Visualization and Navigation of Document Information Spaces Using a Self-Organizing Map

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Visualization and Navigation of Document Information Spaces Using a Self-Organizing Map. Daniel X. Pape Community Architectures for Network Information Systems [email protected] www.canis.uiuc.edu CSNA’98 6/18/98. Overview. Self-Organizing Map (SOM) Algorithm

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Visualization and Navigation of Document Information Spaces Using a Self-Organizing Map

Daniel X. Pape

Community Architectures for Network Information Systems

[email protected]

www.canis.uiuc.edu

CSNA’98

6/18/98

Overview
• Self-Organizing Map (SOM) Algorithm
• U-Matrix Algorithm for SOM Visualization
• Document Representation and Collection Examples
• Problems and Optimizations
• Future Work
Basic SOM Algorithm
• Input
• Number (n) of Feature Vectors (x)
• format:

vector name: a, b, c, d

• examples:

1: 0.1, 0.2, 0.3, 0.4

2: 0.2, 0.3, 0.3, 0.2

Basic SOM Algorithm
• Output
• Neural network Map of (M) Nodes
• Each node has an associated Weight Vector (m) of the same dimensionality as the input feature vectors
• Examples:

m1: 0.1, 0.2, 0.3, 0.4

m2: 0.2, 0.3, 0.3, 0.2

Basic SOM Algorithm
• Output (cont.)
• Nodes laid out in a grid:
Basic SOM Algorithm
• Other Parameters
• Number of timesteps (T)
• Learning Rate (eta)
Basic SOM Algorithm

SOM() {

foreach timestep t {

foreach feature vector fv {

wnode = find_winning_node(fv)

update_local_neighborhood(wnode)

}

}

}

find_winning_node() {

foreach node n {

compute distance of m to feature vector

}

return node with the smallest distance

}

update_local_neighborhood(wnode) {

foreach node n {

m = m + eta [x - m]

}

}

U-Matrix Visualization
• Provides a simple way to visualize cluster boundaries on the map
• Simple algorithm:
• for each node in the map, compute the average of the distances between its weight vector and those of its immediate neighbors
• Average distance is a measure of a node’s similarity between it and its neighbors
U-Matrix Visualization
• Interpretation
• one can encode the U-Matrix measurements as greyscale values in an image, or as altitudes on a terrain
• landscape that represents the document space: the valleys, or dark areas are the clusters of data, and the mountains, or light areas are the boundaries between the clusters
U-Matrix Visualization
• Example:
• dataset of random three dimensional points, arranged in four obvious clusters
U-Matrix Visualization

Four (color-coded) clusters of three-dimensional points

U-Matrix Visualization

Oblique projection of a terrain derived from the U-Matrix

U-Matrix Visualization

Terrain for a real document collection

Current Labeling Procedure
• Feature vectors are encoded as 0’s and 1’s
• Weight vectors have real values from 0 to 1
• Sort weight vector dimensions by element value
• dimension with greatest value is “best” noun phrase for that node
• Aggregate nodes with the same “best” noun phrase into groups
• 3D Space-Flight
Document Data
• Noun phrases extracted
• Set of unique noun phrases computed
• each noun phrase becomes a dimension of the data set
• Each document represented by a binary vector with a 1 or a 0 denoting the existence or absence of each noun phrase
Document Data
• Example:
• 10 total noun phrases:

alexander, king, macedonians, darius, philip, horse, soldiers, battle, army, death

• each element of the feature vector will be a 1 or a 0:
• 1: 1, 1, 0, 0, 1, 1, 0, 0, 0, 0
• 2: 0, 1, 0, 1, 0, 0, 1, 1, 1, 1
Problems
• As document sets get larger, the feature vectors get longer, use more memory, etc.
• Execution time grows to unrealistic lengths
Solutions?
• Need algorithm refinements for sparse feature vectors
• Need a faster way to do the find_winning_node() computation
• Need a better way to do the update_local_neighborhood() computation
Sparse Vector Optimization
• Intelligent support for sparse feature vectors
• saves on memory usage
• greatly improves speed of the weight vector update computation
Faster find_winning_node()
• SOM weight vectors become partially ordered very quickly
Faster find_winning_node()

U-Matrix Visualization of an Initial, Unordered SOM

Faster find_winning_node()

Partially Ordered SOM after 5 timesteps

Faster find_winning_node()
• Don’t do a global search for the winner
• Start search from last known winner position
• Pro:
• usually finds a new winner very quickly
• Con:
• this new search for a winner can sometimes get stuck in a local minima
Better Neighborhood Update
• Nodes get told to “update” quite often
• Weight vector is made public only during a find_winner() search
• With local find_winning_node() search, a lazy neighborhood weight vector update can be performed
Better Neighborhood Update
• Cache update requests
• each node will store the winning node and feature vector for each update request
• The node performs the update computations called for by the stored update requests only when asked for its weight vector
• Possible reduction of number of requests by averaging the feature vectors in the cache
Future Work
• Parallelization
• Label Problem
Label Problem
• Current Procedure not very good
• Cluster boundaries
• Term selection
Cluster Boundaries
• Image processing
• Geometric
Cluster Boundaries
• Image processing example:
Term Selection
• Too many unique noun phrases
• Too many dimensions in the feature vector data
• “Knee” of frequency curve