# Discovery of spatial association rules in geo-referenced census data: A relational mining approach

←

**Page content transcription**

If your browser does not render page correctly, please read the page content below

Intelligent Data Analysis 7 (2003) 541–566 541 IOS Press Discovery of spatial association rules in geo-referenced census data: A relational mining approach Annalisa Appice, Michelangelo Ceci, Antonietta Lanza, Francesca A. Lisi and Donato Malerba Dipartimento di Informatica, Universit à degli Studi di Bari, via Orabona 4, 70126 Bari, Italy E-mail: {appice, ceci, lanza, lisi, malerba}@di.uniba.it Received 1 November 2002 Revised 10 January 2003 Accepted 25 February 2003 Abstract. Census data mining has great potential both in business development and in good public policy, but still must be solved in this field a number of research issues. In this paper, problems related to the geo-referenciation of census data are considered. In particular, the accommodation of the spatial dimension in census data mining is investigated for the task of discovering spatial association rules, that is, association rules involving spatial relations among (spatial) objects. The formulation of a new method based on a multi-relational data mining approach is proposed. It takes advantage of the representation and inference techniques developed in the field of Inductive Logic Programming (ILP). In particular, the expressive power of predicate logic is profitably used to represent both spatial relations and background knowledge, such as spatial hierarchies and rules for spatial qualitative reasoning. The logical notions of generality order and of the downward refinement operator on the space of patterns are profitably used to define both the search space and the search strategy. The proposed method has been implemented in the ILP system SPADA (Spatial Pattern Discovery Algorithm). SPADA has been interfaced both to a module for the extraction of spatial features from a spatial database and to a module for numerical attribute discretization. The three modules have been used in an application to urban accessibility of a hospital in Stockport, Greater Manchester. Results obtained through a spatial analysis of geo-referenced census data are illustrated. 1. Introduction Most countries of the world conduct population and economic censuses at regular intervals. Population census information is of great value in planning public services for governments at all levels, such as cities, counties, provinces, and states. Both population and economic census data are also used by private companies or community organizations for various purposes, such as marketing studies, situating new factories or shopping malls, developing social service programs. Therefore, the application of data mining techniques to census data has great potential both in underpinning good public policy and in supporting business developments. However, mining census data is not straightforward and requires challenging methodological research. In this work, we are mainly concerned with one of the research issues, namely the geo-referenciation of census data. The practice of attaching socio-economic data to specific locations has increasingly spread over the last few decades. In the UK, for instance, population census data are provided for each 1088-467X/03/$8.00 2003 – IOS Press. All rights reserved

542 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data enumeration district (ED), the smallest areal unit for which census data are published. At the same time, vectorized boundaries of the 1991 census EDs enable the investigation of socio-economic phenomena in association with the geographical location of EDs. These advances cause a growing demand for more powerful data analysis techniques that can link population data to their spatial, or, more precisely, geographical distribution. Advances in spatial data structures [16], spatial reasoning [10], and computational geometry [38] have paved the way for the study of knowledge discovery in spatial data, and, more specifically, in geo-referenced data. Spatial data mining methods have been proposed for the extraction of implicit knowledge, spatial relations, or other patterns not explicitly stored in spatial databases [23]. Knowledge discovered from spatial data can be in various forms including classification rules, which describe the partition of the database into a given set of classes [22], clusters of spatial objects [35,39], patterns describing spatial trends, that is, regular changes of one or more non-spatial attributes when moving away from a given start object [15], and subgroup patterns, which identify subgroups of spatial objects with an unusual, an unexpected, or a deviating distribution of a target variable [20]. In this paper, we focus our attention on the specific task of discovering spatial association rules, that is, association rules involving spatial objects and relations. Association rules are a class of regularities introduced by Agrawal et al. [1] that can be expressed by an implication of the form: P → Q(s, c), where P and Q are a set of literals, called items, such that P ∩ Q = Ø, the parameter s, called support, estimates the probability p(P ∪ Q), and the parameter c, called confidence, estimates the probability p(Q|P ). We call an association rule P → Q spatial, if P ∪ Q is a spatial pattern, that is, it expresses a spatial relationship among spatial objects. The problem of mining spatial association rules has already been tackled by Koperski and Han [21], who implemented the module Geo-associator of the spatial data mining system GeoMiner [18]. However, the method implemented in Geo-associator suffers from severe limitations due to the restrictive data representation formalism, known as single-table assumption [41]. More specifically, it is assumed that data to be mined are represented in a single table (or relation) of a relational database, such that each row (or tuple) represents an independent unit of the sample population and columns correspond to properties of units. In spatial data mining applications this assumption turns out to be a great limitation. Indeed, different geographical objects may have different properties, which can be properly modeled by as many data tables as the number of object types. In addition, attributes of the neighbors of some spatial object of interest may influence the object itself, hence the need for representing object interactions. The recently promoted (multi-)relational approach to data mining [9] looks for patterns that involve multiple relations of a relational database. Thus data taken as input by these approaches typically consists of several tables and not just a single one, as is the case in most existing data mining approaches. Patterns found by these approaches are called relational and are typically stated in a more expressive language than patterns defined in a single data table. Typically, subsets of first-order logic, which is also called predicate calculus or relational logic, are used to express relational patterns. Considering this strong link with logics, it is not surprising that many algorithms for multi-relational data mining originate from the field of inductive logic programming (ILP) [8,25,34,36]. Extending a single table data mining algorithm to a relational one is not trivial. Efficiency is also very important, as even testing a given relational pattern for validity is often computationally expensive. Moreover, for relational pattern languages, the number of possible patterns can be very large and it becomes necessary to limit their space by providing explicit constraints (declarative bias).

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 543 However, mining spatial association rules is a more complex task than mining relational association rules, whose solutions have already been reported in the literature [7]. Two further degrees of complexity are: 1. the implicit definition of spatial relations and 2. the granularity of the spatial objects. The former is due to the fact that the location and the extension of spatial objects implicitly define spatial relations such as directional and topological relations. Therefore, complex data transformation processes are required to make spatial relations explicit, as in the application of machine learning techniques to topographic map interpretation in [28]. The latter refers to the fact that spatial objects can be described at multiple levels of granularity. For instance, if spatial objects are regions with some administrative autonomy, such as wards, districts and counties, they can be organized hierarchically as follows: Ward → District → County based upon the inside relationship between locations. Interesting association rules are more likely to be discovered at the lowest granularity level (ward) than at the county level. On the other hand, large support is more likely to exist at higher granularity levels (District and County) rather than at a low level. In the next section, a new algorithm for mining spatial association rules is reported. The algorithm, named SPADA (Spatial Pattern Discovery Algorithm), is based on an ILP approach to relational data mining and permits the extraction of multi-level spatial association rules, that is, association rules involving spatial objects at different granularity levels. Details on both the interface of SPADA with a spatial database and the feature extraction process are reported in Section 3. Finally, the application of SPADA to a data mining task involving UK census data is reported in Section 4. 2. Mining spatial association rules The discovery of spatial association rules is a descriptive mining task aiming to detect associations between reference objects and some task-relevant objects. The former are the main subject of the description, that is, the observation units, while the latter are spatial objects that are relevant for the task in hand and are spatially related to the former. For instance, if we are interested in investigating the socio-economic phenomenon of deprivation of some urban areas, we can look for spatial association rules that relate properties of some selected ED (reference objects) with properties of other spatial objects, such as public transport stops (task relevant objects). A spatial association rule which states that (only) “in 10% of reference EDs where the percentage of households with no car is high, there is a public transport stop” can lead to the conclusion that there are some seriously deprived areas in the examined territory. An indication of the gravity of this socio-economic phenomenon is given by the support of the rule: if the percentage is high (e.g., 80%), then there are many reference EDs with a high percentage of no-car-owning households which are not served by public transportation. First-order logic is a useful tool for the formal representation of a spatial association rule. For instance, the association rule in the above example can be easily expressed as follows: is a(X, ed) no-car -owning-households%(X, high) → contains(X, Y ) is a(Y, public transp stop) (80%, 10%).

544 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 1 2 public_transp_stop road 1 bus_or_tram_stop railway _metro_station main_trunk_road motor way regional_road 2 3 bus_stop tram_stop railway_station metro_station ss96 ss16bis ss16 a14 r16 r93 r97 l Fig. 1. Two spatial hierarchies and their association to three granularity levels (l). This is a relational association rules, since the relational pattern is a(X, ed) no-car -owning-households%(X, high) contains(X, Y ) is a(Y, public transp stop) expresses some form of relationship, namely spatial containment, between any reference ED and some spatial object classified as public transport stop. Since the relationship and the objects involved in this pattern are of a spatial nature, the above implication is also a spatial association rule. In spatial association rules, the items are first-order logic atoms, that is, n-ary predicates applied to n terms. In the above example terms can be either variables, such as X and Y , or constants, such as high or bus or tram stop. Since some kind of taxonomic knowledge on task-relevant objects may also be taken into account to obtain descriptions at different granularity levels (multiple-level association rules), finer-grained answers to the above query are also expected, such as: is a(X, ed) no-car -owning-households%(X, high) → contains(X, Y ) is a(Y, bus stop) (70%, 11%). which provides more insight into the nature of the task relevant object Y , according to the spatial hierarchy reported in Fig. 1. It is noteworthy that the support and the confidence of the last rule have changed. Generally, the lower the granularity level, the lower the support of association rules. Therefore, we follow Han and Fu’s [17] proposal to use different thresholds of support and confidence for different granularity levels. The problem of mining association rules can be formally stated as follows: Given – a spatial database (SDB), – a set of reference objects S , – some sets Rk , 1 k m, of task-relevant objects, – a background knowledge BK including some spatial hierarchies H k on objects in Rk , – M granularity levels in the descriptions (1 is the highest while M is the lowest), – a set of granularity assignments Ψ k which associate each object in H k with a granularity level, – a couple of thresholds minsup[l] and minconf[l] for each granularity level, – a declarative bias DB that constrains the search space,

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 545 Find strong multi-level spatial association rules. An ILP approach to mining spatial association rules has already been reported in [31]. Representation problems and algorithmic issues related to the application of our logic-based computational method are discussed in the next two sub-sections. 2.1. Representing spatial data and background knowledge The basic idea in our proposal is that a spatial database boils down to a deductive relational database (DDB) once the spatial relationships between reference objects and task-relevant objects have been extracted. More precisely, we pre-process data stored in a spatial database to represent it in a deduc- tive database. For instance, spatial intersection between objects is represented in a derived relation intersects(X,Y). As observed by Kl ösgen and May [20] this approach has some disadvantages, such as high computa- tional burden, redundant data storage and loose integration between a GIS and the data mining method. However, there are at least two equally important advantages. First, once the data is pre-processed the calculation has not to be repeated, e.g. by constructing join indices. This is important in explorative data analysis, where the main effort is in analyzing data along several dimensions and according to a progressive refinement approach. The case in which an expert decides to throw away selected data and to consider a new data set occurs less frequently than the case in which the expert works on the same data by tuning the parameters of the data mining tool. Second, the expressive power of first-order logic in databases also allows us to specify a background knowledge BK, such as spatial hierarchies and a domain specific knowledge expressed as sets of rules. In particular, the specification of a domain specific knowledge permits the search for patterns which could not be otherwise found in the spatial database. The rules defining the domain specific knowledge are stored in the intensional part of the DDB and can support, amongst other things, qualitative spatial reasoning. Henceforth, we denote the DDB in hand D(S) to mean that it is obtained by adding the data extracted from SDB, regarding the set of reference objects S , to the previously supplied BK . The ground facts 1 in D(S) can be grouped into distinct subsets: each group, uniquely identified by the corresponding reference object s ∈ S , is called spatial observation and denoted O[s]. We define the set: R(s) = {ri |∃k : ri ∈ Rk and a ground fact α(s, ri ) exists in D(S)} as the set of task-relevant objects spatially related to s. The set O[s] is given by O[s] = O[s|R(s)] ∪ Uri ∈R[s] O[ri |S], where: – O[s|R(s)] contains properties of s and spatial relations between s and r i – O[ri |S] contains properties of ri and spatial relations between r i and some s ∈ S . In an extreme case, O[s] can coincide with D(S). This is the case in which s is spatially related to all task-relevant objects. The unique reference object associated to a spatial observation allows us to define the support and the confidence of a spatial association rule (see the definition of spatial association rule 1 In this work we assume that ground facts concern either taxonomic “is a” relationships or binary spatial relationships α(s, r) or object properties.

546 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data below). Note that the notion of spatial observation in SPADA adapts the notion of interpretation, which is common to many relational data mining systems [9], to the case of spatial databases. Let A = {a1 , a2 , . . . , at } be a set of Datalog atoms whose terms are either variables or constants [4]. Predicate symbols used for A are all those permitted by the user-specified declarative bias, while the constants are only those defined in D(S). The atom denoting the reference objects is called key atom. Conjunctions of atoms on A are called atomsets [6] like the itemsets in classical association rules. In our framework, a language of patterns L[l] at the granularity level l is a set of well-formed atomsets generated on A. Necessary conditions for an atomset P to be in L[l] are the presence of the key atom, the presence of taxonomic “is a” atoms exclusively at the granularity level l, the linkedness [19], and safety. In particular, the last property guarantees the correct evaluation of patterns when the handling of negation is required. To a pattern P we assign an existentially quantified conjunctive formula eqc(P ) obtained by turning P into a Datalog query. Definition. A pattern P covers an observation O[s] if eqc(P ) is true in O[s] ∪ BK . Definition. Let O be the set of spatial observations in D(S) and O P denote the subset of O containing the spatial observations covered by the pattern P . The support of P is defined as σ(P ) = |O P |/|O|. Definition. A spatial association rule in D(S) at the granularity level l is an implication of the form P → Q(s%, c%) where P ∪ Q ∈ L[l], P ∩ Q = Ø, P includes the key atom and at least one spatial relationship is in P ∪ Q. The percentages s% and c% are respectively called the support and the confidence of the rule, meaning that s% of spatial observations in D(S) is covered by P ∪ Q and c% of spatial observations in D(S) that is covered by P is also covered by P ∪ Q. The support and the confidence of a spatial association rule P → Q are given by s = σ(P ∪ Q) and c = ϕ(Q|P ) = σ(P ∪ Q)/σ(P ). In multi-level association rule mining, an ancestor relation between two patterns at different granularity levels P ∈ L[l] and P ∈ L[l ], l < l , exists if and only if P can be obtained from P by replacing each spatial object h ∈ H k at granularity level l = Ψk (h) with a spatial object h < h in Hk , which is associated with the granularity level l = Ψk (h ). The frequency of a pattern depends on the granularity level of task-relevant spatial objects. Definition. Let minsup[l] and minconf [l] be two thresholds setting the minimum support and the minimum confidence respectively at granularity level l. A pattern P is large (or f requent) at level l if σ(P ) minsup[l] and all ancestors of P with respect to the hierarchies H k are large at their corresponding levels. The confidence of a spatial association rule P → Q is high at level l if ϕ(Q|P ) minconf [l]. A spatial association rule P → Q is strong at level l if P ∪ Q is large and the confidence is high at level l. The definition of the strong spatial association rule given above suggests that the generation of association rules at different granularity levels should proceed from the most general towards the most specific granularity levels. This is the approach followed in the ILP system SPADA, which has been developed for mining multi-level association rules in spatial databases. In the following section we explain how SPADA performs its search in the space of patterns at a given granularity level l, that is,

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 547 Find large 1-atomsets at level l Cycle on the depth (k > 1) of search in the pattern space 1. Generate candidate k-atomsets at level l from large (k-1)-atomsets by applying the refinement operator ρ 2. Prune candidates that θ-subsume infrequent patterns 3. Prune candidates equivalent under θ-subsumption 4. Evaluate candidates and generate large k-atomsets at level l from candidate k-atomsets Until the user-defined maximum depth Fig. 2. Intra-level search implemented in SPADA. in the space of patterns defined by the language L[l] (intra-level search). Section 2.3 illustrates how SPADA takes advantage of statistics computed at a level l when it searches in the ‘more specific’ space at level l + 1 (inter-level search). 2.2. Intra-level search of the pattern space Given a granularity level l and a pattern language L[l], the task of mining spatial association rules can be split into two sub-subtasks: 1. Find large (or frequent) spatial patterns in the space defined by L[l]; 2. Generate highly-confident spatial association rules at level l. Algorithm design for frequent pattern discovery (step 1) has turned out to be a popular topic in data mining. The blueprint for most algorithms proposed in the literature is the levelwise method [32], which is based on a breadth-first search in the lattice spanned by a generality order between patterns. Given two patterns P1 and P2 , we write P1 P2 to denote that P1 is more general than P2 or equivalently that P2 is more specific than P 1 . The space is searched one level at a time, starting from the most general patterns and iterating between the candidate generation and candidate evaluation phases. The intra-level search algorithm of SPADA implements the afore-mentioned levelwise method (see Fig. 2). The pattern space is structured according to the θ -subsumption [37]. Many ILP systems adopt θ - subsumption as the generality order for clause spaces. In this context we need to adapt the framework to the case of atomsets. More precisely, the restriction of θ -subsumption to Datalog queries (i.e. existentially quantified conjunctions of Datalog atoms) is of particular interest. Definition. Let Q1 and Q2 be two queries. Then Q 1 θ -subsumes Q2 if and only if there exists a substitution θ such that Q2 θ ⊆ Q1 . We can now introduce the generality order adopted in SPADA. Definition. Let P1 and P2 be two patterns. Then P 1 is more general than P 2 under θ -subsumption, denoted as P1 P2 , if and only if P2 θ -subsumes P1 . θ -subsumption is a quasi-ordering, since it satisfies the reflexivity and transitivity property but not the anti-symmetric property. The quasi-ordered set spanned by θ can be searched by a refinement operator, namely a function that computes a set of refinements of a pattern.

548 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data Definition. Let G, θ be a pattern space ordered according to θ . A downward refinement operator under θ -subsumption is a function ρ such that ρ(P ) ⊆ {Q|P θ Q}. In SPADA, the following operator ρ is used. Definition. Let P be a pattern in L[l]. Then ρ (P ) = {P ∧ ai |ai is an atom in L[l] }. It can be easily proven that ρ (P ) is a downward refinement operator under θ -subsumption, that is P θ Q for all Q ∈ ρ (P ). Indeed, Q = P ∧ ai for an atom ai in L[l]. By adopting the set notation we can also write Q = P ∪ {ai }. The inequality P θ P ∪ {ai } holds if P ∪ {ai } θ -subsumes P , that is, a substitution θ exists such that P θ ⊆ P ∪ {a i }. Obviously, θ is the empty substitution. The refinement operator ρ (P ) allows the generation of k-atomsets, that is atomsets of k literals, from (k-1)-atomsets. It is noteworthy that θ on patterns represented as Datalog queries is monotone with respect to support. Property of θ -subsumption monotony. Let G, θ be a pattern space ordered according to θ . For any two patterns P1 and P2 such that P1 θ P2 we have that σ(P1 ) σ(P2 ). Therefore, the refinement operator ρ drives the search towards patterns with decreasing support. If a pattern P is infrequent, all its refinements in ρ (P ) are also infrequent. This is the first-order counterpart of one of the properties holding in the family of the Apriori-like algorithms [1], on which the pruning criterion is based. Indeed, the generation of patterns obtained as refinements of infrequent patterns can be avoided, since those patterns have certainly a support lower than the user-defined threshold. This is what happens at step 1) in the algorithm of Fig. 2. Given a frequent pattern P of k-1 atoms, it may happen that some pattern Q ∈ ρ (P ) θ -subsumes another infrequent pattern P of k atoms, with k < k. This means that Q is certainly infrequent because of the above monotony property, and its evaluation can be avoided (step 2 in Fig. 2). Additional candidates not worth being evaluated are those equivalent under θ -subsumption to some other candidate (step 3 in Fig. 2). Finally, unpruned candidates are evaluated to check whether they are large (i.e., frequent) or not (candidate evaluation phase,step 4). The evaluation of each generated pattern P requires a θ -subsumption test against some spatial observations O[s]. Indeed, if O[s] ∪ BK θ -subsumes P , then eqc(P ) is true in O[s] ∪ BK , that is P covers O[s], according to the definition given in the previous section. Actually, in SPADA the test of a pattern Q ∈ ρ (P ) is performed only against those spatial observations covered by P , since, if a spatial observation O[s] is not covered by P , it cannot be covered by Q without violating the transitive property of θ -subsumption. 2.3. Inter-level search of the pattern space As specified in Section 2.1, to be able to define a pattern P as large (or frequent) at level l two conditions must be satisfied, namely i) σ(P ) minsup[l] and ii) all ancestors of P with respect to the hierarchies H k are large at their corresponding levels. The second condition suggests an additional pruning strategy. Let P and Q be two frequent patterns at levels l and l + 1 respectively, such that P is an ancestor of Q. Suppose that P has been refined into the infrequent pattern P while searching in the pattern space at level l. When the space of patterns at level l + 1 is explored and Q is refined, it is possible to generate a candidate pattern Q whose ancestor is P . In this case, Q can be safely pruned, since it cannot be a large pattern without violating condition ii). In order to support this additional pruning strategy, the refinement operator implemented in SPADA

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 549 1 2 3 4 5 k 1 2 l Fig. 3. Graph of intra-space and inter-space backward pointers. uses a graph of backward pointers to be updated while searching. Backward pointers keep track of both intra-space and inter-space search stages. Figure 3 gives an example of such a graph, where nodes, dotted edges and dashed edges represent patterns, intra-space generality and inter-space parenthood, respectively. The effectiveness of this computational solution is illustrated in [26]. 2.4. From patterns to association rules Once large patterns have been generated, it is possible to generate strong spatial association rules. For each pattern P , SPADA generates antecedents suitable for rules being derived from P . The consequent corresponding to an antecedent is simply obtained as a complement of atoms in P and not in the antecedent. It is noteworthy that the generation of “good” rule antecedents is crucial. A naı̈ve implementation would consist of a combinatorial computation step followed by a pruning step. The former would output combinations of atoms occurring in P , while the latter would discard those that are not well-formed, e.g. without the key atom in the antecedent or not respecting the constraints of linkedness and safety. Backward pointers can also be exploited to speed up the generation of association rules instead. In particular, SPADA recursively retrieves the predecessors of a frequent pattern and returns only those yielding strong rules. This eliminates the need for evaluating rules a posteriori. 2.5. Filtering patterns and association rules In many applications, not all large patterns or strong association rules are deemed interesting by the user. The presentation of thousands of rules can discourage users from interpreting them in order to find ‘nuggets’ of knowledge. SPADA provides users with two filtering mechanisms, one for patterns and one for association rules. They are part of the declarative bias that constrains the search space. More precisely, the user can define the following pattern constraint: pattern constraint(AtomList, M in occur), where AtomList is a list of atoms (for atomic constraints) or a list of atom lists (for conjuctive constraints), while Min occur is a positive number which specifies the minimum number of constraints in the list that must be satisfied. Patterns that do not satisfy this constraint are filtered out.

550 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data In addition, the user can define a constraint either on the antecedent or on the consequent of a spatial association rule, by specifying one of the following types of declarative bias: body constraint(AtomList, M in occur) head constraint(AtomList, M in occur), where AtomList and Min occur have the same meaning as in the pattern constraint. The application of this pattern/rule filtering approach proved very useful in the application to census data mining. 3. Interfacing SPADA to the spatial database The application of the ILP approach to spatial databases is made possible by a middle-layer module for feature extraction. This layer is essential to cope with one of the main issues of spatial data mining, namely the requirement of complex data transformation processes to make spatial relations explicit. This function is partially supported by the spatial database (SDB), which offers spatial data types in its data model and query language and supports them in its implementation, providing at least spatial indexing and efficient algorithms for spatial join [16]. Thus spatial databases supply an adequate representation of both single objects and spatially related collections of objects. In particular, the abstraction primitives for spatial objects are point, line and region. Among the operations defined on spatial objects, spatial relationships are the most important because they make it possible, for example, to ask for all objects in a given spatial relationship with a query object. 3.1. Spatial features Many spatial features (relations and attributes) can be extracted from spatial objects stored in SDB. According to their nature, features can be categorized as follows: 1. locational features, when they concern the location of objects; 2. geometrical features, when they are based on the principles of Euclidean geometry; 3. directional features, when they regard (relative) spatial orientation in 2D or 3D; 4. topological features, when they are relations preserving themselves under topological transforma- tions such as translation, rotation, and scaling; 5. hybrid features, when they merge properties of two or more of the previous categories. Locational features Locational features are the simplest and more intrinsic features of spatial objects, since they are the attributes concerning the location. Depending on the abstraction primitives, meaningful locational features are: in the case of an areal object, the coordinates of the centroid, in the case of a linear object, the coordinates of the extremes and the coordinates of the point itself. Geometrical features Geometrical features are the most classical ones, since they are based on principles of Euclidean geometry. Generally, they depend on some distance/metric computations. Region area, perimeter, length of axes and shape properties are typical examples of attributive geometrical features, while distance and angle of incidence are typical examples of geometrical relations.

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 551 A0 ∩ B 0 A 0 ∩ ∂B A0 ∩ B − R ( A, B ) = ∂A ∩ B 0 ∂ A ∩ ∂B ∂A ∩ B − − A ∩ B0 A − ∩ ∂B A− ∩ B − Fig. 4. The 9-intersection model represented as a matrix. Directional features Directional features concern information about relative spatial orientation in 2D or 3D. They are fundamental in image processing and are ‘natural’ relations to be considered when assuming as a reference system a regular gridding system. Directional features are defined on the basis of the neighborhood concept. The most common metrics adopted to define neighborhoods are the city block distance (d 4 ), and the chess board distance (d 8 ). Given two points, p and q , with co-ordinates (i, j ) and (h, k), respectively, such distance functions are defined as follows: d4 (p, q) = |i − h| + |j − k| d8 (p, q) = max{|i − h|, |j − k|} The neighbors of a point p are the points having unitary distance from p. The neighborhood of a point p is constituted by all its neighbors and the point p itself. When the 4-distance is adopted, there are only 4 neighbors that are all adjacent to p along the main directions: north, east, south, and west. When the more general 8-distance is used, there are 8 neighbors which are adjacent to p along all the possible directions: north, north-east, east, south-east, south, south-west, west, and north-west. Topological features The 9-intersection model was proposed by Egenhofer and Franzosa [11] and Egenhofer and Her- ring [12] to categorize binary topological relations in geographic databases. It is independent of the concepts of distance and direction and is based upon purely topological properties. Currently, it can be considered the only comprehensive framework for qualitative spatial reasoning The 9-intersection model applies to spatial objects represented by regions, lines, and points. It is based on the consideration that for each spatial object A it is possible to distinguish three parts: its interior (A 0 ), its boundary (∂A) and its exterior (A− ). In the case of spatial objects described by the Cartesian space R2 , regions have non-empty interiors, both lines and points have empty interiors, lines have non-empty boundaries (coincide with them), while points have empty boundaries. Binary topological relations between two objects can be described in terms of part intersections. There are nine possible intersections between two parts, hence the name of the model. In Fig. 4 the 9-intersection model is concisely represented as a 3 × 3 matrix. Different topological relations have different 9-intersections, each being intersection empty (Ø) or non-empty (¬Ø). By considering the possible combinations of the two values Ø and ¬Ø one can distinguish 29 (= 512) binary topological relations. Not all the configurations correspond to physically feasible relations between two spatial objects. Indeed, there are restrictions on the combinations of values that could occur in the intersection matrix for the topological components of objects and only those combinations that comply with consistency constraints for topological object relations can occur. Relations between two regions In the bidimensional Cartesian space 8 relations can hold between two regions with connected bound- aries. The existence of topological relations corresponding to the 9-intersections has been verified by

552 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data producing prototypical geometric configurations in R 2 . The relations correspond to disjoint, contains, inside, equal, meet, covers, covered by, and overlap. This set is mutually exclusive and closed for regions, that is one and only one of the eight relations holds between any two regions. Relations between two lines Globally, there are 57 relations between two lines. In particular, 33 relations can be realized between simple lines, that is, lines composed of only one segment. Twenty-four other relations exist specifically for complex lines. Relations between a region and a line The topological relations between a region and a line involve two objects of different dimensions, therefore conditions that hold between a region and a line do not necessarily hold between a line and a region. There are 20 meaningful 9-intersections between a region and a line. One of them can be realized only if the line is a non-simple line. In Fig. 5 twelve feasible 9-intersections between a region and a line are reported. They are used later in the application to urban accessibility. Relations between a point and a non-point Since the boundary of a point is empty, it is irrelevant to analyze its three boundary intersections. Consequently, there are only 6 significant intersections to describe the topological relations between a non-point (region or line) B and a point A, and there are only 2 6 possible relations. Only 3 combinations of intersections between a point and a non-point are physically feasible for point-region and point-line configurations, respectively: They represent the three situations in which the point A is external to the region or to the line B, the point A is internal to the region or is on the line B, and, finally, the point A is on the boundary of the region B or on one of the two extremes of the line B. Relations between two points In the case of two points, we observe that both boundaries are empty. Then, there are only 4 relevant intersections: the intersections between interiors and exteriors. There are only 2 combinations of intersections for which the corresponding topological relations, disjoint and equal, can be realized between two points. Hybrid features Hybrid spatial features merge properties of two or more spatial feature categories. For instance, the features that express the conditions of parallelism and perpendicularity of two lines are both topological and geometrical. They are topological since they are invariant with respect to translation, rotation and stretching, while they are geometrical since their semantics is based on the angle of incidence. Another example of a hybrid spatial feature is represented by the relation of “faraway-west”, whose semantics mixes both directional and geometric concepts. Moreover, we call hybrid those features that mix spatial relations with aspatial properties, such as the feature that describes coplanar roads by combining the condition of parallelism with information on the type of spatial objects (road). 3.2. Spatial features for census data mining Three different kinds of spatial analysis can be performed on geo-referenced census data:

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 553 Fig. 5. Twelve feasible relations between a region and a line according to the 9-intersection model. – Intra-ED analysis: spatial features concern geographic objects enclosed within the boundaries of an ED, while aspatial features are aggregated census data concerning a single ED. An example of intra-ED analysis is the characterisation of a site (residential, industrial area, and so on) for land allocation purposes. – Inter-ED analysis: spatial features concern relations between EDs, while aspatial features are mainly extracted from census data for all EDs. An example of inter-ED analysis is the evaluation of the accessibility of a site for transport planning.

554 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data – Mixed intra-inter ED analysis: it is the most complex situation in which both spatial relations between geographic objects in an ED and spatial relations between EDs are required. An example of mixed analysis is the study of the impact that land allocations might have on the transportation system. Consequently, the choice of spatial features that are meaningful for census data mining depends on the kind of analysis to be performed as well as on the specific task to be tackled. For intra-ED analysis, man-made and natural features, ranging from houses and factories to roads and rivers, seem to be the kind of data to be considered. First, the relations “contains”, “inside” and “internal to” can be used to define which different objects are present in a specific ED, since contains gives information on the existence of areal objects (such as the factories), inside gives information on linear objects (such as the roads), and internal to gives information on punctual objects (such as the bus stops). Then, the topological relations existing between the specific ED and its different objects and between the objects themselves might be used to obtain useful information. For example, if we are interested in discovering whether an ED is strongly urbanized, we might define a hybrid relation that checks the conditions of parallelism and perpendicularity between two roads, in order to detect a regular grid system of roads, which is typical of an urban area. Actually, similar relations have been defined and used for map interpretation tasks within planning contexts. In particular, they are described in Esposito and Lanza [13] for the application of machine learning techniques to technical charts of the Apulian region to identify the two land morphologies: cliffs and ravines. Descriptions of other features that have been adopted for the applications of machine learning to topographic maps can be found in Esposito et al. [14] and Malerba et al. [29]. These features were applied to localize some environmental categories important for the environmental protection (i.e., fluvial landscapes, royal cattle tracks, systems of cliffs and regular grid systems of farms) in the territory around the Ofanto river, Southern Italy. For inter-ED analysis tasks, most of the spatial relations listed in the previous sub-section can be useful. In particular, topological relations between a region and a line might be used to investigate the accessibility of an ED from a road or a railway or a bus line. For example, if the disjoint relation (see Fig. 5) holds between a specific ED and a bus line of interest, we can conclude that the ED is not reachable directly by means of that bus line, so we have to search for other bus lines. Moreover, topological relations between two regions might be used to express spatial dependencies between EDs. In fact, only two cases might occur between two EDs: they are adjacent, i.e. the meet relation holds, or they are disjoint, i.e. the disjoint relation holds. In addition, the geometrical relation distance might be useful to evaluate the closeness of bus stops to public services (hospitals, railway stations, and so on). Finally, all the simple and hybrid features described in Section 3.2 might be useful for more complex mixed analysis tasks. 3.3. Extracting features with FEATEX In order to generate features of spatial objects (points, lines, or regions) a feature extractor module, named FEATEX, has been devised. It enables a loose coupling of SPADA with the SDB. FEATEX is implemented as an Oracle package of procedures and functions, each of which implements a different feature. FEATEX functions can be used in SQL queries. For example, the query: SELECT FEATEX.DIRECTION (x.geom) FROM river va polyline x;

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 555 returns the geographic direction for each river in the table river va polyline. In this way, it is possible to formulate complex SQL queries involving both spatial and aspatial data (e.g., census data). The geographic direction of a spatial object is the only directional feature generated by means of FEATEX for the application. The corresponding FEATEX function returns the geographic direction (“north east”, “north west”, “east”, “north”) of the object identified by geom if the object is a line, “error” otherwise. Its specification is the following: FEATEX.DIRECTION(geom) RETURN VARCHAR2. Three hybrid features extractable by means of FEATEX are almost-parallel, almost-perpendicular and density. The first two concern the parallelism and perpendicularity conditions respectively between two spatial objects. The adverb ‘almost’ is justified by the fact that in cartography, as well as in nature, it is almost impossible to find two exactly parallel or perpendicular objects. For instance, two contour slopes are rarely exactly parallel, while two incidental roads do not always form a perfect angle of 90 ◦ . The feature concerning parallelism is extracted by means of the function: FEATEX.ALMOST PARALLEL(geom1, geom2, tolerance) RETURN VARCHAR2. The first two parameters specify the geometries of the objects of interest. The tolerance parameter is used in distance computations. The function returns “true” if the condition holds, “false” otherwise. The perpendicularity condition is extracted by means of the function: FEATEX.ALMOST PERPENDICULAR(geom1, geom2, tolerance, angularT olerance) RETURN VARCHAR2. The definition of the function is based on the computation of the incidence angle between linear objects. The last parameter is the tolerance on the incidence angle. The density is computed by means of the function: FEATEX.DENSITY(geom1, dim1, geom2, dim2) RETURN NUMBER, where dim1 and dim2 are the dimensional information arrays corresponding to the first and second object. This function determines the relation between two objects according to the 9-intersection model, and then it computes their areas by means of the Gauss method. If the object identified by geom1 is contained in the object identified by geom2, this function returns the ratio between the two areas, otherwise it returns zero. Two geometrical features can be generated by FEATEX. One is the distance between two objects, which can be computed by means of the function: FEATEX.DISTANCE(geom1, dim1, geom2, dim2) RETURN NUMBER. It returns the distance between two objects identified by the geometries geom1 and geom2 and can be used even when objects have different geometries. The other geometrical feature extracted is line shape. Its corresponding function is: FEATEX.LINE SHAPE(geom, tolerance) RETURN VARCHAR2.

556 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data The tolerance parameter specifies the angular tolerance in radians for the computation. The function returns the values “straight” or “curvilinear”, if the shape of the line identified by geom is linear or curvilinear, respectively. It returns “error” if the object identified by geom is not a line. A detailed description of the algorithms underlying the computation of the above features can be found in [24], where an application to topographic map interpretation is also reported. The topological features are computed by means of the following function: FEATEX.RELATE(geom1, dim1, geom2, dim2) RETURN VARCHAR2. It analyses the geometries of the two objects of interest, which are identified by geom1 and geom2, to determine the spatial relationship that holds between them, based on the 9-intersection model. The relate function returns the name of the topological binary relation (e.g. Disjoint, Along). In the case of topological relations involving lines, only those defined for simple lines are computed. The result of a FEATEX function is an object-relational table. To transform it into a set of atoms, a function call is passed to the GENERATE function. The syntax of the GENERATE function is: FEATEX.GENERATE(queryStr, predicateN ame, path, f ileN ame, f ileT ype) RETURN . INTEGER The function executes a generic SQL query, given as a string parameter (queryStr) and outputs a text file where an atom is reported for each tuple. The predicate name used for the generated atoms is one of the arguments of the GENERATE function. More specifically, the result of a query: SELECT attr1, attr2 , . . . , attrn FROM table1, table2, tablem WHERE condition, where attri (i = 1..n) can also be a FEATEX function, is translated into a set of the atoms: predicateN ame(arg1 , . . . , argn ), where (arg1 , . . . , argn ) is a tuple in the query set. The parameters path and filename in the GENERATE function identify the output file, while filetype specifies whether the output file is opened in append or write mode. The GENERATE function returns 1 if no errors occur, 0 otherwise. 3.4. Discretizing numerical attributes Since SPADA, like many other association rule mining algorithms, cannot process numerical data properly, it is necessary to perform a discretization of numerical features with a relatively large domain. For this purpose we have implemented the relative unsupervised discretization algorithm RUDE [27], which discretizes an attribute of a relational database in the context defined by other attributes. Formally, the problem can be stated as follows: Given – a database table T consisting of m tuples, – a continuous attribute in T to be discretized (target attribute),

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 557 – a set of continuous attributes (source attributes) in T that define the context for the discretization of the target attribute, – a relative tolerance between split points (minimal difference) s Find a set of split points that minimize loss of correlation between attributes. The algorithm RUDE is based on two general procedures: a prediscretization procedure, used to pre-process the source attributes, and a clustering procedure, used to group target attribute values corresponding to some source attribute value or interval. Therefore, several different “specializations” of the RUDE algorithm can be generated by varying the two procedures. RUDE is implemented as a Java package. Two prediscretization algorithms are implemented, namely equal width and equal frequency, as well as two clustering algorithms, EM [40] and AutoClass [5]. RUDE proves to be suitable for dealing with numerical data in the context of association rule mining. An experimental study not reported in this paper showed that better performance can be obtained by using the equal width prediscretization procedure and the Autoclass algorithm. This combination has been used in the application to mining UK census data. SPADA, FEATEX and RUDE have been integrated in the client-server system ARES, which is available at the URL: http://www.di.uniba.it/∼malezba/software/ARES/. 4. Mining UK census data: An application to urban accessibility In this section we describe a practical example that shows how it is possible to perform a spatial analysis on UK 1991 census data. The application has been developed in the context of the European project SPIN! (Spatial Mining for Data of Public Interest) [33]. Census data concern Stockport, one of the ten districts in Greater Manchester, UK. In total 89 tables, each having 120 attributes on average, have been made available for policy analysis. Census attributes provide statistics on the population (resident at the census time, ethnic group, age, marital status, economic position, and so on), on the households in each ED (number of households with n children, number of households with n economically inactive people, number of households with two cars, and so on) as well as on some services available in each ED (e.g., number of schools). Stockport is divided into twenty-two wards for a total of 589 EDs. Spatial analysis is enabled by the availability of vectorized boundaries of the 1991 census EDs as well as by other Ordnance Survey digital maps of the district, where several interesting layers are available, namely roads, bus priority lines, and so on. By joining UK 1991 census data available at the ED summarization level with some spatial objects (e.g., EDs, roads, and railways) it is possible to investigate socio-economic issues from a spatial viewpoint. For the application of our spatial association rule mining method we have focused our attention on transportation planning, more specifically, on an important issue reported in the Unitary development Plan of Stockport, the accessibility of the Stepping Hill Hospital. The concept of “accessibility” appears initially in the context of geographical science and was progressively introduced in transport planning in the 1960’s and 1970’s. Many different definitions of accessibility and many ways to measure it can be found in the literature. In this work we are interested in urban accessibility, which refers to local (inner city) daily transport opportunities. A great effort has been made to define urban accessibility indices, which can be used to assess/compare transportation facilities within different regions of an urban area or between urban regions [2]. Accessibility is usually measured with respect to key activity locations for individuals (e.g., home, workplace) and evaluates the transportation services provided in these key

558 A. Appice et al. / Discovery of spatial association rules in geo-referenced census data Fig. 6. Stockport map around Stepping-Hill Hospital. Spatial objects are the following: one-hundred and fifty-two task relevant EDs (white regions), five task-relevant EDs (yellow regions), the only bus priority line (thick light-blue line), crossing roads (blue lines), crossing railways (green lines). locations to assess their relative advantages [3]. In this work, we are interested in the accessibility “to” the Stepping Hill Hospital “from” the actual residence of people living within in the area served by the hospital. Since (micro) data on the actual residence of each involved household are not available, we study the accessibility at the ED level. Moreover, our study does not aim to synthesize a new accessibility index, but to discover human interpretable patterns that can also contribute to directing resources for facility improvement in areas with poor transport accessibility. We decided to mine association rules relating five EDs close to the Stepping Hill Hospital (task relevant objects) with one-hundred and fifty-two EDs within a distance of 10 Km of the hospital (reference objects). The goal is to understand which reference EDs have access to the task relevant EDs. To define the accessibility we used the Ordnance Survey data on transport network, namely the layers of roads, railways and bus priority lines (see Fig. 6). By using FEATEX we extracted facts concerning two topological relationships between EDs and the only bus priority line reported in the spatial database for that area. Two examples are the following: external touches to(ed 03bsfq29, bus priority line 1). comes from(ed 03bsfl27, bus priority line 1). The constants ed 03bsfq29 and ed 03bsfl27 denote two distinct EDs, while bus priority line 1 is the only constant associated to a bus priority line. The topological relations external touches to and comes from are schematized in Fig. 5. The set of topological relationships between EDs and roads is more varied. Some facts extracted by FEATEX are the following: along(ed 03bsfk28, road 15329).

A. Appice et al. / Discovery of spatial association rules in geo-referenced census data 559 comes from(ed 03bsfb23, road 12212). crosses(ed 03bsfc13, road 12245). external ends at(ed 03bsfc01, road 11501). external touches to(ed 03bsfb22, road 15260). external comes from(ed 03bsfc01, road 11502). goes out of(ed 03bsfh01, road 10884). inside(ed 03bsfc01, road 11494). internal ends at(ed 03bsfc01, road 11500). runs along boundary ends inside(ed 03bsfg22, road 10884). runs along boundary(ed 03bsfc23, road 12312). In this case constants road # refer to roads crossing the interested area. It is noteworthy that the topological relations above are mutually exclusive, that is, it is impossible for two of them to concern the same pair of constants (ED, road). Finally, we used FEATEX to extract spatial relationships between EDs and railways. Some examples of facts generated by the Oracle package are: along(ed 03bsfg25, rail 2453). comes from(ed 03bsfc05, rail 2355). crosses(ed 03bsfc13, rail 2391). external ends at(ed 03bsfc05, rail 2389). external touches to(ed 03bsfc20, rail 2389). inside(ed 03bsfc01, rail 2341). internal ends at(ed 03bsfc23, rail 2418). overlapped shortcut(ed 03bsfh12, rail 2487). runs along boundary ends inside(ed 03bsfg11, rail 2429). runs along boundary(ed 03bsfc10, rail 2391). The total number of facts is 1,147. Despite the complexity of the spatial computation performed by FEATEX to extract these facts, the results are still not appropriate for the goals of our data analysis tasks. Indeed, we are interested in relationships between EDs, such as those stating that two EDs are ‘connected’ by the same bus priority line or the same road or the same railway. To solve this problem we specified the following rules to the domain specific knowledge: 1. crossed by bus line(X) :- external touches to(X,bus priority line 1). 2. crossed by bus line(X) :- comes from(X,bus priority line 1). 3. connected by bus line(X,Y) :- crossed by bus line(X), crossed by bus line(Y), X=Y. 4. crossed by road(X,Z) :- along(X,Z), is a(Z,road).

You can also read