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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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and application in Remote Sensing

  • Introduction to classification problem
  • an application of classification in remote sensing: vegetation classification
    • band selection
    • multi-class classification
  • 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.
  • 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
  • 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


Class A

Class B

value feature 2

Class C

value feature 1

Feature scatterplot
  • 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)
  • 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
  • include context
    • e.g. in images, signals
  • integrate multiple classifiers
  • 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.



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



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


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





unmixing with sand

Sparse Moss


Sparse Grass


Sparse Marram


Unmixing with sand