Lecture 5

Readings

  • in Witten: Chapter 3
  • Extra: linear algebra

Additional resources

  • Data Mining: Concepts and Techniques by Jiawei Han, Micheline Kamber. Jian Pei
  • Weka Manual. P.34, you can output a jpeg, png or eps file.

Knowledge Representation

  • How does a computer program represent knowledge?
    There are two types of representations: declarative and procedural. A set of rules is an example of declarative.

  • Can a program create a new concept or can it only represent concepts that you have programmed or presented as data?
  • What is a linear model? Need numeric data. Look at P. 63
    there is a straight line that separates Iris setosa and versicolor. One such line is represented by a linear equation: 

    2 - 0.5*Petal_Length - 0.8*Petal_Width = 0

    There are many possible lines.
    On one side of the line 2 – 0.5*Petal_Length – 0.8*Petal_Width > 0,
    on the other side < 0
    What happens if you only use one attribute or the wrong two attributes?

  • What is a decision tree? There are internal nodes and leaf nodes.
  • Decision trees: given 2 attributes, outlook {sunny, overcast, rainy}
    and windy {yes, no}, how many decision trees can you make?

  • Binary search tree -> k-D trees. This extends to decision trees 
       suppose you want to be able to search based on either of two keys
    K1 and K2.  The branching at even levels could
    be done with K1 and odd levels with K2
  • Ball trees (Chapter 4)

More Advanced Concepts

  • Defining the distance between two instances. This is important
    for clustering and for classification algorithms.
    There are many possibilities. They are based on a few basic abstract properties

    1. distances are ≥ 0
    2. distance is 0 if and only if the two instances are identical
    3. symmetry
    4. triangle inequality: the distance from a to b + distance from
      b to c ≤ distance from a to c.
  • there are many measures that satisfy these properties, e.g. Euclidean distance, but this only works for numeric attributes.
  • Distance works for boolean attributes: the proportion of attributes that are the same.
  • Another approach is similarity using correlation. The correlation coefficient is given by 
     ∑  (X - Xbar) * (Y - Ybar) 
 --------------------------
    sd(X) * sd(Y)
  • In general, there may be too many attributes. We may need to reduce the
    number. Principal components is a way to do this.

Filtering data

  • A filter can be almost any function that transforms the input
  • There are different types of filters: supervised and unsupervised, attribute filters,
    instance filters.

  • Examples: 
      StratifiedRemoveFolds (supervised, instance) -- why is this supervised?
  SpreadSubSample (supervised, instance)