class 4 – more classifiers

Class 4 – More Classifiers

Ramoza Ahsan, Yun Lu, Dongyun Zhang, Zhongfang Zhuang, Xiao Qin, Salah Uddin Ahmed

Lesson 4.1Classification Boundaries

Classification Boundaries• Visualization of the data in the

training stage of building a classifier can provide guidance in parameter selection• Weka visuilization tool• 2 dimensional data set

Boundary Representation With OneR

• Color diagram shows the decision boundaries with training data• Spatial representation of

the decision boundary on OneR algorithm

Boundary Representation With IBk

• Lazy classifier (instance based learner)

• Chooses nearest instance to classify

• Piece wise linear boundary• Increasing k will give blurry

boundaries

Boundary Representation With Naïve Bayes• Naïve Bayes treats each of the

two attribute as contributing equally and independently to decision

• When multiple along the two dimensions get a checkerboard pattern of probabilities.

Boundary Representation With J-48

• Increasing the minNumObj parameter will result in simpler tree

Classification Boundaries• Different classifiers have different capabilities

for carving up instance space. (“Bias”)• Usefulness:

• Important visualization tool.• Provides insight how the algorithm works on data.

• Limitations:• Restricted to numeric attributes and 2-dimensional

plot.

Lesson 4.2Linear Regression

What Is Linear Regression?• In statistics, linear regression is an approach to model

the relationship between a dependent variable y and one or more explanatory variables denoted X.

Straight-line regression analysis: one explanatory variable.Multiple linear regression: more than one explanatory variable

• In data mining, we use this method to make predictions based on numeric attributes for numeric classes.

NominalToBinary filter

Why Linear Regression?• A regression models the past relationship

between variables to predict the future behavior.• Businesses use regression to predict such things

as future sales, stock prices, currency exchange rates, and productivity gains resulting from a training program.• Example: A person’s salary is related with years

of experience. The dependent variable in this instance is salary and the explanatory variable (also called independent variable) is experience here.

Mathematics Of Simple Linear Regression

• The simplest form of regression function is:

Where y is the dependent variable, x is the explanatory variable, b and w are regression coefficients. By thinking regression coefficients as weight, we could get:

Where:

Previous ExampleSalary Dataset

• From the given dataset we could get:

• Thus, we could get • For the instances, we can predict that a person with 10

years experience will get the salary of $58,600 per year.

XYears of Experience

YSalary in $1000s

3 308 579 64

13 723 366 43

11 5921 901 20

16 83

Run This Dataset On Weka

Multiple Linear Regression • Multiple linear regression is an extension of straight-line

regression so as to involve more than one predictor variable. It allows the dependent variable to be modeled as linear summary of n predictor variables described by tuple ( ).

Then adjust weights to minimize square error on training data:

This equation is hard to solve by hand, so we need a tool like Weka to do it.

Non-linear Regression

• Often no linear relationship between dependent variable(class attribute) and explanatory variables.

• Often convert into a linear by a patchwork of serial linear regression models

In Weka, we have “model tree” named M5P method, which can solve this problem. A "model tree" is a tree where each leaf has one of these linear regression models. And we can calculate coefficients for each linear function and then we could make prediction based on this “model tree”.

Lesson 4.3Classification By Regression

Review: Linear Regression

• Several numeric attributes: • Weights of each attributes plus a constant: • Weighed sum of the attributes: • Minimize the squared error:

Using Regression In Classification

• Convert the class values to numeric values(usually binary)• Decide the class according to the

regression result• The result is NOT the probability!!!

• Set the threshold

2-Class Problems

• Assign the binary values to the two classes• Training: Linear Regression•Output prediction

Multi-Class Problems

•Multi-Response Linear Regression•Divide into n regression problems• Build different model for each problem• Select the model with the largest

output

More Investigations

• Cool stuff• Lead to the foundation of Logistic Regression• Convert the class value to binary• Add the Linear Regression result as an attribute• Detect the split using OneR

Lesson 4.4Logistic Regression

Logistic Regression

• In linear regression, we use

to calculate weights from training data• In Logistic Regression, we use

to estimate class probabilities directly.

(1)(2)

Classification

• Email: Spam / Not Spam?• Online Transactions: Fraudulent (Yes / No)?• Tumor: Malignant / Benign?

0: “negative class” (e.g., Benign tumor)1: “positive class” (e.g., Malignant tumor)

Coursera – Machine Learning – Prof. Andrew Ng from Stanford University

(Yes) 1

Malignant?

(No) 0

h (𝑥)

Tumor Size

Threshold classifier output y at 0.5:

If predict “”If predict “”

0.5


𝑥1

(Yes) 1

Malignant?

(No) 0

h (𝑥)

0.5

Threshold classifier output y at 0.5:

If predict “”If predict “”


𝑥1 𝑥2

Classification: y = 0 or 1

In Linear Regression, can be >1 or <0

Logistic regression:


Logistic Regression Model

• We want

• Sigmoid functionLogistic function

h𝑤 (𝑥 )= 11+𝑒−(𝑤0+𝑤1𝑥)


(3)(4)

Interpretation Of Hypothesis Output

= estimated probability that on input Example: if

Tell patient that 70% chance of tumor being malignant().

“Probability that , given , parameterized by .


(5)(6)(7)

Lesson 4.5Support Vector Machine

Things About SVM

• Better on small and not linear separable data

• Low dimensions => High dimensions

• Support Vectors

• Maximum Marginal Hyperplane

Overview

• The support vectors are the most difficult tuples to classify and give the most information regarding classification.

SVM searches for the hyperplane with the largest margin, that is, the Maximum Marginal Hyperplane (MMH).

SVM Demo

• CMsoft SVM Demo Tool•Question(s)

MoreVery resilient to overfitting• Boundary depends on a few points• Parameter setting (regularization)

Weka: functions>SMORestricted to two classes• So use Multi-Response linear regression … or pairwise linear

regression

Weka: functions>libsvm• External library for support vector machines• Faster than SMO, more sophisticated options

Lesson 4.6Ensemble Learning

Ensemble Learning

• Take the training data• Derive several different training sets from it• Learn a model from each training set• Combine them to produce an ensemble of

learned models

• In brief, instead of depending on a single classifier, we take vote from different classifiers to reach a verdict.

Ensemble Learning

We will discuss 4 types of ensemble methods:• Bagging• Randomization- Random Forest• Boosting• Stacking

Ensemble Learning -- Bagging

• Several training datasets of the same size are chosen at random from the problem domain or produced by sampling with replacement• A particular machine learning technique is used to

build a model for each dataset• For each new test instance we get the prediction from

each model• The class that has the largest support or vote from

the models becomes the resultant class

Ensemble Learning -- Bagging In Weka

Ensemble Learning -- Randomization

• One training dataset• Randomize the choices of classifier algorithm to build

several model for the same dataset• For each new test instance we get the prediction from

each model• Very similar to bagging , the class that has the largest

support or vote from the models becomes the resultant class• Ex: Random Forest – uses J48, instead of choosing the

best attribute, randomly pick from k best options

Ensemble Learning -- Random Forest In Weka

Ensemble Learning -- Boosting

• One training dataset• A particular classifier is used iteratively several

times to produce several models• Output of a iteration becomes input for the next

iteration.• Extra weight is assigned to misclassified

instances to encourage the next iteration to correctly classify• For a test instance, the class that has the

largest vote from the models becomes the resultant class• Ex: AdaBoostM1 with C4.5 or J48

Ensemble Learning -- Boosting In Weka

Ensemble Learning -- Stacking

• One training dataset is the input for several base learners or level-0 learners• Output predictions of base learners become

input of a meta learner or level-1 learner• Base learners are different classifiers• An instance is first fed into the level-0 models,

the guesses are fed into the level-1 model, which combines them into the final prediction.• Ex: StackingC with LinearRegression

Ensemble Learning -- Stacking In Weka

Ensemble Learning

•Usefulness:• Diversity helps, especially with “unsta

ble” learners •Disadvantages:• It is hard to analyze - it is not easy to

understand what factors are contributing to the improved decisions.

class 4 – more classifiers

Documents

linear relationship

linear regressionwhat

linear function

regression resultthe

boundary representation

model tree

explanatory variables

decision boundary