Gaussian Mixture
This module implements a 1D Gaussian Mixture class that allows to fit a distribution of points along a onedimensional axis.
Install
npm install gaussianmixture
Require
var GMM = require('gaussianmixture');
GMM
Instantiate a new GMM.
Parameters

nComponents
Number number of components in the mixture 
weights
Array array of weights for each component in the mixture, must sum to 1 
means
Array array of means for each component 
vars
Array array of variances of each component 
options
Object an object that can define thevariancePrior
,separationPrior
,variancePriorRelevance
andseparationPriorRelevance
. The priors are taken into account when the GMM is optimized given some data. The relevance parameters should be nonnegative numbers, 1 meaning that the prior has equal weight as the result of the optimal GMM in each EM step, 0 meaning no influence, and Infinity means a fixed variance (resp. separation).
Examples
var gmm = new GMM(3, [0.3, 0.2, 0.5], [1, 2, 3], [1, 1, 0.5]);
Returns GMM a gmm object
sample
Randomly sample from the GMM's distribution.
Parameters

nSamples
Number desired number of samples
Returns Array An array of randomly sampled numbers that follow the GMM's distribution
memberships
Given an array of data, determine their memberships for each component of the GMM.
Parameters

data
Array array of numbers representing the samples to score under the model 
gaussians
Array (optional) an Array of length nComponents that contains the gaussians for the GMM
Returns Array (data.length * this.nComponents) matrix with membership weights
membership
Given a datapoint, determine its memberships for each component of the GMM.
Parameters

x
Number number representing the sample to score under the model 
gaussians
Array (optional) an Array of length nComponents that contains the gaussians for the GMM
Returns Array an array of length this.nComponents with membership weights, i.e the probabilities that this datapoint was drawn from the each component
logLikelihood
Compute the loglikelihood for the GMM given data.
Parameters
Returns Number the loglikelihood
optimize
Compute the optimal GMM components given an array of data.
If options has a true flag for initialize
, the optimization will begin with a Kmeans++ initialization.
This allows to have a datadependent initialization and should converge quicker and to a better model.
The initialization is agnostic to the other priors that the options might contain.
The initialize
flag is unavailable with the histogram version of this function
Parameters

data
(Array  Histogram) the data array or histogram 
maxIterations
Number? maximum number of expectationmaximization steps (optional, default200
) 
logLikelihoodTol
Number? tolerance for the loglikelihood to determine if we reached the optimum (optional, default0.0000001
)
Returns Number the number of steps to reach the converged solution
initialize
Initialize the GMM given data with the Kmeans++ initialization algorithm. The kmeans++ algorithm choses datapoints amongst the data at random, while ensuring that the chosen seeds are far from each other. The resulting seeds are returned sorted.
Parameters

data
Array array of numbers representing the samples to use to optimize the model
Examples
var gmm = new GMM(3, [0.3, .04, 0.3], [1, 5, 10]);
var data = [1.2, 1.3, 7.4, 1.4, 14.3, 15.3, 1.0, 7.2];
gmm.initialize(data); // updates the means of the GMM with the Kmeans++ initialization algorithm, returns something like [1.3, 7.4, 14.3]
Returns Array an array of length nComponents that contains the means for the initialization.
model
Return the model for the GMM as a raw JavaScript Object.
Returns Object the model, with keys nComponents
, weights
, means
, vars
.
fromModel
Instantiate a GMM from an Object model and options.
Parameters
model
options
Examples
var gmm = GMM.fromModel({
nComponents: 3,
weights: [0.3, 0.2, 0.5],
means: [1, 2, 3],
vars: [1, 1, 0.5]
});
Returns GMM the GMM corresponding to the given model
Histogram
Instantiate a new Histogram.
Parameters

h
Object? an object with keys 'counts' and 'bins'. Both are optional. An observation x will be counted for the key i if bins[i][0] <= x < bins[i][1]. If bins are not specified, the bins will be corresponding to one unit in the scale of the data. The keys of the 'counts' hash will be stringified integers. (optional, default{}
)
Examples
var h = new Histogram({counts: {'a': 3, 'b': 2, 'c': 5}, bins: {'a': [0, 2], 'b': [2, 4], 'c': [4, 7]}});
var h = new Histogram({counts: {'1': 3, '2': 2, '3': 5}});
var h = new Histogram();
Returns Histogram a histogram object. It has keys 'bins' (possibly null) and 'counts'.
add
Add an observation to an histogram.
Parameters

x
Array observation to add tos the histogram
Returns Histogram the histogram with added value.
flatten
Return a data array from a histogram.
Returns Array an array of observations derived from the histogram counts.
value
Return the median value for the given key, derived from the bins.
Parameters
key
Returns Number the value for the provided key.
fromData
Instantiate a new Histogram.
Parameters

data
Array? array of observations to include in the histogram. Observations that do not correspond to any bin will be discarded. (optional, default[]
) 
bins
Object? a map from key to range (a range being an array of two elements) An observation x will be counted for the key i ifbins[i][0] <= x < bins[i][1]
. If not specified, the bins will be corresponding to one unit in the scale of the data. (optional, default{}
)
Examples
var h = Histogram.fromData([1, 2, 2, 2, 5, 5], {A: [0, 1], B: [1, 5], C: [5, 10]});
// {bins: {A: [0, 1], B: [1, 5], C: [5, 10]}, counts: {A: 0, B: 4, C: 2}}
var h = Histogram.fromData([1, 2, 2, 2, 2.4, 2.5, 5, 5]);
// {counts: {'1': 1, '2': 4, '3': 1, '5': 2}}
Returns Histogram a histogram object It has keys 'bins' (possibly null) and 'counts'.