## 5 Methodology
### Indexing Parameters  
The creation of a vector space model for the patent corpus was achieved using the MATLAB-based Text to Matrix Generator (TMG) software environment [15]. TMG utilizes a graphical user interface to implement MATLAB and Perl scripts for document indexing. Specifically, we used the TMG functions for reading the patent documents, creating a term dictionary, and generating a term-by-document matrix for subsequent document similarity calculations. Further, this software environment employs the popular _Bag of Words_ model for its indexing scheme. In this model, individual words are considered without evaluating the order in which they appear in a document. This approach was selected for the case study as a means to gathering ground truth information regarding the data set of interest. The TMG interface has many built-in parameters that directly affect the quantity and quality of the resulting term-by-document matrix. The filtering techniques that were extensively tested throughout this study included the local minimum and maximum term frequency thresholds, global minimum and maximum document frequency thresholds, local and global weighting, and the use of a stop words list (_i.e._, removal of unimportant words such as \(a\), _the_, and _of_). The local thresholds limited the inclusion of a term in the dictionary based on the term's frequency within one document. For example, a local maximum value of \(10\) would exclude any word from the document dictionary that occurred more than \(10\) times within a document; whereas a local minimum value of \(10\) would exclude any word that occurred less than \(10\) times in a document. On the other hand, the global document frequency thresholds limited the inclusion of a term in the dictionary based on theterm's frequency throughout the corpus. That is, a global maximum threshold of \(10\) excluded a word from the document dictionary that occurred in more than \(10\) documents; whereas a global minimum of \(10\) excluded a term if it was found in fewer than \(10\) documents. In addition to these thresholds, TMG permits multiple local and global term weighting strategies. In this study, we used two types of local weighting methods: Binary and term frequency. A _binary_ local weight used a \(0\) or \(1\) to represent the presence or absence, respectively, of a term within a particular document. A _term frequency_ local weight included the number of occurrences to represent a term's presence within a document, and \(0\) otherwise. On the global level, we used either no global scheme or the _inverse document frequency_ (IDF) option. Equation 1 defines the inverse document frequency of term \(t_{i}\) with respect to document \(n_{i}\) in a set of \(N\) documents. \[IDF\left(t_{i}\right)=log\left(\frac{N}{n_{i}}\right) \tag{1}\]  
Using the parameters described above, three different models were implemented. Each model contained a unique combination of the local and global term frequency methods. Table 2 summarizes the three models used. We utilized the SMART stoplist provided by Cornell University [18]. Common words unique to the patent corpus (e.g., _united_, _states_, and _patent_) were also added to the stoplist. Further, a second list of stop words was created for documents that included numerical words. This list contained common numerical information such as years, figure labels, and reference numbers. While there are many numerical words which appear to be the result of inaccuracies with the OCR conversion (e.g., 1998 Watson, 010111 Jan), it is not guaranteed that all numerical words will be removed by term frequency. For example, the object label _1a_ occurs multiple times within one document, and exists in almost every document. To ensure obvious unimportant words were not included in a documents term dictionary, additions were made to a stop list to include labels, years, dates, and other common numerical terms.