Learning From Data Lecture 10 Nonlinear Transforms

Learning From Data Lecture 10

Nonlinear Transforms

The Z-space Polynomial transforms Be careful

M. Magdon-Ismail

CSCI 4100/6100

recap: The Linear Model

linear in x: gives the line/hyperplane separator

s = wtx

linear in w: makes the algorithms work

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Perceptron Linear Regression Logistic Regression

Classification Error PLA, Pocket,. . .

Squared Error Pseudo-inverse

Cross-entropy Error Gradient descent

c AML Creator: Malik Magdon-Ismail

Nonlinear Transforms: 2 /18

Limitations of linear -

The Linear Model has its Limits

(a) Linear with outliers

(b) Essentially nonlinear

To address (b) we need something more than linear.

c AML Creator: Malik Magdon-Ismail

Nonlinear Transforms: 3 /18

Change the features -

Change Your Features

Years in Residence, Y

Y 3 years

no additional effect beyond Y = 3;

Y 0.3 years

no additional effect below Y = 0.3.

Income

c AML Creator: Malik Magdon-Ismail

Nonlinear Transforms: 4 /18

`Transform' your features -

Change Your Features Using a Transform

Income Income

Years in Residence, Y

z1

z1 Y

c AML Creator: Malik Magdon-Ismail

Nonlinear Transforms: 5 /18

Feature transform I: Z-space -

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