Ml ch17

May 30, 20190 likes76 views

This document discusses support vector machines (SVMs), including: 1) SVMs can handle nonlinear and high-dimensional data through kernel functions that transform data into a higher-dimensional space. Common kernel functions include linear, polynomial, radial basis function (RBF), and sigmoid kernels. 2) The RBF kernel is often the best choice as it can adapt to different learning strategies by adjusting its hyperparameters to create flexible decision boundaries. 3) SVMs are used for classification, regression, and outlier detection tasks. They are robust against overfitting and can efficiently handle large datasets.

CH 17
GOING A STEP BEYOND USING
SUPPORT VECTOR
MACHINES
10766012��h�� Jason

Revisiting the Separation
Problem
? Nonseparability of classes
? There is no straight line that traces a precise border
between different examples.
? Other options
? K-Nearest Neighbors : Ch14
? Logistic regression : Ch15
? Transforming the features : Solves the problem by
employing both feature creation
? Decision trees��Neural networks

Characteristics of
Support Vector Machines
? Binary and multiclass classification, regression, and
detection of anomalous or novelty data
? Robust handling of overfitting, noisy data, and outliers
? A capability to handle situations with many variables
? Easy and timely handling of up to about 10,000
training examples
? Automatic detection of nonlinearity in data

SVM - Linear
Negative hyperplane
Positive hyperplane
Support Vector

Applying Nonlinearity
? Nonlinearly
separable points
requiring feature
transformation
(left) to be fit by a
line (right).
? Make the existing
features onto a
feature space of
higher
dimensionality

Applying Nonlinearity
? Problems and limits :
? The number of features increases exponentially, making
computations cumbersome Ӌ�㷱�}
? The expansion creates many redundant features,
causing overfitting. ��N��
? Difficult to determine becoming linearly or not, requiring
many iterations of expansion and test

Kernel functions
? kernel functions project the original features into
a higher dimensional space by combining them
in a nonlinear way
? rely on algebra calculations

Discovering the different
kernels
? Linear: Suitable for linear
? No extra parameters
? Radial Basis Function: Suitable for non-linear
? parameters: gamma
? Polynomial: suitable for non-linear
? parameters: gamma, degree, and coef0
? Sigmoid: Binary classification like Logistic Regression
? parameters: gamma and coef0
? Custom-made kernels: Depends upon the kernel

Radial Basis Function
? An RBF kernel
that uses
diverse hyper-
parameters to
create unique
SVM solutions.
? The RBF kernel can adapt itself to different
learning strategies
? the error cost is high -> bended hyperplane
? the error cost is low -> smoother curve line

Kernels
? The polynomial and sigmoid kernels aren��t as
adaptable as RBF, thus showing more bias
? Most data problems are easily solved using the
RBF
sigmoid polynomial

Classifying and Estimating
with SVM
? handwritten recognition task
? the digits dataset (from Scikit-learn)
? nonlinear kernel, using the RBF
? a series of 8-x-8 grayscale pixel images of
handwritten numbers ranging from 0 to 9.

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Ml ch17

1. CH 17 GOING A STEP BEYOND USING SUPPORT VECTOR MACHINES 10766012��h�� Jason

2. Revisiting the Separation Problem ? Nonseparability of classes ? There is no straight line that traces a precise border between different examples. ? Other options ? K-Nearest Neighbors : Ch14 ? Logistic regression : Ch15 ? Transforming the features : Solves the problem by employing both feature creation ? Decision trees��Neural networks

3. Characteristics of Support Vector Machines ? Binary and multiclass classification, regression, and detection of anomalous or novelty data ? Robust handling of overfitting, noisy data, and outliers ? A capability to handle situations with many variables ? Easy and timely handling of up to about 10,000 training examples ? Automatic detection of nonlinearity in data

4. Explaining the Algorithm

5. SVM - Linear Negative hyperplane Positive hyperplane Support Vector

6. Applying Nonlinearity ? Nonlinearly separable points requiring feature transformation (left) to be fit by a line (right). ? Make the existing features onto a feature space of higher dimensionality

7. Applying Nonlinearity ? Problems and limits : ? The number of features increases exponentially, making computations cumbersome Ӌ�㷱�} ? The expansion creates many redundant features, causing overfitting. ��N�� ? Difficult to determine becoming linearly or not, requiring many iterations of expansion and test

8. Kernel functions ? kernel functions project the original features into a higher dimensional space by combining them in a nonlinear way ? rely on algebra calculations

9. Discovering the different kernels ? Linear: Suitable for linear ? No extra parameters ? Radial Basis Function: Suitable for non-linear ? parameters: gamma ? Polynomial: suitable for non-linear ? parameters: gamma, degree, and coef0 ? Sigmoid: Binary classification like Logistic Regression ? parameters: gamma and coef0 ? Custom-made kernels: Depends upon the kernel

10. Radial Basis Function ? An RBF kernel that uses diverse hyperparameters to create unique SVM solutions. ? The RBF kernel can adapt itself to different learning strategies ? the error cost is high -> bended hyperplane ? the error cost is low -> smoother curve line

11. Kernels ? The polynomial and sigmoid kernels aren��t as adaptable as RBF, thus showing more bias ? Most data problems are easily solved using the RBF sigmoid polynomial

12. Classifying and Estimating with SVM ? handwritten recognition task ? the digits dataset (from Scikit-learn) ? nonlinear kernel, using the RBF ? a series of 8-x-8 grayscale pixel images of handwritten numbers ranging from 0 to 9.

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Ml ch17

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