Classification

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Classification

• Slides by Greg Grudic, CSCI 3202Fall 2007
• Modified by Longin Jan Latecki

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Why Classification?
Signals
Uncertainty
Classification
Not typically addressed in CS
Symbols
(The Grounding Problem)
Agent
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Identifying (and Navigating) Paths
Data
Data
Construct a Classifier
Classifier
Data
Path labeled Image
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This Class Classification Models

• Collect Training data
• Construct Model happy F(feature space)
• Make a prediction

High Dimensional Feature (input) Space
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Goal of Classification

• Give Training Data
• GOAL
• Construct a model
• Model Property Minimum error rate on future
  (unseen) data

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Measuring Model Accuracy Classification

• Assume a set of data
• Classification accuracy

Where
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Binary Classification

• A binary classifier is a mapping from a set of d
  inputs to a single output which can take on one
  of TWO values (e.g. path/no path)
• In the most general setting
• Specifying the output classes as -1 and 1 is
  arbitrary!
• Often done as a mathematical convenience

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A Binary Classifier
Given learning data
A model is constructed
Classification Model
Not in learning set!
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Classification Learning Data

Example 1 0.95013 0.58279 1
Example 2 0.23114 0.4235 -1
Example 3 0.8913 0.43291 1
Example 4 0.018504 0.76037 -1

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The Learning Data

• Matrix Representation of N learning examples of d
  dimensional inputs

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Graphical Representation of 2D Classification
Training Data
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Linear Separating Hyper-Planes Discriminative
Classifiers
How many lines can separate these points?
NO!
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Is this Data Linearly Separable?
NO!
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Is this Data Linearly Separable?
YES!
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Is this Data Linearly Separable?
NO!
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Is this Data Linearly Separable?
YES!