文档介绍：Pattern Recognition
&
artificial Intelligence
Lecture 11: 聚类算法(七)
1
Artificial works
Biological and petitive petitive Learning
anizing Map (SOM)
Adaptive Resonance Theory (ART)
Relationship between K-means, FCM petitive work
Model-based clustering (2)
2
Biological and works
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Biology:
Biological and works
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Artificial
The artificial work is a group of anized in several layers:
Input layer: receives inputs from sources external to work;
Output layer: generates outputs to the external world.
Hidden layer(s): layers in between of the input and output layers, not visible from outside work.
Learning laws: mathematical rules for modifying the weights of work iteratively according the inputs (and outputs if the learning is supervised).
Biological and works
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Mathematical Explanation
A neuron is modeled mathematically as the following:
Activation - input signal:
input to the ith node is a weighted sum of all inputs:
Where is the input signal from the jth node, is the synaptic connectivity between the jth node and the ith node.
Biological and works
6
Mathematical Explanation
Output signal: The output of the ith node is a function of input
Where is an activation function which can be a sigmoid function, as plotted in the figure below. This function can be either one-sided (top) or two-sided (bottom)
:
Biological and works
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Mathematical Explanation
One-sided:
Two-sided:
where is a parameter that controls the slop of Specially, when es linear, but when es a threshold function:
Biological and works
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Mathematical Explanation
Curve of Sigmoid function
Competitive works
9
Competitive learning
Competitive learning is a typical unsupervised work, similar to the statistical clustering analysis methods (k-means). The purpose is to discover groups/posed of similar patterns represented by vectors in the n-D space.
petitive work has two layers.
Competitive works
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Competitive learning
the input posed of nodes to which an input pattern is