10 - 601 B Recitation 11
نویسنده
چکیده
The Gaussian kernel encourages similarity between inputs based on their Euclidean distance. Because we’re not dealing with probabilities which must sum to 1, we can omit the normalization constant found in the Gaussian distribution. But the shape is the same: we strongly encourage similarity among nearby inputs, while as inputs get further away, we encourage similarity by an amount that decreases exponentially to 0. For simplicity, we prove that the feature mapping is infinite-dimensional for one-dimensional inputs where 2σ = 1: k(x, x′) = exp ( −(x− x′)2 ) = exp(−x) exp(−x′2) exp(2xx′) = exp(−x) exp(−x′2) ∞ ∑
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