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# Supervised Learning Regression, Classification Linear regression, k- NN classification - PowerPoint PPT Presentation

Supervised Learning Regression, Classification Linear regression, k- NN classification. Debapriyo Majumdar Data Mining – Fall 2014 Indian Statistical Institute Kolkata August 11, 2014. An Example: Size of Engine vs Power.

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### Supervised LearningRegression, ClassificationLinear regression, k-NN classification

Debapriyo Majumdar

Data Mining – Fall 2014

Indian Statistical Institute Kolkata

August 11, 2014

An Example: Size of Engine vs Power

• An unknown car has an engine of size 1800cc. What is likely to be the power of the engine?

Power (bhp)

Engine displacement (cc)

An Example: Size of Engine vs Power

• Intuitively, the two variables have a relation

• Learn the relation from the given data

• Predict the target variable after learning

Power (bhp)

Target

Variable

Engine displacement (cc)

• Predict y for x = 2.5

y

x

• Assume: the relation is linear

• Then for a given x (=1800), predict the value of y

Training set

Power (bhp)

Engine displacement (cc)

• Linear regression

• Assume y = a . x + b

• Try to find suitable a and b

Power (bhp)

Engine displacement (cc)

Optional exercise

Exercise: using Linear Regression

• Define a regression line of your choice

• Predict y for x = 2.5

y

x

• 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

Goal: minimizing the deviation from the actual data points

y

x

• Goal: minimize J for all values of a and b

• Start from some a = a0and 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?

b

a

Δ

Y

• 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

Training set

High blood sugar

N

Age

Y

• One approach: what other data points are nearest to the new point?

• Other approaches?

High blood sugar

N

?

24

Age

• The k-nearest neighbor classification

• Naïve Bayes classification

• Decision Tree

• Linear Discriminant Analysis

• Logistics Regression

• Support Vector Machine

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?

### Classification

• Training set

• Owns a flat

• Does not own a flat

Monthly income (thousand rupees)

Age

• Given a new person’s age and income, predict – does (s)he own a flat?

• Training set

• Owns a flat

• Does not own a flat

Monthly income (thousand rupees)

Age

• Nearest neighbor approach

• Find nearest neighbors among the known data points and check their labels

• Training set

• Owns a flat

• Does not own a flat

Monthly income (thousand rupees)

Age

• The 1-Nearest Neighbor (1-NN) Algorithm:

• Find the closest point in the training set

• Output the label of the nearest neighbor

The k-Nearest Neighbor Algorithm

• Training set

• Owns a flat

• Does not own a flat

Monthly income (thousand rupees)

Age

• The k-Nearest Neighbor (k-NN) Algorithm:

• Find the closestk point in the training set

• Majority vote among the labels of the k points

• 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)

• 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

• Test set accuracy: the correct performance measure

• Need to know the true test labels

• Option: usetrainingset itself

• Parameterselection (fork-NN) byaccuracy on training set

• Overfitting: a classifier performs too good on training set compared to new (unlabeled) test data

• Leave one out:

• 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

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

• Lecture videos by Prof. Andrew Ng, Stanford University

Available on Coursera (Course: Machine Learning)