Transcript Association Rule Mining - Indian Statistical Institute

Supervised Learning
Regression, Classification
Linear regression, k-NN classification
Debapriyo Majumdar
Data Mining – Fall 2014
Indian Statistical Institute Kolkata
August 11, 2014
Power (bhp)
An Example: Size of Engine vs Power
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Engine displacement (cc)
 An unknown car has an engine of size 1800cc. What is likely
to be the power of the engine?
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Power (bhp)
An Example: Size of Engine vs Power
Target
Variable
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Engine displacement (cc)
 Intuitively, the two variables have a relation
 Learn the relation from the given data
 Predict the target variable after learning
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Exercise: on a simpler set of data points
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x
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2.5
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y
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y
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3
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x
 Predict y for x = 2.5
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Power (bhp)
Linear Regression
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Training set
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Engine displacement (cc)
 Assume: the relation is linear
 Then for a given x (=1800), predict the value of y
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Power (bhp)
Linear Regression
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180
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0
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1000
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Engine Power
(cc) (bhp)
800
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1000
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1200
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1400
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1500
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1800
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2400
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Engine displacement (cc)
 Linear regression
 Assume y = a . x + b
 Try to find suitable a and b
Optional exercise
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Exercise: using Linear Regression
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x
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2.5
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y
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y
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x
 Define a regression line of your choice
 Predict y for x = 2.5
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Choosing the parameters right
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Goal: minimizing
the deviation from
the actual data
points
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y
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x
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The data points: (x1, y1), (x2, y2), … , (xm, ym)
The regression line: f(x) = y = a . x + b
Least-square cost function: J = Σi ( f(xi) – yi )2
Goal: minimize J over choices of a and b
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How to Minimize the Cost Function?
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a
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Goal: minimize J for all values of a and b
Start from some a = a0 and b = b0
Compute: J(a0,b0)
Simultaneously change a and b towards the negative
gradient and eventually hope to arrive an optimal
 Question: Can there be more than one optimal?
Δ
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Another example:
High blood sugar
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Training set
N
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Age
 Given that a person’s age is 24, predict if (s)he has
high blood sugar
 Discrete values of the target variable (Y / N)
 Many ways of approaching this problem
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Classification problem
High blood sugar
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N
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Age
 One approach: what other data points are nearest to
the new point?
 Other approaches?
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Classification Algorithms
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The k-nearest neighbor classification
Naïve Bayes classification
Decision Tree
Linear Discriminant Analysis
Logistics Regression
Support Vector Machine
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Classification or Regression?
Given data about some cars: engine size, number of
seats, petrol / diesel, has airbag or not, price
 Problem 1: Given engine size of a new car, what is
likely to be the price?
 Problem 2: Given the engine size of a new car, is it
likely that the car is run by petrol?
 Problem 3: Given the engine size, is it likely that the
car has airbags?
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Classification
Example: Age, Income and Owning a flat
Monthly income
(thousand rupees)
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Training set
• Owns a
flat
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• Does
not own
a flat
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Age
 Given a new person’s age and income, predict – does
(s)he own a flat?
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Example: Age, Income and Owning a flat
Monthly income
(thousand rupees)
250
Training set
• Owns a
flat
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150
• Does
not own
a flat
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50
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Age
 Nearest neighbor approach
 Find nearest neighbors among the known data points
and check their labels
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Example: Age, Income and Owning a flat
Monthly income
(thousand rupees)
250
Training set
• Owns a
flat
200
150
• Does
not own
a flat
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50
0
0
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Age
 The 1-Nearest Neighbor (1-NN) Algorithm:
– Find the closest point in the training set
– Output the label of the nearest neighbor
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The k-Nearest Neighbor Algorithm
Monthly income
(thousand rupees)
250
Training set
• Owns a
flat
200
150
• Does
not own
a flat
100
50
0
0
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30
40
50
60
70
Age
 The k-Nearest Neighbor (k-NN) Algorithm:
– Find the closest k point in the training set
– Majority vote among the labels of the k points
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Distance measures
 How to measure distance to find closest points?
 Euclidean: Distance between vectors x = (x1, … , xk)
and y = (y1, … , yk)
 Manhattan distance:
 Generalized squared interpoint distance: S is the
covariance matrix
The Maholanobis distance (1936)
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Classification setup
 Training data / set: set of input data points and given
answers for the data points
 Labels: the list of possible answers
 Test data / set: inputs to the classification algorithm
for finding labels
– Used for evaluating the algorithm in case the answers are
known (but known to the algorithm)
 Classification task: Determining labels of the data
points for which the label is not known or not passed
to the algorithm
 Features: attributes that represent the data
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Evaluation
 Test set accuracy: the correct performance measure
 Accuracy = #of correct answer / #of all answers
 Need to know the true test labels
– Option: use training set itself
– Parameter selection (for k-NN) by accuracy on training set
 Overfitting: a classifier performs too good on training
set compared to new (unlabeled) test data
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Better validation methods
 Leave one out:
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For each training data point x of training set D
Construct training set D – x, test set {x}
Train on D – x, test on x
Overall accuracy = average over all such cases
Expensive to compute
 Hold out set:
– Randomly choose x% (say 25-30%) of the training data, set
aside as test set
– Train on the rest of training data, test on the test set
– Easy to compute, but tends to have higher variance
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The k-fold Cross Validation Method
 Randomly divide the training data into k partitions
D1,…, Dk : possibly equal division
 For each fold Di
– Train a classifier with training data = D – Di
– Test and validate with Di
 Overall accuracy: average accuracy over all cases
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References
 Lecture videos by Prof. Andrew Ng, Stanford University
Available on Coursera (Course: Machine Learning)
 Data Mining Map: http://www.saedsayad.com/
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