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Originally published as: J.A. BARCELO, M. PALLARES, 1996 A critique of GIS in Archaeology. From Visual seduction to Spatial Analysis Archeologia e Calcolatori No. 6, 1996

A CRITIQUE OF G.I.S. IN ARCHAEOLOGY. From visual seduction to spatial analysis. Juan A. Barceló and Maria Pallarés Universitat autonoma de barcelona Area de Prehistoria. Facultat de Lletres 08193 Bellaterra (Spain) Abstract The purpose of this paper is to critically explore the role of Geographical Information Systems in the archaeological research. Currently some archaeologists seem largely captivated by new computing technologies believing that the sofisticacion of powerful software outputs will lend respectability by itself. In our opinion GIS is merely a set of techniques to visualize and manage large amounts of georeferenced data. There thus must be other tools to move from visualization to explanation, which fall within the domain of Spatial Analysis The ultimate aim of this paper is to show how we can integrate these already existing tools (geostatistics, intra-site statistical tests, digital image processing, artificial intelligence, etc.) in a GIS framework, in order to move from beautiful images to hard analysis. We finally criticise the lack of theoretical background in archaeological uses of G.I.S. technology arguing that G.I.S is only software and may benefit our research only in the frame of a sound theory and well defined archaeological problems. 1.- SPATIAL ANALYSIS IN ARCHAEOLOGY AND GIS SOFTWARE Most archaeological information is spatial in nature, because it deals with the placement of archaeological finds, contiguity and neighbourhood relationships between archaeological entities. Since archaeologists realized the potencial benefits of studying relationships between behaviour and the spatial distribution of material culture, new ways of representing, visualize and analyze archaeological findings have been proposed. Mapping, or the map-based approach has represented the earliest phase of spatial analysis in archaeology insofar as it has been for centuries an extremely efficient storage medium for condensing a large amount of spatial data and associated attribute variables

into a single sheet of information. In this respect, until earlier 70's archaeological spatial analysis had relied on descriptive informal methods based upon map inspection and almost intuitive impressionistic interpretation. This visual analysis benefited from the dissolution of composite maps into overlay plans showing selected features and categories, to examine their degree of correspondence and to make some subjective judgments about the strengths of the relationships between them. Although in the initial and exploratory stages of many types of archaeological spatial analysis such methods are still valuable, the human eye-brain system is not always a very precise instrument to assess the strengths of spatial relationships. This fact lead to the adoption of formal quantitative methods borrowed from other disciplines such as plant ecology and geography in order to get more objectivity in data recording and analysis. Nonetheless, it is beyond of the scope of this paper to detail the development of quantitative spatial analysis in archaeology since much research time and effort has been spent on this subject (see among others KINTIGH & AMMERMAN, 1982, COGWILL, KINTIGH 1991; BLANKHOLM, 1991, READ 1989). This quantitative movement got off on the wrong foot because it made too often the straightforward assumption that archaeological problems were easy to solve and that statistics and archaeology shared the same problem solving logic (AMMERMAN, 1992). This thoughts yielded a mechanical non-reflective aplication of mathematical techniques to solve bad defined archaeological problems, without considering the analogy between mathematical models and real problems. For more criticisms of quantitative spatial analysis approach see, among others (ALDENDERFER 1987; G.LOCK 1992; AMMERMAN 1992; BARCELO ET ALII 1994). In such an atmosphere of disappointment about the performance of formal techniques as they have been applied over the last two decades one may understand the rapid growth and expansion of Geographical Information Systems during the 80s. Currently, GIS software has been proposed as the best solution for nearly all archaeological problems, because it has the ability to store not only the locational and attribute data for each archaeological entity but also the spatial relationships between them. These relationships can be very complex and diverse, including topological, metrical and social attributes (HERNANDEZ 1995). Therefore, GIS techniques are being used to organize different spatial features in different map layers, producing new layers to represent the results of specific combinations of geographical information. Nevertheless, despite widespread recognition that spatial analysis is central to the purpose of GIS, most applications to date have only shown their power to input, storage and manipulate spatial data, in order to elaborate computer mapping. Their lack of analytic capacities and modelling has been largely considered as a major shortcoming in the research literature

(BIRKIN ET AL. 1987; GOODCHILD 1987; BATTY, 1988; FRENCH AND WIGGINS, 1990; CLARKE 1990; OPENSHAW, 1990, FISHER & NIJKAMP, 1992; FOTHERINGHAM & ROGERSON, 1993; ANSELIN & GETIS 1992). In fact many of the current archaeological GIS projects are only a database containing a discrete representation of archaeological data in a static two-dimensional space, with a functionality largely limited to primitive geometrical operations to compute simple relationships between points in the space, and to simple query and summary descriptions (GOODCHILD et al. 1992). Such systems are basically concerned with describing the Earth surface rather than analyzing it. Or if you prefer, traditional 19th. century geography reinvented and clothed in 20th century digital technology (OPENSHAW 1987). In our view, the main problem is that archaeologists explore the relationships among large spatial data sets following some inductive approaches which consist in simple spatial operations such as multilayer spatial overlay, geometric distance, morphological calculations, topological operators or spatial comparision, to produce a large volume of maps which condense the information considered necessary to describe spatial patterns. It seems as if the last objective was to insert the maximum quantity of information into a map. This indiscriminate map production is related with a lack of prior theory or hypotheses about the kind of problems archaeologists want to solve or about the expected relationships between spatial data, believing that mapping equals spatial analysis. Certainly, GIS has reduced archaeological research and problem solving to the making of pretty but meaningless pictures applying costly resources to answering irrelevant or poorly posed questions. In the same way most archaeological GIS systems lack a coherent body of theory and organizing principles by which real-world spatial entities can be represented. Data structure for archaeological entities is often defined to optimize computer storage and retrieval operations to fit the prevalent GIS data model, without consideration for accurate representation of socio-historical reality (GAFFNEY, 1995). This tendence can explain why many recent applications of GIS, particularly in regional settlement location studies, reflect an envionmentally deterministic approach to archaeological explanation (as have been pointed out by GAFFNEY & VAN LEUSEN 1995, VERHAGEN & MCGLADE 1995, LOCK, 1995). Archaeologists are mainly working with environmental variables that are amenable to cartography describing the topography, lithology and hidrology of an area and that are relatively simple to map, forgetting the importance of social distances in the analysis. Indeed, archaeologists seem largely concerned with locational patterning of regions and they use GIS to produce models that focus on relationships between regional site distribution and mappable attributes of the environment, considering social action as dependent upon the environment and economy.

Archaeological data are inherently difficult to handle and current archaeological spatial descriptions suffer from different kinds of endemic errors that prevent the use of analytical tools (spatial statistics) to understand dependence relationships in the archaeological record. Despite these problems, most of archaeologists believe that GIS software may provide an easy solution to their problems, without considering that GIS is not even an archaeological method, but a purely technique. It can be useful if we used it in a specific way and in the frame of a comprehensive reasoned theoretical base. On the contrary, its results will be misleading if we use it blindly, thinking that techniques are enough to explain historical phenomena. The reseach challenge lies in building on these principles a new theory of spatial relationships and using a new set of spatial analytical tools. 2.- THE NEED OF A SOCIO-SPATIAL THEORY 2.1. THE CONCEPT OF SOCIAL SPACE Even nowadays most archaeologist still do not recognize that space is a very general concept used in many different contexts to denote different things. There are abstract mathematical spaces (structures made up of arbitrary elements according to a set of axioms), psychological spaces, economical spaces, physical spaces or the "real" space in which human activity evolves, etc. (HERNANDEZ, 1994). The word "Space" seems to denote a "set" of entities to which may be attached associated attributes or properties, togeher with a relation or relationships, defined on that set (GATRELL 1983, 1991, SMITH ET AL. 1987, PEUQUET 1988). Space is then the network of all underlying spatial relationships between different entities. From this point of view a straight line between two entities is one of these possible relations, but this is only one way to conceptualize distance. There are other ways to look at spatial relationships, for instance through topological relationships: two entities or objects are far apart from each other; they are close together, but do not touch; they touch, or they overlap. A spatial variable is, consequently, any quantitative or qualitative property of data varying spatially (topologically or according a specific distance measure), and which contribute to explain the dependency relationships between the locations of those entities (CRESSIE 1991). Given thise features, we can define social space as any network of spatial relationships linking any set of social units. 2.2. SOCIAL ACTIVITY AREAS These social units are not always sets of people (families, local groups, villages, tribes, political territories, etc.),

but any set of social actions (productive, reproductive) that have been performed in a single location. We may call these units Social Activity Areas. Given the fact that there are many different possible associations between social actions performed at a single location, there are many different ways to describe those social units, and thus many levels of representations. In this respect some isolated finds may define a low-level social activity area, whereas the spatial relationships among those low-level units may contribute to the definition of higher-level units. Here, low or high level refers not to any importance hierarchical importance order, but to the degree of complexity and representation language needed. Some examples of social activity areas may be: · an empty area, for instance, a ceremonial area after ritual cleaning. · an isolated grindstone · a hearth · a garbage pit or dumping area · a storage pit · any activity area wihin the settlement (butchering area, tool manufacturing area, food preparing area, metallurgical or artesanal activity area, etc.) · a house · a village (a set of houses, storage and garbage pits, activity areas, etc.) · a grave (the set of rituals and ceremonies performed in that location, not the people buried there) · a burial area (a set of graves and ritual structures) · a territory (for instance all its village components and the set of social interaction networks among them) Social activity areas are not geometrical figures but spheres of social interaction without any fixed boundaries; they are characteristically `fuzzy' (GOODCHILD 1987, BURROUGH 1990, CASTLEFORD 1992, USERY 1993). Moreover, their features and topological characteristics change/vary according to time (KAHN & GORRY, 1977, ALLEN, 1984; ZHU ET AL. 1987, LANGRAN, 1989), because the units of social space are not only multidimensional, but dynamic. Consequently, not any single partition method of geographical space results in a model of the social space in use.

Archaeologists used to mechanically define social activity areas from de discovered artifact concentrations. However, there is not a direct correspondence between the observed properties of archaeological contexts and social activities because of the enormous variety of transformational processes with different dimensions and temporal rythms that can have acted upon the archaeological record. Consequently, in order to divide physical space in spatial areas where some social actions were performed, we have to discover temporally dynamic, multidimensional and fuzzy sets of spatial associations among archaeological finds. It had also been wrongly assumed that spatial association implied "tool-kits" and specific activity areas in space. However we are not looking only for tools but for any association of artifacts, elements or features useful to diagnose a social activity. In the same way, as it was shown by early etnoarchaeological studies (YELLEN, 1977) activity areas needed not be spatially dispersed but there are different alternative models which embraces: · Dispersed or segregated activity areas that assumes that different objects and features are partitioned into spatially distinct units or loci, each corresponding to a single activity or group or related activities. (SPETH,1976,) · Agglomerated or multifuncional activity areas, characterized by the overlapping of different social activities. Given the effects due to time, we have to distinguish between more or less stable (fixed) areas and dynamic (temporally modified) ones. This temporal distance may be present in a single continuos episodic occupation but it is stronger as a product of different processes of reoccupation and reuse. Insofar as the archaeological record is the product of repeated depositional events over different periods of time, we must also take into account this change through time. 2.3. RELATIONSHIPS BETWEEN SOCIAL ACTIVITY AREAS Social activity areas are not spatially undifferentiated or isolated. They are in a intrinsically better or worse location for some purpose because of their position relative to some other meaningful unit: Social groups build their own space because they appropriate some biophysical spatial areas and are able to defend them against the members of their own species (TRICOT & RAFFESTEIN 1979). Consequently, space, or spatiallity is not a property of distinct areas existing outside and prior to society, but it is socially constructed (LEFEBVRE, 1974; SOJA,1980,1985; SAYER, 1985; PRED,1985; COUCELIS,1988, VERHAGEN & MCGLADE 1995, BARCELÓ, 1995 PALLARÉS, 1993). Given that social interaction is the formation process of social spaces, from an archaeological point of view, "space" is interesting only when viewed as something constituted, reproduced and changed by social relations, and in turn constraining the unfolding of such relations (COUCELIS, 1988). The fundamental premise of the socio-

spatial dialectic, alredy pointed out by Lefebvre is that social and spatial relationships are dialectically inter-reactive, interdependent; that social relations of production are both space-forming and space-contingent (SOJA, 1980). In this respect, as spatiality is simultaneously the medium and outcome of social action and relationship, it is not only a product but also a producer and reproducer of the relations of production and reproduction (LEFEBVRE 1974, SOJA & HADJIMICHALIS, 1979). Human behavior influence the organization of constructed environments and constructed environtment influence the behaviour; each of them can be modified by the other (ALTMAN, 1975; CANTER ET ALii 1975; RAPAPORT 1970; LAVIN 1981; MAXWELL 1983, SANDERS). As a result, in order to study social spaces we should discover the spatial properties of all relationships linking those areas defined by the set of associated social actions performed there. Social Space is not only a partition of geographical space into "social" areas, but a network of distances between those units. These distances are built upon difference/similarity relationships between social activity areas. For instance: · distance produced by the spatial proximity between each area · distance produced by the diversity on resources in each area · distance produced by the diversity of production activities in each area · distance produced by the differences in volume of production in each area · distance produced by the diversity of consumption activities in each area · distance produced by the differences in volume of consumption in each area · distance produced by the differences on quantity (density) of social agents in each area · distance produced by the differences on the nature of social agents in each area · distance produced by the differences on quantity of social interactions (contact) in each area · distance produced by the diversity of interactions (contact) in each area If we arrive to integrate in a GIS environment different layers showing fuzzy social activity areas at different levels of complexity and temporal modifications, and we extract similarity relationships between any kind of units to define a multidimensional non-euclidean distance metric, we will be in the position to describe the structure of a social space. However, current commercially GISs are still generally designed around basic geometric models of spatial data, using a representation subscribing to the map model of reality, instead of an accurate representation of social reality. The basic raster and vector models place primary importance on locations of geographic phenomena, sacrificing the rich analysis capabilities provided by structuring entities on the basis of

classification attribution and interrelationships (GOODCHILD 1987, USERY 1993). The principal limitation results from the requirement to structure geographic entities as mathematical points, lines, and areas for vector-based systems and as grid cells for raster systems. Neither of these models exists in historical/anthropological reality, since settlements are not points, activity areas are not cercles, and grid-cell structures are arbitrary partitions of space corresponding to no definable geographic entity. This innappropriate language of representation is a consequence of the very fact that GIS systems lack a coherent body of theory and organizing principles by which real-world archaeological entities can be represented in a social space. A representation based on "geography" and "social theory", including the complex interrelations of the social and physical characteristics of locations, in which the content is emphasized over the underlying geometric structure, has the potential to better support archeological models and analytical procedures. Geographers now widely recognize that the spatial context of many human activities cannot fully be described in terms of the distance measures associated with euclidean space. The realization that human spatial behavior may be described and analyzed more accurately through the use of alternative topologies is an important discovery in human geography (GORENFLO & GALE (1990). The same can be true in the case of archaeological space. The proper way of analyzing social spaces needs the construction of non-euclidean representations of spaces based on the geometrical relationships among the above mentioned variables. New models must be developed to fully support spatial analysis and to relate particular social processes to particular spatial associations of objects, elements and relationships. 3.INTEGRATING SOCIAL SPACE THEORY AND SPATIAL ANALYSIS TECHNIQUES IN GIS PROJECTS Some basic features of social spaces can be determined automatically through a combination of analytical and statistical processing, using set theory. For example, several social activity areas are defined by the presence/absence of specific archaeological finds. In those cases we can built a production rule associating the presence of archaeological material with their interpretation as a distinct social activity area. An Expert System may be programmed to do this job, provided we have the right knowledge-base with ethnoarchaeological and experimental information. If we want to map the resulting social areas, we should stablish links between the GIS program and the Expert System, as if the Expert System was an "intelligent" component in the database.

Nevertheless, understanding the complexity of spatial processes and therefore how relational patterns are produced, controlled, and reproduced is not an easy task. Most social space categories are fuzzy, because it is not possible to specify a rule that identifies all of its members and only its members. For example, in most cases food preparing activity areas and food consumption activity areas overlap in space and we cannot identify diagnostic categories or features that separate clearly both activities. The solution comes from a multidimensional approach that accepts the existence of social activity areas at different resolution levels. The goal of the analysis is not to reduce the underlying dimensionality, but to analyze how lowlevel areas are oganized in higher-level units, and how distance relationships between low-level areas contribute to explain the multidimensional structure of social space. This can be done through the combination of geographic locations, attributes, topology, classification attribution, interrelationships and contextual information to the established categories or features (USERY, 1993). Here, contextual information is not definable in absolute terms such as environmental contextual data (soil productivity, sol erosion, vegetation, etc) or the "backgroung variable" as most actual GIS projects attempt. Rather, they are defined (sensu Carr) relative to te phenomenon of interest and the current model being applied to understand it. In this respect, contextual data become more essential to the process of identifying a phenomenon as its characteristics become more ambiguous. In the following sections we introduce some methods and techniques to discover, analyze and modelling spatial dependence, which can be integrated in a GIS platform to study the social space defined by the human group we are investigating. 3.1. FROM ARTIFACT DISTRIBUTION TO SOCIAL ACTIVITY AREAS Because activity areas have two relevant dimensions of variation -spatial discreteness and content- the analytic problem is to simultaneously identificate discret units in what seems a continuous space defining the spatial structure, and then, to detect the specific associations of elements, objects and features that reflect social activities. One of the failures of initial research on spatial analysis was the underlying assumption about the homogeneity of structuring processes across space. It was traditionally assumed that artifact concentration could directly "map" activity areas, but an expanding array of actualistic, ethnographic and archaeological studies have shown that spatial patterning of artifacts/features does not necesarly reflect activity organization, since more than one single process can influence archaeological spatial distributions. Indeed, it has largely accepted that spatial arrangements are the product of multiple spatially non-uniform process and recent work has focused on

ways to isolate local effects and to dissect spatial arrangements into their component parts or spatially homogeneous subsets, prior to using techniques that make global, homogeneity assumptions. (f.i. WHALLON,1984, READ 1989,Carr etc etc) Because artifact concentrations do not correspond, necessary with social spaces, there is difficult to imagine that a single statistical or whatever method, is able to translate a series of coordinates into a geometrical representation of social space. Some attention has been paid in the research literature to demonstrate that a single-method approaches to spatial data oversimplify artifact distributions (f.ex. WHALLON, 1984, BLANKHOLM, 1991, KINTIGH, 1991; GREG et al.. 1991; PALLARËS 1993; BARCELÓ, 1995) We defend the use of several methods in a complementary fashion. Here we propose some of them. 3.1.1.- POINT PATTERN ANALYSIS There is a fertile literature concerned with different techniques to identifying spatial patterning and thus isolate discrete areas. This task has been specially performed by means of different clustering methods, that try to partition objects and features into groups based on observed similarities or differences. First appoaches to spatial analysis applied methods which assumed that an assemblage was the result of a single spatially uniform process acting uniformly over a site or a territory area and only provided indices of spatial patterning, reducing a spatial distribution to summary statistics, indicating a tendency towards clustering, regular or random patterning. One of the most prominent exemples in this kind of formal spatial analysis has been the classic application of the nearest-neighbor as a global index of the patterning of a distribution, whose limitations have been largelly summarized. As these procedures did not characterized the nature of spatial arrangements, Whallon (1984) advocated use of less reductive methods, more consistent with anthropological models of behavior and which make minimal assumptions about the data structure. A similar strategy was later proposed by Kintigh & Ammerman (1982) to respond to archaeological needs. The methods of pattern recognition that at present seem to have a major performance are Pure locational clustering, Unconstrained Clustering, and Presab, as has been demonstrated by their resolution power over ethnoarchaeological cases and successively disturbed simulated materials (see KINTIGH 1991, BLANKHOLM, 1991; GREGG ET ALii 1991). Although this tecniques have been specially applied to intrasite spatial analysis they are equally valid for intersite spatial analysis (RIDING & SAMPSON, 1990, BLANKHOLM 1991; BARCELÓ 1995).

Pure locational clustering or k-means spatial analysis (KINTIGH & AMMERMAN 1982, KINTIGH, 1991; BLANKHOLM, 1990, GREGG et alii 1991; PALLARÉS, 1993, BARCELÓ, 1995) performs a nonhierarchical divisive clustering analysis which atempts to minimize the intracluster variances while maximizing the intercluster istances. It does not provide an index to test spatial clustering, but it focuses on artifact density and location defining discrete clusters in the space with their component points. Another alternative is an assemblage composition approach that tries to find definable differences in assemblage composition directly disregarding the physical location of points/density. This can be done by means of the Unconstrained clustering (WHALLON, 1984), a multistep analytical approach that tries to operate under as few constraints as possible concerning size, shape, density, composition and internal organization or structure. It groups areas of a site in terms of their proportional artifact class composition (WHALLON, 1984; KINTIGH,1991; BLANKHOLM, 1991; GREG et alii 1991, PALLARÉS, 1993), by using relative density vectors as the basis for a Ward clustering analysis of locations. These methods have been applied specially to continuos data, but they may also be used with binary data as H.P.Blankholm proposes developing his Presab method (Blankholm 1991, 1993). In this case, instead of dealing with absolute or relative densities, frequencies or nearest neighbour istances, Presab deals with the presence or absence of data categories which are clustered by means of the k-means algorithm. So, activity areas are defined according to which categories of items that were used in them and not by their frequencies or discard rates. There are also other statistical methods that have been applied to isolate discrete areas, for instance Correspondance Analysis, (JOHNSON, 1984, DJINDJIAN 1988, BLANKHOLM 1991). Nevertheless, it is beyond the scope of this paper to detail technical questions or to make a comparative evaluation of the shortcomings and resolution power of each method and technique. We simple advocate the use of those methods which have been developed to solve archaeological problems and operate under as few constrainsts as possible. If we use them in a complementary fashion, working both with continuous/binary data, and cordinate/gridded data, thus they may be useful to isolate discrete activity areas. Moreover, their complementarity with other methods which we propose in the following sections and the integration of contextual information thanks to the classificatory power of GIS can overcome some of the classic limitations of this statistical tests. 3.1.2.- IMAGE PROCESSING TECHNIQUES

Image processing techniques are powerful exploratory and quantitative tools that have been greatly underutilized in archaeology. There are tree main types of image processing: detection of spatial structures, spatial modelization, and regionalization (VOIRON CANICIO, 1993). Currently applications in archaeology have focused mainly on field survey data, and regional intersite analysis, in order to locate sites and features, define physiographic regions, soil zones, etc. Nevertheless, most of these techniques can also be applied with any spatially dense data in two or three dimensions- raw count, weigth, and quantity data- at the intrasite scale, to investigate spatial organization and thus establish social activity areas (see Hartmann 1988, Lang, 1992). The purpose of image processing is not to see images, but to analyse information contained in an image, searching for unknown structure by removing the effects of noise or blurring, or to find a relation between an input image and an archaeological model. Digital image processing techniques can be divided into two major areas, spatial-domain methods which involve operations directly on the pixel values, and frequency-domain methods which make use of some transforms to change the image into a representation of the frequency information of the data. (LANG, 1992) In the first stage the image is digitized and pre-processed using local convolution operators to improve the image data suppressing unwilling distortions or enhancing some image features important for further processing. Some of these methods are geometric transformations, brightness interpolation, smoothing, edge detectors, neighbourhood, etc.( SONKA, HLAVAC& BOYLE +referencies) The second stage of the analysis is Segmentation. It is the process of dividing an image into regions or parts of uniform appearance that have a strong correlation with objects or areas of the real world contained in the image (SONKA, HLAVAC& BOYLE). In archaeology this can be used to locate areas where archaeologicl sites are likely to be found. Edge detection and image enhancement are techniques used to identify specific cultural features. Morphological mathematical transformations may constitute the third stage of the analysis. They are based on geometry and shape and deals with binary morphological sets and with numerical morphological functions (VOIRON CANICIO 1993). Their function is to simplify images and preserve the main shape characteristics of objects. Between the big number of possible morphological transformations, the most common are dilation, erosion, opening, closing, and skeleton. (SONKA, HLAVAC& BOYLE) Continuos or discrete Image transforms are widely used in image filtering, image data compression and image description processes (SONKA, HLAVAC& BOYLE). There are many different image

transforms (f. instance, fourier transform, hadamard transform, discrete image transforms, lowpass and higpass filters), but the must common image enhancement problems include noise suppresion, edge enhancement and structured noise removal. The last processing step evaluates results of morphology using different mumerical descriptors or a syntactic approach classification. One approach has been to use usual methods of multivariate analysis, however, these techniques do not really exploit the spatial component of the data because they assume that data vectors in neighbouring pixels are independent, but clearly this is not so (CRESSIE, 1991). There are some spatial dependencies caused by the contamination resulting from oversampling and resampling, spatial continuity of the ground clases and problems of scale that can result in biased estimates of the covariance matrix, and hence in an increased classification error rate (Cressie,1991). Therefore, the accuracy with which a remotely sensed image may be classified is dependent on the characteristics of the training data and the nature of the classifier (Mather, 1987; Schalkoff, 1992; Foody et alii, 1995). A wide range of techniques which make no assumption about the statistical distribution of the data may also be used such as non-parametric classifiers, fuzzy classifiers, or neural network tecniques (see among others HEPNER et al. 1990; SHORT, 1991; FOODY ET alii, 1995; BENEDIKTSSON et al. 1990; CHEN ET Alii, 1995). 3.1.4.- ARTIFICIAL INTELLIGENCE METHODS In terms of spatial interaction modelling, a neural net approach brings with it the promise of being able to offer a new view on the nature of the spatial interaction functions that can be deduced from instances of interaction data . We can use a Kohonen self-organising map to discover a continuous topological mapping of a function from one n-dimensional space to another mdimensional space by means of self-organisation based on data examples. It has been shown to be capable of representing highly complex and non-linear functions. This type of net are often used as pattern detectors but in a spatial interaction context the mapping to be learnt might be considered to involve a spatial interaction field.(Openshaw 1993) 3.2. COMPARING LEVELS SOCIAL ACTIVITY AREAS AT DIFFERENT COMPLEXITY

Once we have defined some discrete units by means of different complementary methods the next stage of the analysis consist of comparing these social activity areas at different complexity levels. The objective is to integrate in a GIS environment several layers with different information concerning location, morfology, size, content and contextual information of every

discret unit in order to extract similarity relationships between them that permit us to describe the structure of a social space. This process must be done by means of a formal GIS language with a defined syntax and vocabulary specific to map analysis which can define any model of spatial inte-relationships. In this respect, it is needed a mapalgebra that defines not a simple arithmetic combination of map layers but integrates some more complex spatial operators. Specially relevant for us are the posibilities to compute mathematical and boolean operatons with points and clusters of points. This paradigm is based on the formalized system for expressing GIS functions developed by C.Dana Tomlin (Tomlin 1990, Mills 1994). The representation language described by Mills ( MILLS, 1994), seems one of the most powerful modelling paradigm because it works with different operations that seem able to induce any kind of associative principes, conections and relationships betwen the variables of interest to describe social spaces. This language, called MapAlgebra recognize that in all geographic analysis, there are only four fundamental types of spatial operators: · local operations apply familiar mathematical functions (ADD, SUBSTRACT, MULTIPLY, DIVIDE) to each point's value (or values) on one or more layers. A single example is the sum of two map layers. · focal operations compute a new value for each point as a function of the existing values, distances, and/or directions within its neighbourhood/containment and adjaceny/. Neighbourhoods may be defined in terms of physical separation, travel cost, or intervisibility. MapAlgebra has the possibility of calculating "spreading" and "radiating" nonEuclidean funtions, which extend the concept of neighbourhood to include neighbourhoods defined by time and other factors (including those operating within other layers). For example, we can define cluster of points defined by a ring-shaped nighbourhood, with a diameter more than 1 km. but less than 5 km. · zonal operations compute a new value for each location as a function of the existing values from one layer that are contained in zones of another layer. A simple example is summing the individual residence units on one layer, controlled by the site-catchements boundaries on another. · incremental operations characterize each location as an increment of one, two or three-dimensional geographic form. The size and shape of these increments are inferred from the value (or values) of each location relative to those of its adjacent neighbours on one or more specified layers. A simple

example is a map showing the direction of drainage at each location. Some useful MapAlgebra expressions may be : Density = ZonalSum of activity areas within a settlement In this case it is assumed that we started with one map layer having a `1' for activity areas -or a count of activity areas per cell- and another with each settlement. Direction= IncrementalDrainage of Altitude Runoff = FocalSum of 1 spreading through Direction The first operation Incremental Drainage, results in a layer showing the direction of drainage from each cell. The second uses the focal operation modifiers "spreading thorugh" to sum values along the connected drainage directions 3.3. GEOGRAPHICAL DISTANCE BETWEEN SOCIAL ACTIVITY AREAS Our first task is to measure the degree of spatial variation in each layer of social activity areas. If the observed spatial variability between social areas has not any known source (time, function, ethnic, cultural, economic, social, etc.), then we shall not expect any spatial association. Spatial heterogeneity occurs when there is a lack of spatial uniformity in relationships between the variables under study. When the variation is not wholly erratic, and there is some regularity, we say that there is a certain degree of spatial dependence between spatial units (OLIVER & WEBSTER 1990): "everything is related to everything else, but near things are more related than distant things". This type of dependence is often referred to as spatial autocorrelation (CLIFF & ORD 1973) or network autocorrelation (DOREIAN 1982) although the notion of autocorrelation is more limited than that of dependence. The analysis then pretends to examine if the characteristics in one location have anything to do with characteristics in a neighbour location through the definition of a general (some times linear) model of the space. What we are looking is if what happens in one location is related (depends on) with what happens in the mean of neighbour locations. The result of the analysis may be an answer to this question (yes, all neighbour locations are similar, or not) or an statistical model representing how differences between locations depend on their mutual distances. The question is not only to discover the degree of spatial dependence, but to explain why the location of social activity

areas show that level of spatial homogeneity or heterogeneity, and if that level of geostatistical association is significative in social behaviour terms. Moreover, spatial dependence has to be analyzed between similar social activity areas in the same layer, and between categorically different social areas in different layers. EJEMPLO There are many different techniques to compute this "degree" of spatial dependence: G STATISTIC (GETIS & ORD,1992) . INDEX DE CONCENTRACIÓ DE TRICOT (PERÒ DISCUTIR RELACIÓ CONCENTRACIÓ/GRAU D'ESPECIALITZACIÓ DE L'ESPAI SOCIAL. NO ESTIC D'ACORD). . PEARSON'S C2GOODNESS-OF-FIT TEST (CRESSIE 1991) . MORISITA INDEX . MORA'S I . KERNEL ESTIMATORS OF DENSITY FUNCTIONS (SILVERMAN 1986, BAXTER). . RIPLEY'S K FUNCTION. Polinomial surfaces of various orders may be fitted to the maps containing social activity areas in an attempt to model the spatial relationships among social units or whatever archaeological categories. In this case the goal is to obtain a geometrical surface generalizing the observed distribution of data to portray their overall patterns of location. Existing methods of surface interpolation can be divided into: trend surface analysis, whereby polynomials or sometimes trigonometric functions are fitted by least squares regression on the spatial coordinates as predictors (Hodder and Orton 1976). This approach has several shortcomings: it loses detail because of powerful smoothing; instability caused by outliers or observational errors or when enough terms are included in the function to retain local detail; and variation in one part of the region affects the fit os the surface elsewere (Oliver and Webster 1990). other interpolation techniques such as low order polynomials, spline functions, polyhedra, Delauney's triangulation, and weighted moving averages. Each of these methods has its own disadvantage, but the following remarks apply to all traditional interpolators. First, spatial dependence in the data is assumed implicitly; there is no provision to determine whther the assumption holds. No account is taken of the form of the spatial variation. None of the methods provides any estimates of errors of estimators. Kriging (Schiepatti 1985, Oliver and Webster 1990, Cressie 1991, Voiron Canicio 1993, Davis et al. 1994) is essentially a method of estimation by local weighted averaging, using weights to ensure that there is no bias and minimize the estimation variance. In other words, it refers to making inferences on

unobserved values of a random process considered the cause of spatial distribution of observed points. Spatial continuity is estimated weighting the influences of data points by their statistical distance instead of their geometric distance from one another. Kriging can be expected to consistently replicate data at the observation locations, but the resulting surface has greater continuity than reality because of the smoothing effect of the process (Davis et al. 1994). Kriging overcomes many of the shortcomings of the traditional methods of interpolation. The kriging weights are determined by the spatial structure existing on data points (the variogram). It is an optimal interpolator in the sense that the estimates are unbiased and have known minimum variances. Since the estimation variances can be determined and mapped like the estimates, and assuming a particular distribution, we can calculate the confidence we can place in the estimates. (Oliver and Webster 1990) In Archaeology we can use this last method to analyze a series of settlement locations in a region or the localisation of some intrasite activity areas within the settlement. In contrast with the geological method, we are not interested in calculating the value of empty zones (locations without archaeological remains) (Voiron Canicio 1986). The method allows the discovery of spatial structures between recorded locations, determining the existence of sub-spaces and their limits. It is also a means of comparison of different spaces in different periods of time: if sub-spaces have had allways the same structures, boundaries and components. Kriging is then a method to analyse the patterning existing in our spatial data, discovering all differences and discontinuities and ordering them by their relevance.

3.4. OTHER DISTANCE MEASURES BETWEEN SOCIAL ACTIVITY AREAS Our task is to explain the discontinuities measured on the spatial dependency model according with the differences in social action documented for each area or location. This can be done allocating each location in the archaeological or the geographical layer to an area in the social space structure layer. This allocation can be done by a neural network, whose objective is to create a non-linear rule able to assign a classificatory label to some clusters of data. (Chen et al. 1995, Foody et al., 1995). Neural Network generalization is far better than classical statistical prediction methods because it is possible to take into account data errors and different measurement scales. They also make weaker assumptions about the statistics of the input data than a parametric Bayes classifier; and they are capable of forming highly nonlinear

decision boundaries in the feature space and therefore has the potential of outperforming a parametric Bayes classifier when feature statistics deviate significantly from the assumed Gaussian satistics. The result is not a new map, but an alternative to regression models. The neural network computes a distribution-free discriminant function for the discontinuities in the social space layer, based on the distiguishing features of the training set: all archaeological and biophysical evidences for social actions performed in those locations. These kind of representation allows also the assignation of weights of importance to each input data variable if the relative quality or relevance of these variables is known with respect to the classes of interest. Different weighting factors may be assigned for different classes. This option allows to include detailed information about how individual features and classes are related based on theoretical assumptions (degree of social complexity, degree of human dependence to the ecosystem, etc.). USAR FIG. 4, EN FOODY ET AL. p. 394. One way of exploiting this classification is introducing "abstract maps". They contain for each object in a scene a data structure with the same neighbourhood structure as the domain required for the task at hand. We obtain as a result dependency networks. The user can make queries to the map, asking, for example for the existence of especific dependency path between two nodes, for instance, between a hunter and a gatherer involving an arc labelled "exchange". TRANSPARENCIAS EN HERNANDEZ p. 76 5.6. Network Analysis and Fuzzy sets Social spaces do not end with contextual classification. We need to build a general model to understand how the space was used by a human society. We can build this model from relationships (distances and dependences) between classes discovered in the last stage of our analysis. A way of modelling the qualitativeness of "cognitive space" is by using a relative representation of spatial knowledge based on locative relations (over selected spatial dimensions) among objects, and between objects and distinguished reference structures. Consequently, a scene is represented as a net of mutually constraining locative relations. Inference is done by general constaint satisfaction mechanisms extended to take the structure of the domain into account, and by specialized procedures, which operate on data structure that analogically reflect the structure of the relational domain on a higher level of abstraction. The advantage of these data structures is that, since they have th same structure as the relational domain they represent, operations such as a change in point of

view or the composition of efficiently (Hernández 1994).

relations

can

be

performed

(WANG, HALL SUBARYONO, 1990) define A FUZZY RELATIONAL DATA MODEL TO IMPROVE THE REPRESENTATION OF INFORMATION IN GIS. GEOGRAPHICAL INFORMATION THAT IS PROTRAYED SPTIALLY IN CARTOGRAPHIC FORM IS CONVENTIONALLY REPRESENTED BY THEMATIC MAPS. A THEMATIC MAP IS A SET OF SPATIAL ENTITIES, PONTS, LINES AND AREAS, THAT ARE DESCRIBED BY THEIR NON-SPATIAL ATTRIBUTES ABOUT A SINGLE THEME. SUCH A METHOD CANNOT PROPERLY REPRESENT COMPLEX SITUATIONS SUCH AS A MIXTURE OF COVER AND INTERMEDIATE CONDITIONS WHICH OCCUR QUITE OFTEN. IN A FUZZY REPRESENTATION, CLASSES CAN BE DEFINED AS FUZZY SETS AND SPATIAL ENTITIES AS SET ELEMENTS. EACH SPATIAL ENTITY IS ASSOCIATED WITH A GROUP OF MEMBERSHIP GRADES TO INDICATE THE EXTENTS TO WHICH THE ENTITY BELONGS TO CERTAIN CLASSES. (WANG, HALL SUBARYONO, 1990) (FER UNA SINTESI DEL QUE PROPOSEN). DESARROLLAR LA IDEA DE CLASIFICACION CONTEXTUAL Y CATEGORIZACION (usery) The inference engine extracts knowledge from the fuzzy knowledge base and makes inferences via rules and facts. A typical spatial inference involving fuzzy terms may be expressed as follows (Leung 1993): Rule: If distance to the main site center (X) is short (A) then Interaction (Y) is high (B) Fact: Distance to site Center (X) of polygon K is very short (A1) ______________________________________________ Approximate conclusion: Interaction (Y) in polygon is veru high (B1) Knowledge-based information systems will play an important role in decision analysis in the future. Spatial Analysis tools without "intelligence" have very little chances to meet challenges commonly encountered in the highly complex and imprecise social spaces configurations. Our hability to efficiently and effectively integrate databases, knowledge (dclarative and procedural), expertise, intuition, inference, and graphics into an unified system is crucial. A lattice of locations evokes the idea of regularly spaced points , linked to nearest neighbours, second nearestneighbours, and so on. Of all possible spatial structures that can generate, a data set whose spatial locations are a regular graph is the closest analogue to a time series observed at equally spaced time points. Lattice theory can be applied to digital immage processing, analyzing spatial relationships among pixels: any bit-mapped image is a lattice of regularly distributed pixels in a bidimensional-space. Assuming data can be thought of as a partial realization of a random phenomenon (i.e., a stochastic process), we can imagine

that the spatial variable is a countable collection of spatial sites at which data are observed. Mathematically speaking we can translate these individual points into vertices which are conected by edges to points with the same value on the spatial variable. We call it the neighbourhood structure, because we suppose that the closer the points, the closer the measures of spatial space. EJEMPLO: PRIGOGINE y el Mississipi. A graph of neighbourhood structure can be represented using a Fuzzy Cognitive Map. DESCRIBIR. Image data are represented usually as gray tones. We can consider them as fuzzy sets. Suppose 0 denotes de absence of findings and 1 denotes the presence; values between 0 and 1 denotes the confidence we have in the presence of an archaeological item in that point. DESARROLLAR FUZZY SETS. The only difficulty is how to build neighbourhood relationships based on observed data. This is a straigthforword statistical problem, that can be solved using any of the classical clustering methods or similarity indexes. Statistical similarity is problamatic (Tversky, Osherson.... ) Using Neural Nets and Machine Learning to estimate asymetrical similarity indexes. What we can do with the neighbourhood structure once we have built the lattice? It should be deteermined whether the locations: are regular or irregular represent points or regions are indices for continuous or discrete random variables. In other words, a lattice of geometrically linked points can be analyzed to discover and measure the degree of spatial dependence in more easier way that using stochastic models and plans interpolation. TEORIA DE LAS SOCIAL NETWORKS. Racine (1979, Progogine, Harary. FUZZY COGNITIVE MAPS AS A coherence and stability in social spaces. DYNAMIC SIMULATION. Studing the

Often the lattice can, in principle, be partitioned into regions corresponding to different areas or spatial units. Neighbourhood structure can consequently be described and analyzed at different levels, depending on the degree of segmentation and the meaning of each unit. emember Clarke classification of archaeological units: we can investigate a lattice of archaeological types at a micro-level or a lattice of technocomplexes at a macro-level.

5.5. Virtual Reality visualization is a way of explanation: it transforms the symbolic into the geometric, enabling researchers to observe their simulations and computations. Visualization in a GIS environment then has to be a part in the process of scientific discovery, helping archaeologists to detect regularities in the patterns of spatial relationships among social contexts. Visual processing in the brain is tied to cartographic cognition which is a unique process as it involves the use of the brain to recognize patterns and relationships in their spatial context. This cannot be easily replicated by GIS software with essentially linear analytical processess based on data structures which are topological, sequential, or object oriented. In many cases the data in such systems can only be fully understood by displaying them in map form. It is in the cognitive field, especially in the emerging area of visualization, where modern cartography have their closest interaction (Taylor 1993) A.M.MacEachren Visualization is foremost an act of cognition, a human ability to develop mental representations that allow geograhers to identify patterns and to create or impose order p. 101. Geographic visualization will be defined here as the use of concrete visual representations-whether on paper or through computer displays or other media- to make spatial contexts and problems visible, so as to engage the most powerful human information-processing abilities, those associated with vision DiBiase (1990) suggests that visualization tools may play different roles at different stages of scientific research. Identifies four stages: exploration, confirmation, synthesis and presentation. Scientific visualization is applied to use of computer graphics and image processing technology in data-intensive scientific applications p. 8. Muehrcke. 906. The more visualization options we have, the better we understand the nature of individual visual expressions. p. 9 Computer vision is the construction of explicit, meaningful descriptions of physical objects from images so that they can be modeled in digital form (Ballard i Brown 1982) Peuquet 891, p. 378 GIS may be used as a means of presenting a series of hypothetical scenarios which are relevant to our understanding of human/environmental relationships. This can be done principally through the construction of a `territorial' model designed to articulate a set of semi-autonomous activity

spheres which are said to be implicated in the rproduction and organization of a specific archaeological locus, or settlement (Verhagen et al. 1995). Lang visualització científica que pot ser definida, segons un article del 87 de la National Science Foundation from the Association for Computing Machinery: Visualization is a method of computing. It transforms the symbolic into the geometric, enabling researchers to observe their simulations and computations. Visualization offers a method for seeing the unseen. It enriches the process of scientific discovery and fosters profound and unexpected insights.... Visualization embrances both image understanding and image syntesis. That is, visualization is a tool both for interpreting image data fed into a computer, and for generating images from complex multi-dimensional data sets. It studies those mechanisms in humans and computers wich allow them to perceive, use and communicate visual information. An estimated 50 percent of the brain's neurons are associated with vision. Visualization in scientific computing aims to put that neurological machinery to work. (MCCormick et al. 1987). La visualització científica està emergint com la disciplina per presentar dades abstractes en formes més interpretables pel sistema visual humà: tridimensionals, imatges en color que canvien al llarg del temps Experimentation with virtual archaeological formations may lead to new insights into data recording and analysis. The key concept here is virtual, an allusion to a model, a replica, the notion that something can act as a surrogate or replacement for an original. In other words, it refers to a description of an archaeological formation or to a simulated archeological formation. (A simulated data set will normally be shaped by the criteria used for recording an actual formation). (Reilly 1992). The challenge is no longer only to model terrain, structures o distributions with simple geometry, but to model those amorphous humps, bumps and hollows, typically found in the course of fieldwok. Data visualization refers to those techniques which allow visual interpretation of data through the representation, modeling and display of solids, surfaces, properties and animations, involving the use of graphics, image processing, computer vision and user interfaces. It is a manifestation of "seeing the unseeable". Data visualization is a means whereby much more multi-dimensional data can be brought within the range of human experience and cognition. It should be stressed that the graphical aspect of solid modelling systems is not necessarily their prime function. These systems also embody large volumes of structured three-dimensional information which can be exploited to establish links to many different kinds of

database. (Reilly 1992). Realism in solid modelling is achieved not only by modeling natural lighting effects, but by trying to embody some element of the social cntext and function of the subject in the visualization and thereby bring the visualization to life. The object of this kind of graphical application is to provide a description of the archaeological data in a way which is optimized to communicate the maximum of information, with as little spurious addition as possible. 3D VISUALIZATION: the aim might simply to illustrate, but often there may be some more purposeful intention -to investigate or to simulate thoughts towards an archaeological interpretation. Ad a tool for scientific analysis, the visualizing process resulting from solid modelling can sometimes rveal rlationships within an archaeological `reconstruction' more clearly than other current methods of display. However, when archaeological data is the source, soid modelling will usually entail a high proportion of dubjective judjment, since so many controlling paameters are not completely known (colour, texture, dimensions, etc.)(Fletcher and Spicer 1992). The object of representation of a surface is the communication of information in the most efficient manner possible. Fletcher and Spicer shows how to build terrain surface from topographic information, and how the solid modelling of that surface provides information about social space, or more specifically, the constraints of topographic space on social space. The criterion is simply to show the surface of the ground in as naturalistic a way as possible, so as to utilize fully the human abilities to observation and perception, and to couple it with the experience and intuition of an arcaheological training. It uses georeferenced data (topographic points in a cartesian space x,y,z) and contextual information about the aspect of surface (colour, texture, light, visibility, etc.). (Fletcher and Spicer 1992). Reilly comments an example of solid modelling applied to intrasite analysis: "In order to make it possible to see whether material in the features was similar to and perhaps, therefore, connected with material in the local parts of the overlying layers, the digitised plans of the cut features (i.e. pits, post-holes) were extruded to form prisms. These prisms were then intersected with a solid model of the overlying layers which, indicentally, were composed of box-shaped contexts intended to lend a degree of precission in spatial provenancing within these deposits. Colour-codes were employed to signify different properties (e.g. average sherd size). The application of a clipping plane down the sides or o the top of the model could then be used to expose internal details and any visual correlations between properties of the cut features and local box-contents could be assesed and, if interesting, investigated further (Reilly 1992, Reilly and Shennan 1989).

Grafland is another project: Rather than reduce the record to a series of abstract single context plans and sections, each context is defined as a three-dimensional solid which can be examined from any elevation or sectional view. The `naturalism' of the solid-modelled contexts is illusionary, of course, for archaeological excavators could never experience these entities in the manner that the solid modelling program allows, because the archaeologist never actually sees a whole or complete formation through excavation. It is by integrating each separate perceptions of the formation that a clearer idea of its totality may be reached. Recorded primary data is a metaphor for elements of the material continuum that is is raw archaeological material. It is this metaphorical data that forms the basis of archaeological discussion. By enhancing and enriching the quality of this metaphorical data w hope to stimulate more and new archaeological discussions. Contexts modelled as solid geometries are susceptible to a much wider range of transformations and interactions than the older methods of representation allowed. This increased freedom to explore multi-dimensional data sets opens the way for further insights into the nature of three-dimensional deposits and thei recording. With GIS is possible to introduce the actual physical characteristics of a region into computer simulation. We no longer need to make such simplifying assumptions as a `featureless and level two-dimensional plane. The actual landform, soils, vegetation, hydrology, and other features of a region can be incorporated for the simulation background, allowing greater realism and undoubtedly better insights (Kvamme 1995). COMENTAR VISTAPRO Y KPT BRYCE.

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MATHERON,G., 1965, Les variables estimation. Paris: Masson.

regionalisées

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