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Lecture 36

Classifiers

DATA 8

Spring 2022

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Announcements

  • Homework 11 due tomorrow (04/21)
    • Turn in tonight for a bonus point
  • Project 3 Checkpoint due Friday (04/22)
    • Entire project due Friday (04/29)

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Classifiers

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Nearest Neighbor Classifier

NN Classifier

Use the label of the most similar training example

Attributes of an example

Predicted label of the example

Population

Sample

Labels

Training

Set

Test

Set

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The Google Science Fair

  • Brittany Wenger, a 17-year-old high school student in 2012
  • Won by building a breast cancer classifier with 99% accuracy

(Demo)

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Distance

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Pythagoras’ Formula

(x₀, y₀)

(x₁, y₁)

y₀ - y₁

x₀ - x₁

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Distance Between Two Points

  • Two attributes x and y:
  • Three attributes x, y, and z:
  • and so on ...

(Demo)

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Rows

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Rows of Tables

Each row contains all the data for one individual

  • t.row(i) evaluates to ith row of table t
  • t.row(i).item(j)is the value of column j in row i
  • If all values are numbers, then np.array(t.row(i)) evaluates to an array of all the numbers in the row.
  • To consider each row individually, use�for row in t.rows:� ... row.item(j) …
  • t.exclude(i)evaluates to the table t without its ith row

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Nearest Neighbors

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Finding the k Nearest Neighbors

To find the k nearest neighbors of an example:

  • Find the distance between the example and each example in the training set
  • Augment the training data table with a column containing all the distances
  • Sort the augmented table in increasing order of the distances
  • Take the top k rows of the sorted table

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The Classifier

To classify a point:

​

  • Find its k nearest neighbors

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  • Take a majority vote of the k nearest neighbors to see which of the two classes appears more often

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  • Assign the point to the class that wins the majority vote

(Demo)

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Evaluation

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Accuracy of a Classifier

The accuracy of a classifier on a labeled data set is the proportion of examples that are labeled correctly

Need to compare classifier predictions to true labels

If the labeled data set is sampled at random from a population, then we can infer accuracy on that population

Sample

Labels

Training

Set

Test

Set

(Demo)

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Before Classifying

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Dog or Wolf?

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Start with a Representative Sample

  • Both the training and test sets must accurately represent the population on which you use your classifier

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  • Overfitting happens when a classifier does very well on the training set, but can’t do as well on the test set

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Standardize if Necessary

Chronic Kidney Disease data set

  • If the attributes are on very different numerical scales, distance can be affected
  • In such a situation, it is a good idea to convert all the variables to standard units

(Demo)