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Projection pursuit algorithms approximate a function of p variables by a sum of nonlinear functions of linear combinations: \ (1) f (x₁, , xₚ) ₈ = ₁ⁿ gᵢ ({a₈₁ x₁ + + a₈ xₚ) }. \ We develop some approximation theory, give a necessary and sufficient condition for equality in (1), and discuss nonuniqueness of the representation.
Diaconis et al. (1984) studied this question.
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