SOMTrain Create (train) a Self-Organising Map

SOMTrain.kr(bufnum, inputdata, netsize, numdims, traindur, nhood, gate, initweight)

This UGen trains a self-organising map (a well-known type of neural net), which is a system which learns to map a high-dimensional feed of input data onto a lower-dimensional array of "nodes". The neural net is stored in a Buffer. Once trained, the net can be analysed or can be used to transform other incoming data (using SOMRd).

- bufnum - A reference to the buffer where the map will be created. Initialising the map is up to you (see below).

- inputdata - An Array of the input signals for the net to learn.

- netsize - The size of the neural net along one dimension.

- numdims - The dimensionality of the neural net. Choose from 1, 2, 3, or 4.

- traindur - The length of the training period; the number of data frames that will come in before the net gradually "freezes" into its final state

- nhood - The initial size of the neighbourhood used in training. (The size always shrinks to zero as the training progresses.) The size is expressed as a fraction of netsize. Default is 0.5, and you probably don't need to change it.

- gate - A simple on-or-off control. When off (gate<=0) the incoming data is ignored.

- initweight - How heavily the algorithm weights the data points at first (the weighting always tails off to zero as the training progresses, in a reciprocal curve). Default is 1, and you usually don't need to change this.

The UGen outputs an array of three values: the number of data points still to come in before training finishes; the "reconstruction error" of the single data point that has most recently been input (the squared-distance between it and the node nearest it); and the frame index of the most recent matching node. The "reconstruction error" will vary a lot but should in general decrease as the net comes closer and closer to mapping the data well. The frame index gives a direct index into the Buffer, and can be converted to a multidimensional location in the SOM structure using SOMRd.bufIndexToCoords.

Note: this UGen does not cope well if the buffer is freed or changed during running. For efficiency purposes, it doesn't keep checking the buffer while running; so you should avoid changing the buffer while the training is running.

BUFFER SIZE AND NUMBER OF NODES/DIMENSIONS:

The number of nodes in the net is defined by netsize AND numdims.

If the netsize is 10 and the numdims is 2, the actual number of nodes is 10 x 10 = 100.

Or if numdims is 3, the number of nodes is 10 x 10 x 10 = 1000.

The buffer must contain the same number of frames as the number of nodes; and it must have the same number of channels as the inputdata array. The SOMTrain class provides a convenience function for allocating a buffer of the right size:

~asuitablebuffer = SOMTrain.allocBuf(s, netsize, numdims, numinputdims); // Calls Buffer.alloc on your behalf

INITIALISING THE MAP

The values held by the SOM nodes must usually be initialised to some state before the training begins. In the literature on SOMs there are a couple of common options such as random intialisation, or initialisation using the principal components of the input data. It's up to you - since the map is just a regular Buffer object, you can use Buffer's loadCollection methods (etc) to fill the map in any way. However, the SOMTrain class provides a couple of conveniences:

SOMTrain.initBufRand(b); // Each node gets an independent randomly-distributed co-ordinate (i.e. ignores where its neighbours might be)

SOMTrain.initBufGrid(b, netsize, numdims, spinmatrix); // The nodes are initialised as a grid, oriented according to the supplied rotation matrix (nested array, size [numinputdims][numdims])

SOMTrain.initBufGridRand(b, netsize, numdims); // The nodes are initialised as a grid, randomly oriented in the input space

The first of these options is simple but not recommended: starting with a completely random arrangement of nodes is quite likely to lead to a resulting map with "twists" in it, which may be an unhelpful local-minimum solution.

Examples

An SOM will try to fit a smooth-ish surface to the given data, so as a test case let's create a single sine-wave undulation in a Buffer, and see if a one-dimensional SOM can fit nicely to that sinewave. (For higher dimension examples see SOMTrain_2D_example, SOMTrain_3D_example)

s.boot;

~numnodes = 20;

~traindur = 10000;

// First create the data

~dataspace = Buffer.alloc(s, s.sampleRate); // Let's have 1 second of data

~dataspace.sine1([1], true, false);

~dataspace.plot;

// Allocate space for the SOM, and initialise it

~som = SOMTrain.allocBuf(s, ~numnodes, 1, 2);

// Typically wewouldn't recommend initBufRand, so let's use initBufGridRand:

SOMTrain.initBufGridRand(~som, ~numnodes, 1, [1,0], 1.5);

~som.plot(minval:nil.dup, maxval: nil.dup); // Quick peek at how the SOM nodes are initially positioned

// Also, just for demonstration purposes, we're going to write the error values to a buffer so we can see how they evolve

~errorvals = Buffer.alloc(s, ~traindur);

// Now train the SOM. To train it with data "randomly sampled" from the data buffer, we just wiggle the phase around and feed [phase, val] to the SOM.

(

x = {

var phase, val, remain, err, loc, trig;

trig = 1;

phase = WhiteNoise.kr.range(0, ~dataspace.numFrames-1);

val = BufRd.kr(1, ~dataspace, phase, 1);

phase.poll(trig, label: "phase");

val.poll(trig, label: "val");

// Note: phase is rescaled to 0--2 range here, so it can be similar range to other dimension

# remain, err, loc = SOMTrain.kr(~som, [phase*2/s.sampleRate, val], ~numnodes, 1, ~traindur, nhood: 0.75, gate: trig);

remain.poll(trig, label: "remain");

err.poll(trig, label: "err");

loc.poll(trig, label: "wrote at frame index");

BufWr.kr(err.sqrt, ~errorvals, ~traindur-remain);

Out.ar(0, Pan2.ar(K2A.ar(val) * 0.01));

}.play

)

// Once the training is finished (i.e. once "remain" drops to zero):

x.free;

// We should be able to look at the 2D data points represented in the SOM and see if they line up with the sinewave.

// This plot is nice if you have OctaveSC installed:

o = OctaveSC.new;

o.init

(

~som.loadToFloatArray(action: {|arr|

o[\xtemp] = arr[0,2..].as(Array).postln;

o[\ytemp] = arr[1,3..].as(Array).postln;

o.("figure; hold off");

o.("plot(xtemp, ytemp, '-@')");

o.("hold on");

o.("spls = [0:0.01:2]; plot(spls, sin(spls*2*pi/2))");

});

);

// Otherwise here's a quick 2D plot in pure SC - does it look like the sinewave you started with?

(

~som.loadToFloatArray(action: {|arr| {

w = GUI.window.new("SOM nodes", Rect(200, 800, 600, 600)); // SCWindow

w.view.background = Color.white;

(0,2..arr.size-1).do{|index|

GUI.staticText.new(w, Rect(

arr[index] * 600 / 2,

600 - (arr[index+1] + 1 * 300), 10, 10)).string_("x") // SCStaticText

};

w.front;

}.defer})

)

// How do the errors look? Should be a very noisy curve gradually decreasing, but won't necessarily stabilise

~errorvals.plot(maxval: nil, minval: nil);