USO POTENCIAL DEL SUELO

As mentioned earlier, one of the research issues considered in this thesis is how to anal- yse large numbers of discovered frequent patterns trends. It is proposed that clustering is a fitting method to categorise large numbers of patterns and trends. Clustering is a

commonly adopted method used to group data. This section describes the basic con- cept of clustering. The approach adopted in this thesis is to use Self Organising Maps (SOMs). SOM technology is therefore considered in Sub-section 2.5.1, followed by a short discussion on cluster analysis in Sub-section 2.5.2.

Clustering is an unsupervised learning method for grouping similar data into “clus- ters”. Clustering has been used in many areas such as biomedical analysis, marketing strategies and environmental monitoring. Clustering algorithms operate in different ways. In some cases the desired number of data clusters is predefined, in other cases the clustering algorithm “works it out for itself”. Clustering algorithms typical operate using some measure of similarity, usually a distance measure is used. Clustering tech- nique can be categorised into partitioning methods, hierarchical methods, density-based methods, grid-based methods and model-based methods [52]. Among the most popular clustering algorithms and techniques are K-Means, K-Nearest Neighbour, Hierarchical Clustering and Self Organising Maps:

1. K-Means is a data partitioning technique that divides a dataset into K clusters, where K is predetermined a priori. Each data record belonging to a given dataset is assigned to one of the k-clusters by calculating its distance to the nearest cluster centroid. The algorithm then re-calculates the centroids for the clusters and processes the data again. This procedure continues until the centroids become “fixed”.

2. K-Nearest Neighbour is a clustering technique that classifies a dataset by calcu- lating distance between data records. Initially, the first data record,d1, in a given

dataset is used to derive a cluster K1; then the next data record is considered

by determining the distance to the d1. If the distance is below, τ, a distance

threshold, then it will be added to K1 otherwise a new cluster, K2, is created.

The process continues in an iterative manner until all records are considered. 3. Hierarchical clustering is a method for clustering relatively similar data records

or sub-clusters based on measured characteristics, i.e. distance and cohesion, by creating a cluster tree or dendrogram. There are two types of hierarchical clustering: (i) Agglomerative (bottom-up), and (ii) Divisive (top-down). The ag- glomerative hierarchical clustering process begins by considering each record to belong to a single cluster. The two most similar clusters are merged. This merg- ing process continues until a suitable cluster configuration is arrived at (measured in terms of cohesion and separation). The Newman method [95] is an established agglomerative hierarchical clustering algorithm. The divisive hierarchical cluster- ing initially groups the entire dataset into one cluster. This cluster is then split into two clusters. This splitting process continues in an iterative manner, until a suitable cluster configuration is arrived at.

4. A Self Organising Map is a topological clustering tool often used to provide a low-dimensional view of high-dimensional data. It groups the records in a given dataset by assigning records to nodes in the map according to a similarity mea- sure. SOMs are discussed in further detail in Sub-section 2.5.1.

2.5.1 Clustering Trends using Self Organizing Maps

Self Organising Maps (SOMs) were first introduced by Kohonen [74, 75]. Fundamen- tally, a SOM may be viewed as a neural network based technique designed to reduce the number of data dimensions in some input space by projecting it onto an×m“node map” which groups (clusters) similar data items together at nodes. SOMs have been utilised in many research areas. For example SOMs have been used for: clustering gene expression data [131], glaucoma image clustering [140], image retrieval [119] and stock price forecasting [48].

The SOM learning process is unsupervised. Nevertheless, the n×m number of nodes in the SOM must be prespecified. Currently, there is no scientific method for determining the best values for n and m. However, the n×m value does define a maximum number of clusters; although on completion some nodes may be empty [32]. The main components of a SOM are the input data (D) and a set of weight vectors (W) to which distance and neighborhood functions are applied to determine which nodes the records in Dshould be associated with. In Figure 2.6, for example, a SOM map (lattice) comprising 4×4 nodes is presented, each node hasnvalues of weight (w) where nis the dimension of the input data. Each weight has its own unique location in the lattice.

Algorithm 2.4: The basic SOM algorithm

input :D, the input dataset

output: SOM Initialize weights;

1

for i←1 to |X| number of training epochs do

2

Get x from D;

3

Find the “winning” map node for the sample input;

4

Adjust the weights of nearby map nodes;

5

end

6

In the SOM map each record is associated with only one SOM node. Algortihm 2.4 describes the basic SOM algorithm. Firstly, the weight vectors are initialised using a random number generator. Then, the algorithm processes the input data, record by record. For each record, each node “bids” for the record and the record is assigned to the “winning” node. This is done using a distance function. The most common distance function is the Euclidean distance function (2.1):

Figure 2.6: A view of 4×4 nodes with nweights d= v u u t n X i=1 (xi−yi)2 (2.1)

wherexi is the ith value of input data and n is the number of dimensions in the input

data. If there are two or more weight vectors with the same shortest distance, the winner node is chosen randomly. Subsequently, the algorithm adjusts the neighbouring weights of the winning node to reflect the nature of the most recently assigned record. The most popular mathematical function used in this calculation is based on the Gaussian function (2.2). The magnitude of the adjustment is decreased as the distance from the current node increases.

hj,i(x)=e

d2j,i

2α2 _(2.2)

Thus SOM generation is an iterative process; it uses a learning function that de- creases with a learning rate ranging between 0 and 1. As the algorithm iterates, it updates (tunes) neighbourhood weights with new values. This adaptive process is based on the function (2.3):

w(t+ 1) =w(t) +α(t)(x(t)−w(t)) (2.3) where w is the selected “excited” weight in the set of topological neighbours, t is the current iteration counter, α is the learning rate in the learning process. Finally, once all records in the training data have been processed, a complete map will be produced representing the records in terms of a set of prototypes (one prototype per node).

With respect to the work described in this thesis, a SOM approach has been adapted to group similar trends, and thus provide a mechanism for analysing social network trend mining results.

2.5.2 Cluster Analysis

This thesis also describes a trend cluster analysis method. Cluster analysis involves observing and recognizing cluster changes in terms of (say) cluster size or cluster mem- bership. There are several reported studies concerning the detection of cluster changes and cluster membership migration. Denny et al. [36] proposed a technique to detect temporal cluster changes using SOMs to visualize emerging, splitting, disappearing, enlarging or shrinking clusters; in the context of taxation datasets. Lingraset al. [82] proposed the use of Temporal Cluster Migration Matrices (TCMM) for visualizing clus- ter changes representing e-commerce site usage. The method clustered the customer records into five groups based on snapshots of their monthly website usage and spend- ing patterns. Then the TCMM are used to visualise the comparison of monthly cluster memberships in the form of a matrix and bar charts. As will become apparent later in this thesis, a related idea founded on the concept of migration matrices, will be proposed. Lingras et al. [84] also compared the conventional Kohonen SOM and the modified SOM with interval cluster sets for non temporal setting analysis and found that the modified SOM grouped the data records in finer clusters. The study also provided an analysis of temporal cluster membership that allowed for the identification of changes in time stamped data. Hido et al. [55] suggested a technique to identify changes in clusters using a decision tree method. However, they did not consider dy- namic cluster analyses with respect to sequences of data episodes as in the case of the work described in this thesis.

Lingras and Huang [85] compared conventional cluster analysis methods, hierar- chical clustering, object-based and cluster-based genetic algorithms, Kohonens SOM and K-means, using highway sections and supermarket customer datasets. Lingras and Huang found that Kohonens SOM was the best method for clustering these large datasets. A modified Kohonen SOM, with lower and upper boundaries of interval clus- ter sets for defining the SOM output configuration, has been proposed for the clustering and analysing of supermarket customer data [83] and web usage data [56]. The use of interval cluster sets was adopted to avoid defining overlapping clusters. With respect to the work described in this thesis, the most appropriate number of trend clusters (SOM configuration) was derived by experimenting with a number of test sets with different SOM output configurations until a suitable SOM output configuration, based on the discovered frequent pattern trends, was identified (see Sub-section 4.4.2 for details).

In the work described in this thesis, as noted above, trends are grouped using a SOM. Each node in the SOM map represents a collection of trends and is referred to

in this thesis as a trend cluster. The envisioned Predictive Trend Mining Framework considers sequences of trend clusters each represented by a SOM map. By compar- ing two SOM maps we can see how patterns may move (or not move) between time stamps. This migration of trends can be conceptualised as a (social) network in its own right. To analyse how trend clusters change over time we can apply cluster analysis techniques to these networks. As will become apparent later in this thesis the analysis will be founded on the concept of hierarchical clustering; more specifically the Newman Hierarchical Clustering algorithm mentioned in Section 2.5. Hierarchical clustering is widely used as a cluster analysis tools. Examples of its application in the context of cluster analysis include: identification of the similarity and dissimilarity between cancer cell clusters [97], detecting road accident “black spots” (road traffic cluster analysis) [130] and determining the relationship between various industries based on the move- ments of financial stock prices [137]. As noted in Section 2.5, Hierarchical clustering can be viewed as a mechanism for identifying communities of clusters according to some similarity value [52].

The following section considers social network analysis and social network mining, the central theme of the work described in this thesis.