Classification

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Classification
Categorization is the process in which ideas and
objects are recognized, differentiated and
understood. Categorization implies that objects
are grouped into categories, usually for some
specific purpose. Ideally, a category illuminates
a relationship between the subjects and objects
of knowledge. Categorization is fundamental in
language, prediction, inference, decision making
and in all kinds of interaction with the
environment. Statistical classification is a
procedure in which individual items are placed
into groups based on quantitative information on
one or more characteristics inherent in the items
(referred to as traits, variables, characters,
etc) and based on a training set of previously
labeled items.
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The essential problem
categorical and topographic
radar
Rasters are better. Each cell is a sample point
with n layers of attributes.
hyperspectral
classification
multispectral
thematic map
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Methods

• Rule-based (overlay analysis)
• Optimization Methods
• Neutral Networks
• Genetic Algorithms
• Fuzzy Logic
• Statistical Methods
• Clustering
• Principal Component Analysis (Ordination
  Analysis)
• Regression (ordinal logistic regression)
• Classification and Regression Trees (CART)
• Bayesian Methods
• Maximum Likelihood
• Spatio-Temporal Analysis
• Spatio-Temporal Clustering

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Image Classification
Legend
Unsupervised
Water/Shadow/Dark Rock
Ponderosa Pine/Pinyon-Juniper
Black Mesa
Pinyon-Juniper (Mixed)
Mixed Grassland w/Scrub
Canyon de Chelly
Mixed Scrub w/Grass
Mixed Scrub (Blackbrush/Shadscale)
Dark Volcanic Rock w/Mixed Pinyon
Unsupervised Classification is a process whereby
numerical operations are performed that search
for natural groupings of the spectral properties
of pixels. (Jensen. Introductory Digital Image
Processing. NJ Prentice Hall. 1996.)
Painted Desert
HopiButtes
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Clustering

• Clustering is the classification of objects into
  different groups, or more precisely, the
  partitioning of a data set into subsets
  (clusters), so that the data in each subset
  (ideally) share some common trait often proximity
  according to some defined distance measure.
• An important step in any clustering is to select
  a distance measure, which will determine how the
  similarity of two elements is calculated. This
  will influence the shape of the clusters, as some
  elements may be close to one another according to
  one distance and further away according to
  another.
• Many methods (Isodata, K-mean, Fuzzy c-means,
  Hierarchical)
• The main requirements that a clustering algorithm
  should satisfy are
• scalability
• dealing with different types of attributes
• discovering clusters with arbitrary shape
• minimal requirements for domain knowledge to
  determine input parameters
• ability to deal with noise and outliers
• insensitivity to order of input records
• high dimensionality
• interpretability and usability.

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Clustering

• Potential problems with clustering are
• current clustering techniques do not address all
  the requirements adequately (and concurrently)
• dealing with large number of dimensions and large
  number of data items can be problematic
• the effectiveness of the method depends on the
  definition of distance (for distance-based
  clustering)
• if an obvious distance measure doesnt exist we
  must define it, which is not always easy,
  especially in multi-dimensional spaces
• the result of the clustering algorithm (that in
  many cases can be arbitrary itself) can be
  interpreted in different ways.

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Principal Component Analysis (PCA)

• Numerical method
• Dimensionality reduction technique
• Primarily for visualization of arrays/samples
• Unsupervised method used to explore the
  intrinsic variability of the data
• Performs a rotation of the data that maximizes
  the variance in the new axes

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PCA

• Projects high dimensional data into a low
  dimensional sub-space (visualized in 2-3 dims)
• Often captures much of the total data variation
  in a few dimensions (lt 5)
• Principal Components
• 1st Principal component (PC1)
• Direction along which there is greatest variation
• 2nd Principal component (PC2)
• Direction with maximum variation left in data,
  orthogonal to PC1

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PCA
Second Principal Component
First Principal Component
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PCA
Second Principal Component
First Principal Component
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Distance Measurement

• An important component of a clustering algorithm
  is the distance measure between data points.
• If the components of the data instance vectors
  are all in the same physical units then it is
  possible that the simple Euclidean distance
  metric is sufficient to successfully group
  similar data instances. This is what is done in
  remote sensing.
• However, even in this case the Euclidean distance
  can sometimes be misleading. Below is an example
  of the width and height measurements of an
  object. As the figure shows, different scalings
  can lead to different clusterings.

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K-Means Clustering

• K-means is one of the simplest unsupervised
  learning algorithms to solve a clustering
  problem. The procedure follows a simple and easy
  way to classify a given data set through a
  certain number of clusters (assume k clusters)
  fixed a priori. The main idea is to define k
  centroids, one for each cluster.
• Procedure (for 3 clusters)
• Make initial guesses for the means m1, m2, ...,
  mk
• Until there are no changes in any mean
• Use the estimated means to classify the samples
  into clusters
• For i from 1 to k
• Replace mi with the mean of all of the samples
  for cluster i
• end_for
• end_until

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Classification of watersheds based on abiotic
factors
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