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Genetic algorithms (GAs) [133] are generally effective for rapid search of large, nonlinear, and poorly understood spaces. Unlike classical feature selection strategies where one solution is optimized, a population of solutions can be modi ed at the same time [190,200,201,330]. This can result in several optimal (or close-to-optimal) feature subsets as output. Section 15.5 discusses the potential usefulness of this aspect of GAs in feature selection. A feature subset is typically represented by a binary string with length equal to the number of features present in the dataset. A zero or one in the j th position in the chromosome denotes the absence or presence of the j th feature in this particular subset. The general process for feature selection using GAs can be seen in Figure 4.16. An initial population of chromosomes is created; the size of the population and how they are created are important issues. From this pool of feature subsets, the typical genetic operators (crossover and mutation) are applied. Again, the choice of which types of crossover and mutation used must be carefully considered, as well as their probabilities of application. This process generates a new feature subset pool that may be evaluated in two different ways. If a lter approach is adopted, the tness of individuals is calculated using a suitable criterion function J (X). This function evaluates the goodness of feature subset X; a larger value of J indicates a better feature subset. Such a criterion function could be Shannon s entropy measure [281] or the dependency function from rough set theory [261].

The error_prepend_string directive sets the string that is prepended to an error message This directive is used with the error_append_string Syntax: error_prepend_string string If you do not log errors, then error messages are shown on screen For example, by using these two directives, you can print error messages in red font color:

Mandatory & Optional Attributes cOMCLSID cOMInterfaceID cOMOtherProgId cOMProgID cOMTreatAsClassId implementedCategories managedBy requiredCategories cn defaultObjectCategory governsID objectClassCategory schemaIDGUID subClassOf auxiliaryClass classDisplayName defaultHidingValue defaultSecurityDescriptor isDefunct IDAPDisplayName mayContain mustContain possSuperiors rDNAttID schemaFlagsEx systemAuxiliaryClass systemMayContain systemMustContain systemOnly systemPossSuperiors appSchemaVersion lastUpdateSequence nextLevelStore versionNumber cn marshalledInterface moniker monikerDisplayName

The error_reporting directive enables you to specify a bit field to specify an error reporting level The bit field can be constructed using the predefined constants shown in Table 15-2 Syntax: error_reporting [bit field] [predefined_ constant]

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For the wrapper approach chromosomes are evaluated by inducing a classi er based on the feature subset, and obtaining the classi cation accuracy (or an estimate of it) on the data [347]. To guide the search toward minimal feature subsets, the subset size is also incorporated into the tness function of both lter and wrapper methods. Indeed other factors may be included that are of interest, such as the cost of measurement for each feature. GAs may also learn rules directly, and in the process perform feature selection [60,170,392]. A suitable stopping criterion must be chosen. This is typically achieved by limiting the number of generations that take place or by setting some threshold that must be exceeded by the tness function. If the stopping criterion is not satis ed, then individuals are selected from the current subset pool and the process described above repeats. Among the selection strategies that have been applied are roulette wheel selection [254] and rank-based selection [396,405]. In roulette wheel selection the probability of a chromosome being selected is proportional to its tness. Rank selection sorts all the individuals by tness and the probability that an individual will be selected is proportional to its rank in this sorted list. As with all feature selection approaches, GAs can get caught in local minima, missing a dataset s true minimal feature subset. Also the tness evaluation can be very costly as there are many generations of many feature subsets that must be evaluated. This is particularly a problem for wrapper approaches where classi ers are induced and evaluated for each chromosome.

Constant E_ALL E_ERROR E_WARNING E_PARSE Meaning Displays all errors, warnings, and notices Displays only fatal run-time errors Displays run-time warnings Displays parse errors

Table F-1 (continued)

Constant E_NOTICE E_CORE_ERROR E_CORE_WARNING E_COMPILE_ERROR E_COMPILE_WARNING E_USER_ERROR E_USER_WARNING E_USER_NOTICE

Meaning Displays notices of likely problems in code Displays fatal errors that occur during PHP s initial startup Displays warnings that occur during PHP s initial startup Displays fatal compile-time errors Displays compile-time warnings (nonfatal errors) User-generated error message User-generated warning message User-generated notice message

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