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49to be the probability that the algorithms will categorize into thejth categoryC j , an element whichactually belongs to the ith category C i (see Figure 4.5 for a graphical illustration). Simply ɛ iji,j ∈ [1,ρ] is the element of the ith row andjth column of what is known as theρ×ρ confusionmatrix, which we denote here asE:⎡E := ⎢⎣Related to these parameters we also define⎤ɛ 11 ɛ 12 ··· ɛ 1ρɛ 21 ɛ 22 ··· ɛ 2ρ. ..⎥ɛ ρ1 ɛ ρ2 ··· ɛ ρρɛ f :=ρ∑i=1,i≠f⎦ . (4.7)ɛ fi (4.8)to denote the probability that a member of category C f is wrongly categorized. Finally we use thenotatione := [ɛ 1 ,ɛ 2 ,··· ,ɛ ρ ]. (4.9)RealcategoriesSystem reliabilityEstimatedcategoriesFigure 4.5: Confusion parameters {ɛ f }.4.5 Statistical analysis using the method of types and informationdivergenceLet us consider a scenario where a search for a subject v ′ turned out to be extremely ineffective,and fell below the expectations, due to a very unfortunate matching of the subject withits surroundings v. This unfortunate scenario motivates the natural question of how often will asystem that was designed to achieve a certain average gain-reliability behavior, fall short of theexpectations, providing an atypically small pruning gain and leaving its users with an atypicallylarge and unmanageable S. It consequently brings to the previously related questions such as forexample, how will this probability be altered if we change the hardware and algorithmic resourcesof the system (change the ɛ f and ρ), or change the setting in which the system operates (changethe p i ).