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%% Iris Clustering
% This example illustrates how a self-organizing map neural network can
% cluster iris flowers into classes topologically, providing insight
% into the types of flowers and a useful tool for further analysis.
% Copyright 2010-2012 The MathWorks, Inc.
%% The Problem: Cluster Iris Flowers
% In this example we attempt to build a neural network that clusters iris
% flowers into natural classes, such that similar classes are grouped
% together. Each iris is described by four features:
%
% * Sepal length in cm
% * Sepal width in cm
% * Petal length in cm
% * Petal width in cm
%
% This is an example of a clustering problem, where we would like to group
% samples into classes based on the similarity between samples. We would
% like to create a neural network which not only creates class definitions
% for the known inputs, but will let us classify unknown inputs
% accordingly.
%
%% Why Self-Organizing Map Neural Networks?
% Self-organizing maps (SOMs) are very good at creating classifications.
% Further, the classifications retain topological information about which
% classes are most similar to others. Self-organizing maps can be created
% with any desired level of detail. They are particularly well suited for
% clustering data in many dimensions and with complexly shaped and
% connected feature spaces. They are well suited to cluster iris flowers.
%
% The four flower attributes will act as inputs to the SOM, which will
% map them onto a 2-dimensional layer of neurons.
%
%% Preparing the Data
% Data for clustering problems are set up for a SOM by organizing the data
% into an input matrix X.
%
% Each ith column of the input matrix will have four elements
% representing the four measurements taken on a single flower.
%
% Here such a dataset is loaded.
x = iris_dataset;
%%
% We can view the size of inputs X.
%
% Note that X has 150 columns. These represent 150 sets of iris flower
% attributes. It has four rows, for the four measurements.
size(x)
%% Clustering with a Neural Network
% The next step is to create a neural network that will learn to cluster.
%
% *selforgmap* creates self-organizing maps for classify samples with as
% as much detailed as desired by selecting the number of neurons in each
% dimension of the layer.
%
% We will try a 2-dimension layer of 64 neurons arranged in an 8x8
% hexagonal grid for this example. In general, greater detail is achieved
% with more neurons, and more dimensions allows for the modelling the
% topology of more complex feature spaces.
%
% The input size is 0 because the network has not yet been configured
% to match our input data. This will happen when the network
% is trained.
net = selforgmap([8 8]);
view(net)
%%
% Now the network is ready to be optimized with *train*.
%
% The NN Training Tool shows the network being trained and the algorithms
% used to train it. It also displays the training state during training
% and the criteria which stopped training will be highlighted in green.
%
% The buttons at the bottom open useful plots which can be opened during
% and after training. Links next to the algorithm names and plot buttons
% open documentation on those subjects.
[net,tr] = train(net,x);
nntraintool
%%
% Here the self-organizing map is used to compute the class vectors of
% each of the training inputs. These classfications cover the feature
% space populated by the known flowers, and can now be used to classify
% new flowers accordingly. The network output will be a 64x150 matrix,
% where each ith column represents the jth cluster for each ith input
% vector with a 1 in its jth element.
%
% The function *vec2ind* returns the index of the neuron with an output
% of 1, for each vector. The indices will range between 1 and 64 for
% the 64 clusters represented by the 64 neurons.
y = net(x);
cluster_index = vec2ind(y);
%%
% *plotsomtop* plots the self-organizing maps topology of 64 neurons
% positioned in an 8x8 hexagonal grid. Each neuron has learned to
% represent a different class of flower, with adjecent neurons typically
% representing similar classes.
plotsomtop(net)
%%
% *plotsomhits* calculates the classes for each flower and shows the number
% of flowers in each class. Areas of neurons with large numbers of hits
% indicate classes representing similar highly populated regions of the
% feature space. Wheras areas with few hits indicate sparsely populated
% regions of the feature space.
plotsomhits(net,x)
%%
% *plotsomnc* shows the neuron neighbor connections. Neighbors typically
% classify similar samples.
plotsomnc(net)
%%
% *plotsomnd* shows how distant (in terms of Euclidian distance) each
% neuron's class is from its neighbors. Connections which are bright
% indicate highly connected areas of the input space. While dark
% connections indicate classes representing regions of the feature space
% which are far apart, with few or no flowers between them.
%
% Long borders of dark connections separating large regions of the input
% space indicate that the classes on either side of the border represent
% flowers with very different features.
plotsomnd(net)
%%
% *plotsomplanes* shows a weight plane for each of the four input features.
% They are visualizations of the weights that connect each input to each
% of the 64 neurons in the 8x8 hexagonal grid. Darker colors represent
% larger weights. If two inputs have similar weight planes (their color
% gradients may be the same or in reverse) it indicates they are highly
% correlated.
plotsomplanes(net)
%%
% This example illustrated how to design a neural network that clusters
% iris flowers based on four of their characteristics.
%
% Explore other examples and the documentation for more insight into neural
% networks and their applications.