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Transcript 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.
The essential problem
Rasters are better.
Each cell is a sample
point with n layers of
thematic map
• Rule-based (overlay analysis)
• Optimization Methods
– Neutral Networks
– Genetic Algorithms
– Fuzzy Logic
• Statistical Methods
Principal Component Analysis (Ordination Analysis)
Regression (ordinal logistic regression)
Classification and Regression Trees (CART)
Bayesian Methods
Maximum Likelihood
• Spatio-Temporal Analysis
– Spatio-Temporal Clustering
Image Classification
Water/Shadow/Dark Rock
Ponderosa Pine/Pinyon-Juniper
Pinyon-Juniper (Mixed)
Mixed Grassland w/Scrub
Mixed Scrub w/Grass
Mixed Scrub
Dark Volcanic Rock
w/Mixed Pinyon
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.)
• 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:
dealing with different types of attributes;
discovering clusters with arbitrary shape;
minimal requirements for domain knowledge to determine input
ability to deal with noise and outliers;
insensitivity to order of input records;
high dimensionality;
interpretability and usability.
• 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 doesn’t 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.
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
• 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 (< 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
Second Principal Component
First Principal Component
Second Principal Component
First Principal Component
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.
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
Classification of watersheds based on abiotic factors