Fuchen Sun Kar-Ann Toh Manuel Grana Romay - Extreme Learning Machines 2013: Algorithms and Applications

Department of Management and Quantitative Methods, AYRNA Research Group, Universidad Loyola Andaluca, Escritor CastillaAguayo 4, Crdoba, Spain

David Becerra-Alonso

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Sensitivity Analysis (SA) is a common tool to rank attributes in a dataset in terms how much they affect a classifiers output. Assuming an optimal classifier, attributes that turn out to be highly sensitive are interpreted as being particularly relevant for the correct classification of the dataset. Low sensitivity attributes are often considered irrelevant or regarded as noise. This opens the possibility of discarding them for the sake of a better classification. But besides an interest in an improved classification, SA is a technique that returns a rank of attributes. When expert information about a dataset is available, researchers can comment on the consistency of certain attributes being high or low in the scale of sensitivity, and what it says about the relationship between those attributes and the output that is being classified.

In this context, the difference between a deterministic and a stochastic classifier is straightforward. Provided a good enough heuristics, a deterministic method will return only one ranking for the sensitivity of each one of the attributes. With such a limited amount of information it cannot be known if the attributes are correctly ranked, or if the ranking is due to a limited or suboptimal performance of the deterministic classifier. This resembles the long standing principle that applies to accuracy when classifying a dataset (both deterministic and stochastic): it cannot be known if a best classifier has reached its topmost performance due to the very nature of the dataset, or if yet another heuristics could achieve some extra accuracy. Stochastic methods are no better here, since returning an array of accuracies instead of just one (like in the deterministic case) and then choosing the best classifier is not better than simply giving a simple good deterministic classification. Once a better accuracy is achieved, the question remains: is the classifier at its best? Is there a better way around it?

On the other hand, when it comes to SA, more can be said about stochastic classifiers. In SA, the method returns a ranked array, not a single value such as accuracy. While a deterministic method will return just a simple rank of attributes, a stochastic method will return as many as needed. This allows us to claim a probabilistic approach for the attributes ranked by a stochastic method. After a long enough number of classifications and their corresponding SAs, an attribute with higher sensitivity will most probably be placed at the top of the sensitivity rank, while any attribute clearly irrelevant to the classification will eventually drop to the bottom of the list, allowing for a more authoritative claim about its relationship with the output being classified.

Section introduces two ways of interpreting sensitivity. The article ends with conclusions about the methodology.