lecture14-SVMs-handout-6-per

# Datasetsthatarelinearlyseparablewithsomenoiseworkoutgr

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Unformatted text preview: onding xi is a support vector.    Then the classifying func)on will have the form:  f(x) = ΣαiyixiTx + b   No)ce that it relies on an inner product between the test point x and the support  vectors xi – we will return to this later.    Also keep in mind that solving the op)miza)on problem involved compu)ng the  inner products xiTxj between all pairs of training points.  12  2 Sec. 15.2.1 Introduc)on to Informa)on Retrieval Sou Margin Classiﬁca)on    Sec. 15.2.1 Introduc)on to Informa)on Retrieval Sou Margin Classiﬁca)on  Mathema)cally    The old formula)on:    If the training data is not  linearly separable, slack variables ξi can be added to  allow misclassiﬁca)on of  diﬃcult or noisy examples.    Allow some errors    Let some points be moved  to where they belong, at a  cost    S)ll, try to minimize training  set errors, and to place  hyperplane “far” from each  class (large margin)  Find w and b such that Φ(w) =½ wTw is minimized and for all {(xi yi (wTxi + b) ≥ 1 ,yi)}   The new formula)on incorpora)ng slack variables:  ξi Find w and b such that Φ(w) =½ wTw + CΣξi is minimized and for all {(xi yi (wTxi + b) ≥ 1- ξi and ξi ≥ 0 for all i ξj ,yi)}   Parameter C can be viewed as a way to control overﬁvng – a  regulariza)on term  13  Sec. 15.2.1 Introduc)on to Informa)on Retrieval 14  Sec. 15.1 Introduc)on to Informa)on Retrieval Sou Margin Classiﬁca)on – Solu)on  Classiﬁca)on with SVMs    The dual problem for sou margin classiﬁca)on:    Given a new point x, we can score its projec)on  onto the ...
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## This document was uploaded on 02/26/2014.

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