XML Miner, XML Rule and Metarule.

Transcription

1 XML Miner, XML Rule and Metarule. Andrew N Edmonds Scientio inc. Wednesday, 30 May 2001 Version 1 Introduction... 1 Knowledge representation... 1 Data representation... 3 Data Location... 4 Fuzzy Logic... 4 Fuzzy sets... 5 Tools that use Metarule... 5 XML Miner... 5 XML Rule... 6 Utilities... 7 Strucfind... 7 Metarule.xsl... 7 Introduction XML is rapidly becoming the Lingua Franca of the Internet age. Using it you can communicate data between disparate computers running disparate software in a format that is recognisable by a wide range of tools. The kinds of data that can be communicated are not just boring old records and fields, but structured hierarchical data capable of representing not just the individual data items, but the relationships between data items. XML encodes data in tree form, and trees match the internal topology of a wide variety of data types that could hitherto only be encoded and transmitted via a proprietary format, or by bludgeoning them into field/record format. As new technologies develop they need tools. The first generation of these have been XML editors, schema editors, and various objects that work on XSL transforms. The next generation of tools will permit the analysis of data in XML, and we proudly present XML Miner as the first of these. XML Miner is Artificial Intelligence and Data-mining for XML. With XML miner and the associated runtime, XML Rule you can analyse, filter, categorise and predict XML data. Wherever data streams between two systems (or inside one system) in XML, XML Miner can extract information and make decisions and predictions that cope with incomplete data, vagueness, and the inherent tree structured nature of XML. Knowledge representation A fundamental part of Artificial Intelligence and Data mining is the representation of knowledge. AI is concerned, amongst other things, with encapsulating human knowledge in a form that computers can use; Data mining is concerned with extracting knowledge from data in a way that humans, and sometimes computers, can read. Scientio inc. has developed a knowledge representation framework called

2 Metarule that services both these needs. Unsurprisingly perhaps, Metarule is a dialect of XML. Because this is the case, Metarule can be transformed with XSL, edited with XML editors and so on. Like XML it is not processor or operating system specific. The first and central premise of Metarule is that the majority of useful knowledge can be represented with rules of 3 simple forms. The degree to which the previous statement is true is extremely hard to quantify. It is fundamentally a philosophical question, but our experience so far is that the application of these forms is very wide indeed. The second premise is that in order to represent, quantify, and handle uncertainty, the logic used should not be Boolean logic, but the superset of Boolean logic that also encompasses uncertainty, Fuzzy Logic. Anyone as yet unconverted to the marvels of fuzzy logic should not worry: if you restrict reasoning to just truth and falsehood, fuzzy logic behaves identically to Boolean logic. Here s a fragment of Metarule and the English language equivalent: <rule> </rule> <if/> <and> <and> </and> <and> </and> <input>petal_width</input> <input>sepal_width</input> <input>petal_length</input> <input>sepal_length</input> </and> <then/> <output>class</output> <willbe/> <category>iris-versicolor</category> <confidence>0.875</confidence> If petal width is small and sepal width is small and petal length is small and sepal length is small then class will be Iris-versicolor. Converting from Metarule to English in HTML is simply performed using an XSL transform which we supply with our products. The three rule types are: 1) If <conditions> then output will be <category>. Used for classification. 2) If <conditions> then output will be <fuzzy set>. Used for prediction.

3 3) If <conditions> then output will be <arithmetic expression>. Used to encapsulate mathematical knowledge. Rules are seldom used singly; a collection is termed a rule set. Data representation Individual data items occur in many primitive types, such as integers strings floats, etc. Metarule is concerned with two different fundamental data types, categorical or numeric. In general we can think of the things in the world as having quantities and / or qualities. Categorical variables hold qualities, numeric ones quantities. For instance male and female are categorical, 0.37metres is numeric. One might assume that any data item can easily be classified into one or the other, but this is not always true. Numbers are often used to represent categories for instance, as in Close encounters of the third kind.! In Metarule you can specifically differentiate between these two data types. Each Metarule document contains a section detailing the inputs and the outputs of the contained rule set. For instance: <outputlist> <outputspec> <output>class</output> <categorical> <category>iris-setosa</category> <category>iris-versicolor</category> <category>iris-virginica</category> </categorical> <execorder>1</execorder> </outputspec> </outputlist> Describes an output with three categories, while the following describes a numeric input defined by three fuzzy sets.

4 <inputspec> <input>sepal_length</input> <numeric> <setdefinition> <set settype = "extremely small"/> <lower>4.3</lower> <middle>5</middle> <upper>5.8</upper> </setdefinition> <setdefinition> <set settype = "very small"/> <lower>5</lower> <middle>5.8</middle> <upper>6.7</upper> </setdefinition> <setdefinition> <lower>5.8</lower> <middle>6.7</middle> <upper>7.9</upper> </setdefinition> </numeric> </inputspec> Data Location In relational databases it s fairly simple to locate a data item using indexes, ids, row numbers and field names. In XML, since the data is tree structured, it is more difficult. The inventors of XML thought of this however and invented XPath as the method to navigate round XML and identify nodes in the true, singly or in groups. All input and output variable names in Metarule can be XPath strings. Furthermore in XML information can be stored either as text between XML elements, for instance <height>1.84</height>, or as attributes: <wardrobe height= 1.84 ></wardrobe>. Metarule uses XPath to permit data in either form to be described and analyzed. Fuzzy Logic Since its invention in 1965 by Lotfi Zadeh, this extension to conventional logic has grown to be a very large field of study all on its own. The key concept is that the often-uncertain state of our knowledge of the universe is best described by a logic that permits degrees of truth. This compares to the traditional statistical view of describing the validity of assertions in terms of probability. Fuzzy logic generates tractable descriptions of uncertainty; probabilistic descriptions are notoriously intractable. In conventional logic it is standard to represent truth with the value 1 and falsehood with 0. Fuzzy logic permits truth to be represented by any real number between and including 0 and 1. Each element of conventional logic has an analogue in fuzzy logic, so there are fuzzy logic operators like and, or, not, that each behave like the conventional version if only 1s and 0s are used; there are fuzzy implication operators and fuzzy sets.

5 Fuzzy sets Fuzzy sets are really important for dealing with numeric variables. In speech we use a variety of quantifiers like big, small, large etc. and when asked how to perform some task we tend to say things like: When I m going too fast I take my foot of the gas or When I m too close to the car in front I put my foot on the brake. Where too fast and too close are vague quantifiers. An important insight in the early days of fuzzy logic was that these linguistic quantifiers corresponded to sets of data values. These sets do not have fixed boundaries, in the normal sense of a set, they have gradual boundaries, and it is possible for the current state of a variable to be in more than one of them. These sets were termed fuzzy sets. The next insight was that these sets could be modelled fairly easily, and once they were modelled it was not too difficult to take a set of instructions such as those above and turn them into a working control system. The above is an example of some fuzzy sets defined for the variable male height. As can be seen, someone who is 5 9 would be deemed by these sets to be 0.5 tall, and 0.5 medium. Tools that use Metarule Metarule would be only of academic interest if tools did not exist that both read and write Metarule data. Scientio have several tools to generate Metarule from a data source, and to allow the evaluation of knowledge stored in Metarule format. XML Miner This COM object takes as input an XML string or URL pointing to an XML data source, and uses fuzzy rule induction to create a Metarule description of the data set. The user must provide an XPath expression selecting the parent nodes of the data items to mine/analyse, and XPath expressions relative to that node locating the input values (those that are to be used in the analysis) and the output value (the leaf node that is to be predicted or classified). The user can optionally supply the type of the inputs and output (categorical/numeric) and the set granularity. XML Miner reads the input data, identifies the inputs and outputs, performs consistency checks, performs a statistical analysis of the data in each input or output and then creates a Fuzzy decision tree before converting the result to a set of rules in Metarule format.

6 The rules that XML Miner generates will predict or classify the output value with a margin of error. There is a trade off between that error and the complexity of the rule set produced, and yet another trade off between the complexity of the rule set and the performance of the prediction on new data that is not part of the training set. XML miner can be told to set part of the training set aside as a test set and supplies the performance for both test and training set as a percentage correct, for categorical outputs, or root-mean-square error for numeric. For batch or automated processing the definitions of the inputs or outputs can be presented in another XML string or file. XML Rule Given a Metarule encoded rule set we can make use of the knowledge contained using XML Rule. This is a COM object that acts as the Metarule runtime package.

7 XML Rule exposes two collections, inputs and outputs, the number, type and name of which are determined by the contents of the Metarule rule set. To use XML Rule you locate each input, set the inputs value, and call the only method, evaluate. The outputs collection will contain the predicted/classified values. Utilities Two utilities are provided with XML Miner. Strucfind This is a control that displays the structure of an XML document in tree form. Each element type in the source document appears only once in the strucfind tree, no matter how many times it occurs in the source. The result is very much like a graphical display of the schema for the source document, except that optional elements defined in the schema that do not appear in the data set also do not appear in the tree. Using strucfind it is easy to select nodes for training, inputs and an output. Strucfind produces a definition file that can be loaded directly into XML Miner. Metarule.xsl This XSL style sheet converts Metarule documents to HTML form for display. The rule set and the input and output definitions are displayed.