Matlab : Can SOM and kmeans be applied to binarize time series data?

I found a similar question asked here Determining cluster membership in SOM (Self Organizing Map) for time series data

and I want to learn how to apply self organizing map in binarizing or assigning more than 2 kinds of symbols to data.

For example, let data = rand(100,1) In general, I would be doing data_quantized = 2*(data>=0.5)-1 to get a binary valued transformed series where the threshold 0.5 is assumed and fixed. It may have been possible to quantize data using more that 2 symbols. Can kmeans or SOM be applied to do this task? What should be the input and output if I were to use SOM in quantizing the data?

X = {x_i(t)} for i =1:N and t = 1:T number of time series, N represents the number of components/ variables. To get the quantized value for any vector x_i is to use the value of the BMU, which is nearest. The quantization error will be the Euclidean norm of the difference of the input vector and the best-matching model. Then a new time series is compared / matched using the symbols representation of the time series. WOuld BMU be a scalar valued number or a vector of floating point numbers? It is very hard to picturize what SOM is doing.

Matlab implementation https://www.mathworks.com/matlabcentral/fileexchange/39930-self-organizing-map-simple-demonstration

I cannot understand how to work for time series in quantization. Assuming N = 1, a 1 dimensional array/ vector of elements obtained from a white noise process, how can I quantize / partition this data using self organizing map?

http://www.mathworks.com/help/nnet/ug/cluster-with-self-organizing-map-neural-network.html

is provided by the Matlab but it works for N dimensional data but I have a 1 dimensional data containing 1000 data points (t =1,...,1000).

It shall be of immense help if a toy example is provided which explain how a time series can be quantized into multiple levels. Let, trainingData = x_i;

T = 1000;
N = 1;
x_i = rand(T,N)  ;

How can I apply the code below of SOM so that the numerical valued data can be represented by symbols such as 1,2,3 i.e clustered using 3 symbols? A data point (scalar valued) can be either represented by symbol 1 or 2 or 3.

function som = SOMSimple(nfeatures, ndim, nepochs, ntrainingvectors, eta0, etadecay, sgm0, sgmdecay, showMode)
%SOMSimple Simple demonstration of a Self-Organizing Map that was proposed by Kohonen.
%   sommap = SOMSimple(nfeatures, ndim, nepochs, ntrainingvectors, eta0, neta, sgm0, nsgm, showMode) 
%   trains a self-organizing map with the following parameters
%       nfeatures        - dimension size of the training feature vectors
%       ndim             - width of a square SOM map
%       nepochs          - number of epochs used for training
%       ntrainingvectors - number of training vectors that are randomly generated
%       eta0             - initial learning rate
%       etadecay         - exponential decay rate of the learning rate
%       sgm0             - initial variance of a Gaussian function that
%                          is used to determine the neighbours of the best 
%                          matching unit (BMU)
%       sgmdecay         - exponential decay rate of the Gaussian variance 
%       showMode         - 0: do not show output, 
%                          1: show the initially randomly generated SOM map 
%                             and the trained SOM map,
%                          2: show the trained SOM map after each update
%
%   For example: A demonstration of an SOM map that is trained by RGB values
%           
%       som = SOMSimple(1,60,10,100,0.1,0.05,20,0.05,2);
%       % It uses:
%       %   1    : dimensions for training vectors
%       %   60x60: neurons
%       %   10   : epochs
%       %   100  : training vectors
%       %   0.1  : initial learning rate
%       %   0.05 : exponential decay rate of the learning rate
%       %   20   : initial Gaussian variance
%       %   0.05 : exponential decay rate of the Gaussian variance
%       %   2    : Display the som map after every update

nrows = ndim;
ncols = ndim;
nfeatures = 1;
som = rand(nrows,ncols,nfeatures);


% Generate random training data
    x_i = trainingData;

% Generate coordinate system
[x y] = meshgrid(1:ncols,1:nrows);

for t = 1:nepochs    
    % Compute the learning rate for the current epoch
    eta = eta0 * exp(-t*etadecay);        

    % Compute the variance of the Gaussian (Neighbourhood) function for the ucrrent epoch
    sgm = sgm0 * exp(-t*sgmdecay);

    % Consider the width of the Gaussian function as 3 sigma
    width = ceil(sgm*3);        

    for ntraining = 1:ntrainingvectors
        % Get current training vector
        trainingVector = trainingData(ntraining,:);

        % Compute the Euclidean distance between the training vector and
        % each neuron in the SOM map
        dist = getEuclideanDistance(trainingVector, som, nrows, ncols, nfeatures);

        % Find the best matching unit (bmu)
        [~, bmuindex] = min(dist);

        % transform the bmu index into 2D
        [bmurow bmucol] = ind2sub([nrows ncols],bmuindex);        

        % Generate a Gaussian function centered on the location of the bmu
        g = exp(-(((x - bmucol).^2) + ((y - bmurow).^2)) / (2*sgm*sgm));

        % Determine the boundary of the local neighbourhood
        fromrow = max(1,bmurow - width);
        torow   = min(bmurow + width,nrows);
        fromcol = max(1,bmucol - width);
        tocol   = min(bmucol + width,ncols);

        % Get the neighbouring neurons and determine the size of the neighbourhood
        neighbourNeurons = som(fromrow:torow,fromcol:tocol,:);
        sz = size(neighbourNeurons);

        % Transform the training vector and the Gaussian function into 
        % multi-dimensional to facilitate the computation of the neuron weights update
        T = reshape(repmat(trainingVector,sz(1)*sz(2),1),sz(1),sz(2),nfeatures);                   
        G = repmat(g(fromrow:torow,fromcol:tocol),[1 1 nfeatures]);

        % Update the weights of the neurons that are in the neighbourhood of the bmu
        neighbourNeurons = neighbourNeurons + eta .* G .* (T - neighbourNeurons);

        % Put the new weights of the BMU neighbouring neurons back to the
        % entire SOM map
        som(fromrow:torow,fromcol:tocol,:) = neighbourNeurons;


    end
end


function ed = getEuclideanDistance(trainingVector, sommap, nrows, ncols, nfeatures)

% Transform the 3D representation of neurons into 2D
neuronList = reshape(sommap,nrows*ncols,nfeatures);               

% Initialize Euclidean Distance
ed = 0;
for n = 1:size(neuronList,2)
    ed = ed + (trainingVector(n)-neuronList(:,n)).^2;
end
ed = sqrt(ed);

I don't know that I might be misunderstanding your question, but from what I understand it is really quite straight forward, both with kmeans and with Matlab's own selforgmap. The implementation you have posted for SOMSimple I cannot really comment on.

Let's take your initial example:

rng(1337);
T = 1000;
x_i = rand(1,T); %rowvector for convenience

Assuming you want to quantize to three symbols, your manual version could be:

nsyms = 3;
symsthresh = [1:-1/nsyms:1/nsyms];
x_i_q = zeros(size(x_i));

for i=1:nsyms
    x_i_q(x_i<=symsthresh(i)) = i;
end

Using Matlab's own selforgmap you can achieve a similar result:

net = selforgmap(nsyms);
net.trainParam.showWindow = false;
net = train(net,x_i);
net(x_i);
y = net(x_i);
classes = vec2ind(y);

Lastly, the same can be done straightforwardly with kmeans:

clusters = kmeans(x_i',nsyms)';