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  • Understanding the Kernel Trick | Monishver Chandrasekaran
    Key Takeaway: The kernel trick enables efficient computation in high-dimensional feature spaces by directly working in the input space This reduces the complexity from \(O\left(\binom{d + p}{p}\right)\) to \(O(d)\), making it feasible to apply machine learning methods to problems with high-degree polynomial or infinite-dimensional feature spaces
  • Understanding High-Dimensional Feature Spaces and the Kernel . . .
    The kernel trick allows certain algorithms to operate in high-dimensional spaces without explicitly transforming the input data It does this by replacing the dot product ϕ(x)^T ϕ(x’) with
  • Lecture 13: Kernels - Department of Computer Science
    Formally, for a data vector x ∈Rd x ∈ R d, we apply the transformation x → ϕ(x) x → ϕ (x) where ϕ(x) ∈RD ϕ (x) ∈ R D Usually D ≫ d D ≫ d because we add dimensions that capture non-linear interactions among the original features





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