We build a directed weighted typed graph from the corpus. The graph is a 5-tuple G = (V, E, t, l, w), where V is the set of nodes, E : V x V is the ordered set of edges, t : V — T is the node type function (T = (ti,..., t|T|} is a set of types), l : E — L is the edge label function (L = ..., } is a set of labels), and w : L — R is the label weight function. We structure our problem domain with the types and labels presented in Figure 1.

In order to transform the text into a graph that conforms to the model shown, we take the output of standard NLP tools and input it as nodes and edges into the graph, indexing nodes by string value to en­sure that identical contents for any given node type are merged into a single node in the graph. To pro­cess the corpus, we run a standard NLP pipeline seperately over the metadata, title and body of the HTML pages, but not before having transformed its contents as much into plain text as possible, by removing HTML tags, javascript code, etc. The pipeline used is composed of tokenization, removal of stop words and infrequent words, and stemming with Porter's algorithm. The resulting graph at this

PersonNameNE

stage consists of the nodes of type Token, Webpage, Metadata, Title and Body, properly interconnected. We then run a named entity recognizer to associate NE tags to the respective documents, via the con­stituent words of the NE. The information about the original URL of page is given by the corpus, while Host is trivially obtained from it. We finalise the graph by inserting an edge of type linked-by between any web page linked by another in the corpus, and an edge of type related-to between any web page re­lated to another in the corpus, as given by Google's related: operator.

For the named entity recognition task, we have compared GATE and OpenNLP toolkits. Although both toolkits show comparable results, OpenNLP demonstrated faster performance. Moreover, some documents in the corpus consisted of very exten­sive lists of names (e.g. phonebook records) which slowed the NER to a halt in practice. To compen­sate for this, we applied a chunking window at the beginning and end of each body content and around each occurrence of the person name being consid­ered (and its variants determined heuristically). The window size used was 3000 characters in length, and an overlap between windows results in a merged window.

To discard irrelevant documents within the corpus, we manually devised two heuristics rules for classi­fication by observing the training data at hand. The heuristics are 1) whether the page has content at all, 2) whether the page contains at least one appearance of mentioned person name with its variants. This simple classification showed high precision and low recall on the training data. We also tried a SVM-based classifier trained on a typical bag-of-words feature vector space obtained from the training data, but found the such classifier not to be sufficiently re­liable.

We aim to determine the similarity between any two nodes of type Webpage in the graph. In our work, similarity between two nodes in the graph is ob­tained by employing a random walks model. A ran­dom walk, sometimes called a "drunkard's walk," is a formalization of the intuitive idea of taking suc­cessive steps in a graph, each in a random direction (Lovasz, 2004). Intuitively, the "harder" it is for a drunkard to arrive at a given webpage starting from another, the less similar the two pages are.

Our model defines weights for each edge type, which, informally, determine the relevance of each feature type to establish a similarity between any two pages. Let Ltd = {l(x,y) : (x,y) G E A T(x) = td} be the set of possible labels for edges leaving nodes of type td. We require that the weights form a probability distribution over Ltd, i.e.

We build an adjacency matrix of locally appropriate similarity between nodes as Wij = 1 ^lfc€L Kv^EK-Hifc! ' G E ] 0, otherwise where Wij is the ith-line and jth-column entry of W, indexed by V. Equation 2 distributes uniformly the weight of edges of the same type leaving a given node. We could choose to distribute them otherwise, e.g. we could distribute the weights according to some string similarity function or language model (Erkan, 2006), depending on the label.

We associate the state of a Markov chain to ev­ery node of the graph, that is, to each node i we associate the one-step probability P(0) (j |i) of a ran­dom walker traversing to an adjacent node j. These probabilities are expressed by the row stochastic ma­trix D-1W, where D is the diagonal degree ma­trix given by Dii = £ k Wik. The "reinforced" similarity between two nodes in the graph is given by the t-step transition probability Pwhich can be simply computed by a matrix power, i.e., P |i) = [(D-1W .

Note that t should not be very large in our case. The probability distribution of an infinite random walk over the nodes, called the stationary distribu­tion of the graph, is uninteresting to us for cluster­ing purposes since it gives an information related to the global structure of the graph. It is often used as a measure to rank the structural importance of the nodes in a graph (Page et al., 1998). For clustering, we are more interested in the local similarities inside a cluster of nodes that separate them from the rest of the graph. Also, in practice, using t > 2 leads to high computational cost requirements, as the matrix becomes more dense as t grows.

Equation 2 introduces the need to learn the func­tion w. In other words, we need to tune the model to use the most relevant features for this particular task. Tuning is performed on the training set by compar­ing the standard purity and inverse purity measures of the clusters against the gold standard, and using a simulated annealing optimization method as de­scribed in (Nie et al., 2005).

The algorithm takes as input a symmetric similarity matrix S, which we derive from the random walk model of the previous section as follows. We com­pute the Euclidean Commute Time (ECT) distance (Saerens et al., 2004) of any two nodes of type Web­page in the graph. The ECT distance is (also) based on a random walk model, and presents the inter­esting property of decreasing when the number of paths connecting two nodes increases or when the length of any path decreases, which makes it well-suited for clustering tasks. Another nice property of ECT is that it is non-parametric, so no tuning is required here. ECT has connections with princi­pal component analysis and spectral theory (Saerens et al., 2004).

In particular, we are interested in the average commute time quantity, n(i,j), which is defined as the average number of steps a random walker, starting in state i, will take before entering a given state j for the first time, and go back to i. That is, n(i, j) = m(j|i) + m(i|j), where the quantity m(jcalled the average first-passage time, is defined as the av­erage number of steps a random walker, starting in state i, will take to enter state j for the first time. We compute the average first-passage time iteratively by means of the following recurrence:

where P| ) is the t-step transition probability of the random walk model over G presented in the pre­vious section.

Informally, we may regard the random walk model presented in the previous section as a "re­fined" document similarity measure, replacing, e.g., the typical TF-IDF measure with a measure that works in a similar way but over all features rep­resented in the graph, whereas we can regard the ECT measure presented in this section as a "booster" to a basic clustering techniques (cf. next section), achieved by means of coupling clustering with a ran­dom walk-based distance which has been shown to be competitive with state-of-the-art algorithms such as spectral clustering (Luh Yen et al., 2007).

Clustering aims at partitioning n given data points into k clusters, such that points within a cluster are more similar to each other than ones taken from dif­ferent clusters. An important feature of the clus­tering algorithm that we require for the problem at hand is its ability to determine the number k of nat­ural clusters, since any number of referents may be present in the web search results. However, most clustering algorithms require this number to be an input, which means that they may break up or com­bine natural clusters, or even create clusters when no natural ones exist in the data.

We use a form of group-average agglomerative clustering as described in (Fleischman and Hovy, 2004), shown in Table 1, which works fast for this problem. A difficult problem (with any clustering approach) has to do with the number of initial clus­ters or, alternatively, with setting a threshold for when to stop clustering. This threshold could po-

Input: symmetric similarity matrix S, threshold 0 Output: a set of clusters C 3. place i and j in the same cluster in C (merging existing clusters of i and j if needed) 4. (average pairs of edges connecting to nodes i,j from any node k) 5. remove j-th column and j-th line from S (effec­tively merging nodes i,j into a single node)