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Classification. and application in Remote Sensing . Overview. Introduction to classification problem an application of classification in remote sensing: vegetation classification band selection multi-class classification. Introduction.

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Presentation Transcript
classification

Classification

and application in Remote Sensing

overview
Overview
  • Introduction to classification problem
  • an application of classification in remote sensing: vegetation classification
    • band selection
    • multi-class classification
introduction
Introduction
  • make program that automatically recognize handwritten numbers:
introduction classification problem
Introduction classification problem
  • from raw data to decisions
  • learn from examples and generalize
  • Given: Training examples (x, f(x)) for some unknown function f.Find: A good approximation to f.
examples
Examples
  • Handwriting recognition
    • x: data from pen motion
    • f(x): letter of the alphabet
  • Disease Diagnosis
    • x: properties of patient (symptoms, lab tests)
    • f(x): disease (or maybe, recommended therapy)
  • Face Recognition
    • x: bitmap picture of person’s face
    • f(x): name of person
  • Spam Detection
    • x: email message
    • f(x): spam or not spam
steps for building a classifier
Steps for building a classifier
  • data acquisition / labeling (ground truth)
  • preprocessing
  • feature selection / feature extraction
  • classification (learning/testing)
  • post-processing
  • decision
data acquisition
Data acquisition
  • acquiring the data and labeling
  • data is independently randomly sample according to unknown distribution P(x,y)
pre processing
Pre-processing
  • e.g. image processing:
    • histogram equalization,
    • filtering
    • segmentation
  • data normalization
feature selection extraction
Feature selection/extraction
  • This is generally the most important step
  • conveying the information in the data to classifier
  • the number of features:
    • should be high: more info is better
    • should be low: curse of dimensionality
  • will include prior knowledge of problem
  • in part manual, in part automatic
feature selection extraction1
Feature selection/extraction
  • User knowledge
  • Automatic:
    • PCA: reduce number of feature by decorrelation
    • look which feature give best classification result
feature scatterplot

K=3

Class A

Class B

value feature 2

Class C

value feature 1

Feature scatterplot
classification1
Classification
  • learn from the features and generalize
  • learning algorithm analyzes the examples and produces a classifier f
  • given a new data point (x,y), the classifier is given x and predicts ŷ = f(x)
  • the loss L(ŷ,y) is then measured
  • goal of the learning algorithm: Find the f that minimizes the expected loss
classification bayesian decision theory
Classification: Bayesian decision theory
  • fundamental statistical approach to the problem of pattern classification
  • assuming that the descision problem is posed in probabilistic terms
  • using P(y|x) posterior probability, make classification (Maximum aposteriori classification)
classification2
Classification
  • need to estimate p(y) and p(x|y), prior and class-conditional probability density using only the data: density estimation.
  • often not feasible: too little data in to high-dimensional space:
    • assume simple parametric probability model (normal)
    • non-parametric
    • directly find discriminant function
post processing
Post-processing
  • include context
    • e.g. in images, signals
  • integrate multiple classifiers
decision
Decision
  • minimize risk, considering cost of misclassification : when unsure, select class of minimal cost of error.
no free lunch theorem
no free lunch theorem
  • don’t wait until the a “generic” best classifier is here!
remote sensing acquisition
Remote Sensing : acquisition
  • image are acquired from air or space.
slide27

Westhoek

Brugge

Hyperspectral sensor:

AISA Eagle (July 2004): 400-900nm @1m resolution

feature extraction
Feature extraction
  • here: exploratory use: Automatically look for relevant features
    • which spectral bands (wavelength) should be measured at what which spectral resolution (width) for my application.
    • results can be used for classification, sensor design or interpretation
feature extraction band selection
Feature extraction: Band Selection

With spectral response function:

class separation criterion
Class Separation Criterion

two class Bhattacharyya bound

multi-class criterion

optimization
Optimization

Minimize

Gradient descent is possible,

but local minima prevent it from giving good optimal values.

Therefore, we use global optimization : Simulated Annealing.

multi class classification
Multi-class Classification
  • Linear Multi-class Classifier
  • Combining Binary Classifiers
    • One against all: K-1 classifiers
    • One against one: K(K-1)/2 classifiers
combining binary classifiers
Combining Binary Classifiers
  • Maximum Voting: 4 class example

Votes:

1 : 0

2 : 2

3 : 1

4 : 3 (Winner)

problem with max voting
Problem with max voting
  • No Probabilities, just class labels
    • Hard classification
  • Probabilities are usefull for
    • spectral unmixing
    • post-processing
combining binary classifiers coupling probabilities
Combining Binary Classifiers :Coupling Probabilities
  • Look for class probabilities pi:

with rij: probability class ωifor binary classifier i-j

    • K-1 free parameters and K(K-1)/2 constraints !
  • Hastie and Tibshirani: find approximations
    • minimizing Kullback-Leibler distance
remote sensing post processing
Remote Sensing: post-processing
  • use contextual information to “adjust” classification.
  • look a classes of neighboring pixels and probabilities, if necessary adjust pixel class
pixel mixing
Pixel mixing

GREEN GRASS

DRY GRASS

MOSS

SAND

unmixing with sand

Sparse Moss

Moss

Sparse Grass

Grass

Sparse Marram

Marram

Unmixing with sand
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