Concept - Linear Model

Linear Model

Linearly combine the features by the weights (02 Pre-processing s.8):

$\mathbf{w}\cdot \varphi (x)={\sum }_{j=1}^d{w}_j\varphi (x{)}_j$

with $\mathbf{w}\in {\mathbb{R}}^d$ (weight vector) and $\varphi (x)\in {\mathbb{R}}^d$ (feature vector) (s.9).

Binary classification (s.9): $f_{\mathbf{w}}(x)=\text{sign}(\mathbf{w}\cdot \varphi (x))$ = $+1$ if $\mathbf{w}\cdot \varphi (x)>0$; $-1$ if $<0$; ”?” if $=0$.

Worked example (s.8): $-1.2(1)+1.4(1)+2.2(1)+0.6(1)+0.5(0)+0.3(5)+0.6(0.85)$; evaluating gives 5.01 > 0 -> +1 (email address) (the slide leaves the sum unevaluated).

Learning the weights (s.10): from data; define a loss function and then optimize it.

Related

Concept - Feature Extraction | Concept - Text Preprocessing

Appears in

• 02 Pre-processing - Chunk 01 (s.1-30)