# 2012Fall7646 Project 2

## Contents

## Important Updates

You are allowed to use NumPy libraries for the linear regression component of this project.

You are NOT allowed to use other peoples code to implement KNN. You must write that yourself.

## Overview

You are to **implement and evaluate** a KNN learner class, and a Linear Regression class in Python named KNNLearner and LinRegLearner respectively.

Your class should implement the following functions/methods for the KNN learner:

learner = KNNLearner(k = 3) learner.addEvidence(Xtrain, Ytrain) Y = learner.query(Xtest)

Where "k" is the number of nearest neighbors to find. Xtrain and Xtest should be ndarrays (numpy objects) where each row represents an X1, X2, X3... XN set of feature values. The columns are the features and the rows are the individual example instances. Y and Ytrain are single dimensional lists that indicate the value we are attempting to predict with X. For an example of how to code an object, take a look at QSTK/qstklearn/kdtknn.py

Similarly for the Linear Regression learner:

learner = LinRegLearner() learner.addEvidence(Xtrain, Ytrain) Y = learner.query(Xtest)

We are considering this a **regression** problem (not classification). So the goal is to return a continuous numerical result (not a discrete numerical result).

Some external resources that might be useful for this project:

- You may be interested to take a look at Andew Moore's slides on instance based learning.
- A definition of correlation which we'll use to assess the quality of the learning.
- numpy corrcoef
- numpy argsort

## The Data

You will find these two files in the Examples/KNN directory:

- data-classification-prob.csv
- data-ripple-prob.csv

Each data file contains 3 columns: X1, X2, and Y. Please don't be misled by the name "data-classification-prob.csv" in to treating the problem as classification. It's regression.

The columns X1,X2 and Y in data-classification-prog.csv represent one set of paired data and data-ripple-prob.csv represents another set. One intent of the assignment is for us to assess how well the learning algorithm works on these different data sets. In each case you should use the **first 60% of the data for training**, and the **second 40% for testing**.

## Software to write

- Create a python object called KNNLearner in a file named KNNLearner.py that implements the methods described above.
- Create a python object called LinRegLearner in a file named LinRegLearner.py that implements the methods described above.
- Create a separate python program called testlearner.py that evaluates your each of your learners in the following manner:
- Selects the first 60% of the data for training (e.g., feed to addEvidence().
- Use the remaining 40% for testing (e.g., query).
- testlearner.py should evaluate the following for each learner:
- Time required for training (average seconds per instance)
- Time required for query (average seconds per instance)
- RMS error (root mean square difference between "correct" Y and the result provided by query()). See http://en.wikipedia.org/wiki/Root_mean_square for example of how to calculate RMS error.
- Correlation coefficient of the response from the learner versus the correct response (using the 40% out of sample data)

## Experiments to run

- Run your test on both data sets and report: avg train time per instance, avg query time per instance, correlation for each data set.
**USE K=3**for this evaluation. - For each data set test values of K from K=1 to ? the find the value of k that provides the best correlation coefficient.
- Plot correlation versus K for each data set and report K and the correlation for the best solution.

## Deliverables

Submit files (attachments) via t-square

- Your code in
**KNNLearner.py**,**LinRegLearner.py**and**testlearner.py** - Plot the correlation coefficient for data-classification-prob.csv and data-ripple-prob.csv, as you vary K from 1 to a large number, combine those plots into your report.
- Report (in a pdf file,
**report.pdf**):- In a table with columns named KNN Ripple (K=3), KNN Ripple (K=best), KNN Classification (K=3), KNN Classification (K=best), LinReg Ripple, LinReg Classification, include the following data:
- The best K for each dataset (the one that maximizes correlation) and
- the corrcoef for each dataset,
- the RMS error for each dataset
- the timing of training
- timing of query

- the two plots

- In a table with columns named KNN Ripple (K=3), KNN Ripple (K=best), KNN Classification (K=3), KNN Classification (K=best), LinReg Ripple, LinReg Classification, include the following data:
- Preferred, but not required: Scatter plots for each experiment that show predicted Y versus actual Y (within the report pdf).
- Important: Disclose and cite any code or ideas you drew from others.

## How to submit

Go to the t-square site for the class, then click on the "assignments" tab. Click on "add attachment" to add your 4 files. Once you are sure you've added the files, click "submit."

## Extra Credit

Write additional code, and add plots to your report that do the following:

- Revise the program Examples/Basic/plot2ddata.py to query the learner from -1 to 1 in steps of .001 in each dimension (1 million queries) and plot the learned model for each dataset.
- Write code to view the original data and the learned model in 3D.