Wittgenstein coined the words “truth table” less than 100 years ago. He used them for logical function representation. What I mean here is something different. Suppose we have three classes: A, B, and C. We suppose we have a way of generating test samples form each set in an unbiased fashion. We also have a pattern recognition system that declares the input to be in one of those three states, We want to estimate all members of a 3x3 matrix whose components are the probabilities of various declarations given various true states, e.g. p(AęA) is the probability of declaring A when a random A is presented and p(AęB) is the probability of declaring A when the truth is B. We can estimate those probabilities by accumulating the results of many fair tests in a matrix such as this.
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A INPUT |
B INPUT |
C INPUT |
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A DECLARATION |
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B DECLARATION |
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C DECLARATION |
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From those data, we can rank the pattern recognition system’s performance in various ways, e.g. Bayesian (Weighting each error rate according to its cost and summing).