Semantics of Feature Selection and Transformations Sample Clauses

Semantics of Feature Selection and Transformations. ‌ Given an attribute A, then, let AI(t, s) be the value of A at the time t and position s under a specific name in the data set I; we use A(t, s) when I is clear from the context. We let A(t — t′, s — s′) be the value of A under the same name, at the time t — t′ and position s′′, where dist(s′′ — s) = s′ is any dimension (thus, A(t — t′, s — s′) is not uniquely defined, but, as it will be immediately clear, this is not a problem). For learning purposes, we can safely assume that if there is no information about time t — t′ and/or position s′′ in I, A(t — t′, s — s′) takes a random value. Now, we use: A(t — t′, s — s′) = {A(t — t′′, s — s′′) | t′′ ≤ t′, s′′ ≤ s′}. fst As a result, under our limiting assumptions, we can model a wide portfolio of selections and transformations of features using this notation. Let us call τfst the specific operator for feature selection and transformation; τfst is defined column-by-column, using auxiliary transformations τ i,j , where 1 ≤ i ≤ n and ≤ j ≤ m. For a specific component i, Pfst[i] is a triple of numbers (T, S, F ). The idea is that T represents the temporal displacement of the i-th attribute (whereas —1 represents de-selecting it), S represents the spatial displacement (in terms of semi-length of xxx xxxx of the outermost hypercube to be considered), and F represents the combining function. Thus, specific values of t and S entail considering a subset of values of Ai to be combined into a single value that substitutes the original one. Accordingly, for example, Pfst[i] = (2, 0, 0) is interpreted as substituting the current value of A with the value of A two time units before the considered time. The semantics of other functions can be decided for specific applications. To ease the notation, if Pfst[i] = (T, S, F ), we let T [i] (resp., S[i], F [i]) denote the temporal (resp., spatial, functional) component; recall that F [i] is a function of the type: Formally, let us define: F [i] : 2dom(A) → dom(A) fst
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