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Machine Learning: Difference between revisions
→Kernel Trick
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\(\DeclareMathOperator{\sign}{sign}\) | \(\DeclareMathOperator{\sign}{sign}\) | ||
Suppose our model is <math>\hat{y}=\sign \sum_{i=1}^{n} w_i y_i \langle x_i, z \rangle</math>. | Suppose our model is <math>\hat{y}=\sign \sum_{i=1}^{n} w_i y_i \langle x_i, z \rangle</math>. | ||
In this case, our model is a linear combination of the training y where <math>\langle x_i, z \rangle</math> represents a similarity between \(z\) and \(x_i\). | In this case, our model is a linear combination of the training data \(y\) where <math>\langle x_i, z \rangle</math> represents a similarity between \(z\) and \(x_i\). | ||
Since we only use <math>\langle x, z\rangle</math> then we only need <math>\phi(x)^T\phi(z)</math> to simulate a non-linear processing of the data. | Since we only use <math>\langle x, z\rangle</math> then we only need <math>\phi(x)^T\phi(z)</math> to simulate a non-linear processing of the data. | ||