use: Some Case Studies.- 9.8. GSPS Evolution.- Notes.- Exercises.- Appendices.- A: List of Symbols.- B: Glossary of Relevant Mathematical Terms.- C: Some Relevant Theorems.- D: Refinement Lattices.- E: Classes of Structures Relevant to Reconstructability Analysis.- References.- Author Index. <s> BIB001 </s> An overview of reconstructability analysis <s> Problem-type: Reconstruction vs. identification <s> Abstract The new discipline of reconstructability analysis has provided a powerful framework for the study of the relationships between parts and wholes. The concentration of effort has been on systems with probabilistic or possibilistic behavior functions. This paper extends aspects of reconstructability analysis to general functions which need not be behavior functions. We refer to a system with such a function as a g-system. First, a g-system is transformed to a dimensionless form (borrowing a term from partial differential equations). A mathematical structure is then induced via a type of isomorphism onto this system which renders it amenable to analysis by established techniques in reconstructability analysis. Absolutely no restrictions are placed on the units or mathematical structure of the g-system. We refer to the system induced from the g-system as a Klir system or k-system. These systems are named in honor of the reconstructability analysis founder. Finally, we explicate some uses of k-systems ... <s> BIB002 </s> An overview of reconstructability analysis <s> Problem-type: Reconstruction vs. identification <s> K-systems exist in general systems theory for the study of the relationships between parts and wholes. We show here that K-systems analysis can be used to solve problems in classical multivariate analysis, and solve them more effectively than existing methods. To demonstrate this, we take on “the analysis of variance” in this paper. The analysis of variance is the most important and powerful technique in the field of statistical inference (quoted from Probability and Statistics by Hines and Montgomery). We apply K-systems analysis to the analysis of variance problem, and we compare the two techniques. We see that K-systems analysis can provide more information. But the major difference is that the analysis of variance guesses a model for the data whereas K-systems analysis uses “the” model that is true and correct for the data. Further, K-systems theory delivers a surprising and important insight: it is generally incorrect to use any model where effects and interactions are represented statically over sub... <s> BIB003 </s> An overview of reconstructability analysis <s> Problem-type: Reconstruction vs. identification <s> About 1,000 sediment cores from a salt water lagoon in Ventura County, CA were incubated between September 6 and October 6, 1981. The data were analyzed using stepwise regression, time series, multichannel information, and entropy data analysis. Stepwise regression analyses were not informative in explaining changes in productivity because the correlations between productivity and individual environmental variables (chlorophyll a, incident radiation, water temperature, mean tidal range, hours of subaerial exposure, benthic community respiration, pheophytin a/chlorophyll a, and initial dissolved oxygen concentration) varied through time. Time series and multichannel information analysis were used to uncover dynamic behavior in the data and to optimize sampling strategy. The information analysis indicated that, for a long range study, considerably more information could be obtained by concentrating samples into a 14-day interval within each month, rather than sampling throughout the month. Entropy data anal... <s> BIB004 </s> An overview of reconstructability analysis <s> Problem-type: Reconstruction vs. identification <s> About 3000 sediment cores from Baratana Estuary, Louisiana, USA, were incubated between 26 Jul and 25 Aug 1983. For the month, benthic microfloral production measured at a subtidal site consisting of muddy sand was almost twice that measured at a sandy intertidal site (27 g C m-' vs 14 g C m-'). However, maximum productivity rates (230 mg C m-' h') were greatest at the sandy site; these rates occurred under periods of subaerial exposure which were limited to late afternoons on 11 d of the study, yet accounted for 43 % of the total monthly production at the sand site. Other variables monitored were chlorophyll a, light intensity, water temperature, salinity, benthic community respiration, productivity of the water column, biological activity (muddy sand site), wave height (sand site), meteorological tides (wind-induced water levels), tide height, and initial dissolved oxygen. Multichannel information analysis indicated that the information accounted for in productivity by these variables peaked at slightly less than 7 and 3 d periods for the sand site and weak peaks occurred at about 10 and 3 d periods for the muddy sand site. K-systems analysis indicated that the environmental variables acted in combination to influence productivity, and that the combinations changed through time. Physical processes (meteorologic, astronomic, and anthropogenic) largely controlled productivity at the sand site. Productivity at the muddy sand site was influenced by a combination of physical and biological activities. <s> BIB005 </s> An overview of reconstructability analysis <s> Problem-type: Reconstruction vs. identification <s> We compare and contrast three different, but complementary views of "structure" and "pattern" in spatial processes. For definiteness and analytical clarity we apply all three approaches to the simplest class of spatial processes: one-dimensional Ising spin systems with finite-range interactions. These noncritical systems are well suited for this study since the change in structure as a function of system parameters is more subtle than that found in critical systems where, at a phase transition, many observables diverge thereby making the detection of change in structure obvious. This survey demonstrates that the measures of pattern from information theory and computational mechanics differ from known thermodynamic and statistical mechanical functions. Moreover, they capture important structural features that are otherwise missed. In particular, a type of mutual information called the excess entropy---an information theoretic measure of memory---serves to detect ordered, low entropy density patterns. It is superior in many respects to other functions used to probe the structure of a configuration distribution, such as magnetization and structure factors. $\epsilon$-Machines---the main objects of computational mechanics---are seen to be the most direct approach to revealing the (group and semigroup) symmetries possessed by the spatial patterns and to estimating the minimum amount of memory required to reproduce the configuration ensemble, a quantity known as the statistical complexity. Finally, we argue that the information theoretic and computational mechanical analyses of spatial patterns capture the intrinsic computational capabilities in spin systems---how they store, transmit, and manipulate configurational information to produce spatial structure. <s> BIB006 </s> An overview of reconstructability analysis <s> Problem-type: Reconstruction vs. identification <s> Reconstructability analysis (RA) is a method for detecting and analyzing the structure of multivariate categorical data. Jones and his colleagues extended the original variablebased formulation of RA to encompass models defined in terms of system states (Jones 1982; Jones 1985; Jones 1985; Jones 1986; Jones 1989). In this paper, we demonstrate that Jones’ previous work comprises two separable ideas: the “g to k” transformation and state-based modeling. We relate the concept of state-based modeling to established variable-based RA methods (Klir 1985; Krippendorff 1986), and demonstrate that statebased modeling, when applied to event and decision tree models, is a valuable adjunct to the variable-based sensitivity analyses commonly employed in risk and decision modeling. Examples are provided to illustrate the approach, and issues associated with the interpretation of state-based sensitivity analyses are explored. <s> BIB007
RA includes reconstruction and identification BIB001 . In reconstruction ABC (see Figure 1 ) is the data, and one goes down the lattice until decomposition losses are unacceptable. Or, one can start at the bottom with A:B:C (the independence model for neutral systems) or AB:C (the independence model for a directed system with output C), and ascend until model error relative to the data is too great or the model is unacceptably complex. Descending the lattice is especially natural for neutral systems, while ascending the lattice is more natural for directed systems. Thus, in reconstruction, a distribution or relation is decomposed (compressed, simplified) into projected distributions (also called "margins") or relations. ABC might, for example, be decomposed into AB and BC, written as structure, AB:BC. Taken together, the two linked bivariate projections would constitute a model of the data which is less complex (has fewer degrees of freedom) than the data. By maximum-entropy (uncertainty) composition of these projections, the model yields a calculated trivariate ABC AB:BC distribution or relation which may differ from the observed ABC data. The difference (error) represents loss of information in the model. By definition, the data itself has 100% information (0% error). Models are also assessed in complexity, where complexity for IRA is df, degrees of freedom, the number of parameters needed to specify a model. For convenience df values may be normalized so that the data is 100% complex and the independence model 0% complex. Reconstruction decomposes data by finding less complex models which preserve either all of its information (lossless decomposition) or a sufficient amount of its information (lossy decomposition), where sufficiency is assessed either statistically or by other standards. Reconstruction is done in either a confirmatory or exploratory mode. In the confirmatory mode for IRA, a specific model or a small number of models, proposed a priori on the basis of theoretical considerations, are tested statistically. In the exploratory mode, one has no prior idea about what model might be suitable, and one examines many structures to find a best model or a family of best models. LL modeling is normally done in the confirmatory mode and, indeed, in the social sciences, exploratory modeling is normally frowned upon. The situation is quite different in machine learning, a field explicitly devoted to exploratory modeling. Identification is pure composition. For example, the observed data might be the two distributions AB and BC. Because they are not derived from a single ABC, AB and BC can be inconsistent if they disagree in their common B projection. If such an inconsistency can be resolved, a calculated ABC can be generated. Identification methods exist which resolve such inconsistencies and make possible the integration of multiple data sets (as in a data-base merge) coming from different sources. The LL and LDL literatures have not articulated the identification problem and are focused exclusively on reconstruction. Reconstruction in the exploratory mode is the typical RA problem. For convenience, call modeling with "few" variables data analysis and modeling with "many" variables data mining. This paper discusses both, but is motivated by the task of data mining, for which adequate RA software is not yet available. (LDL techniques have been used for data mining, but LL methods, not typically implemented for many variables or for exploratory searching, are rarely mentioned in the data-mining literature.) "Few" variables here means that exhaustive evaluation of all possible RA models can be done. This allows us to be certain of the choice of a best single model or it might be done for a very different purpose, namely to characterize the data by the set of errors for all possible decompositions. The limit of exhaustive search is roughly about 7 or 8 variables, in round numbers, 10. Data mining here means exploratory modeling beyond this threshold, i.e., with 10's, 100's, perhaps even 1,000's of variables. Exhaustive search is then no longer possible, and heuristic techniques, which consider only a subset of possible models, must be used instead. This threshold of somewhat less than 10 variables marks the limit of exhaustive analysis of all models, but there is a second threshold involving the number of possible states of the system (as opposed to the number of states observed in the data), which poses limits even for heuristic search. This 2nd threshold presently precludes the use of multipredictive-component RA models for more than about 20 variables, but single-predictive component models can still SBM is less developed than LVBM. Originally an aspect of the "k-systems analysis" of BIB002 BIB003 , SBM is now being more integrated into the standard RA framework BIB007  . VBM reveals information-rich sets of variables, and a variablebased model is a set of complete projections. By contrast, SBM selects information-rich states, i.e., salient conditions (e.g., BIB004 BIB005 . A state-based model is a set of frequency values selected from the original data and its projections, but complete projections do not have to be included. For example, for f(A,B,C) data, the SB model could be the frequencies, f(A 2 ,B 1 ,C 3 ), f(A 1 ,B 2 ), and f(C 2 ). SBM resembles rule-based methods in logic programming and fuzzy control. It also resembles Crutchfield's ε-machines BIB006   . However, latent variable LL software which is usable for exploratory data mining is not available. In LDL, latent variables are standard, functions being typically decomposed using both "free" (observed) and "bound" (latent) variables   . Since the objective of this paper is to explain RA (especially IRA) methodology, no survey is offered of RA applications, and comparisons with other methods are not undertaken. Section II provides details mostly on IRA reconstruction. Section III gives a few applications of RA to data analysis and mining. Section IV is a summary and discussion.