## 3 Problem Formulation  
Our system aims at providing a continuous-valued representation of word relationships in a given sentence. Figure 1 shows a sample sentence with some relationships (connections) between words. Here, subsequences of words, _i.e._, word _n_-grams, involved in each connection are represented in boldface.  
Some general properties of subsequences are the following: (i) subsequences can be made of non-contiguous words, as represented in the first _n_-gram; (ii) subsequences can be overlapped; (iii) a suitable number of subsequences can be generated so as to cover all the words in the sentence; (iv) a subsequence does not usually correspond to a clause, since a grammarless approach is used.  
A sentence with the corresponding subsequences can be represented as a connectionist model. Each word is represented by a node of the network, and the connections between nodes represent word relationships. Weak (or strong) connections model weak (or strong) relationships between its words. Connections strength can be based on the usage of their subsequences on the Web.  
In general, different segmentations of a sentence in subsequences are possible. Hence, a suitable optimization method should be able to identify the better segmentation so as to emphasize subsequences with very low usage.  
Finally, a suitable displaying method should provide an intuitive manner of expressing the relevant information owned by the connectionist model.  
Figure 2 shows an UML activity diagram of the macro activities of our approach to text analysis. Here, activities (represented by oval shapes) are connected via control flow (solid arrow), whereas input/output data object (rectangles) are connected via data flow (dashed arrow).  
At the beginning, the sentence is _parsed_ and then converted into an initial _connectionist model_ instance. The sentence is completely broken up into (overlapped) segments by a _segmentation_ operator. Afterwards, the _connectionist model_ instance goes through an _optimization_ process, which optimizes the connections by using the usage information available in the _raw corpus_ instance, _i.e._ the Web. Finally, _connectionist model_ information is _displayed_, _i.e._, transferred to a visual representation of the sentence, namely a _sentence presentation_ instance [25,34].  
More specifically, Figure 3 shows the macro activities of the optimization process. First, a _segmentation_ of the sentence is performed, producing a series of _n_-grams of the sentence itself. Then, one of two possible operators is applied, namely _generalization_ or _commutation_. The former is an operator that employs the class of a specific word in place of the world itself, whereas the latter is an operator which substitutes a word with another more popular word which is structurally similar. Afterwards, the _usage_ of each _n_-gram in the corpus is rated. Finally, the _n_-grams with the lowest usage  
Figure 1: Example sentence with some arcs showing dependencies between words.  
Figure 2: Overall activities involved in our emergent approach to text analysis.  
are determined. In order to find the best setting, all these activities may be carried out a number of times, as represented by the loop in the Figure.  
Figure 4a shows an example of generalization, in which the individual name \"[PERSON]\" is replaced with any other individual name that can be found in the Corpus by using the wildcard. Figure 4b shows an example of commutation, in which the individual name \"[PERSON]\" is replaced with the more popular name \"[PERSON]\" and the word \"claim\" is generalized. Each of these alternatives affects the _usage rating_ of the phrase, and allows a better robustness of the _optimization_ process. For example, without the generalization operator, usage rating may be strained by an unpopular word.  
In the next section, we introduce some definitions to formalize our method.