Classification Slides by Greg Grudic, CSCI 3202 Fall 2007

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Presentation transcript:

Classification Slides by Greg Grudic, CSCI 3202 Fall 2007 Modified by Longin Jan Latecki Greg Grudic Intro AI

Why Classification? Uncertainty world Signals Sensing Actions Computation Not typically addressed in CS State Symbols (The Grounding Problem) Decisions/Planning Agent Greg Grudic Introduction to AI

Identifying (and Navigating) Paths Non-path Data Data Construct a Classifier Classifier Data Path labeled Image 12/5/2018 Intro AI

This Class: Classification Models Collect Training data Construct Model: happy = F(feature space) Make a prediction High Dimensional Feature (input) Space Greg Grudic Intro AI

Goal of Classification Give Training Data GOAL: Construct a model Model Property: Minimum error rate on future (unseen) data: Greg Grudic Intro AI

Measuring Model Accuracy: Classification Assume a set of data Classification accuracy Where Greg Grudic Intro AI

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 Greg Grudic Intro AI

A Binary Classifier Given learning data: A model is constructed: Classification Model Not in learning set! Greg Grudic Intro AI

Classification Learning Data… Example 1 0.95013 0.58279 1 Example 2 0.23114 0.4235 -1 Example 3 0.8913 0.43291 Example 4 0.018504 0.76037 … Greg Grudic Intro AI

The Learning Data Matrix Representation of N learning examples of d dimensional inputs Greg Grudic Intro AI

Graphical Representation of 2D Classification Training Data Greg Grudic Intro AI

Linear Separating Hyper-Planes: Discriminative Classifiers How many lines can separate these points? NO! Greg Grudic Intro AI

Greg Grudic Intro AI

Greg Grudic Intro AI

Greg Grudic Intro AI

Greg Grudic Intro AI

Is this Data Linearly Separable? NO! Greg Grudic Intro AI

Is this Data Linearly Separable? YES! Greg Grudic Intro AI

Is this Data Linearly Separable? NO! Greg Grudic Intro AI

Is this Data Linearly Separable? YES! Greg Grudic Intro AI