An implementation of a Gaussian Mixture class in one dimension, that allows to fit models with an Expectation Maximization algorithm.
npm install gaussianMixtureThis module implements a 1D Gaussian Mixture class that allows to fit a distribution of points along a one-dimensional axis.
sh
npm install gaussianMixture
`$3
js
var GMM = require('gaussianMixture');
`----------------
GMM
Instantiate a new GMM.
Parameters
-
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 the variancePrior, separationPrior, variancePriorRelevance and separationPriorRelevance.
The priors are taken into account when the GMM is optimized given some data. The relevance parameters should be non-negative 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
`javascript
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
-
Number desired number of samplesReturns 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 GMMReturns 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 GMMReturns 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 log-likelihood for the GMM given data.
Parameters
-
data (Array \| Histogram) the data array or histogramReturns Number the log-likelihood
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 K-means++ initialization.
This allows to have a data-dependent 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 functionParameters
-
data (Array \| Histogram) the data array or histogram
- maxIterations Number? maximum number of expectation-maximization steps (optional, default 200)
- logLikelihoodTol Number? tolerance for the log-likelihood
to determine if we reached the optimum (optional, default 0.0000001)Returns Number the number of steps to reach the converged solution
initialize
Initialize the GMM given data with the K-means++ initialization algorithm.
The k-means++ 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 modelExamples
`javascript
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 K-means++ 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
, weights, means, vars.fromModel
Instantiate a GMM from an Object model and options.
Parameters
-
model
- options Examples
`javascript
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
-
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
`javascript
var h = new Histogram({counts: {'a': 3, 'b': 2, 'c': 5}, bins: {'a': [0, 2], 'b': [2, 4], 'c': [4, 7]}});
`javascript
var h = new Histogram({counts: {'1': 3, '2': 2, '3': 5}});
`javascript
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
-
Array observation to add tos the histogramReturns 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 if bins[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
`javascript
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}}
`javascript
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'.