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* @license Apache-2.0
*
* Copyright (c) 2018 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var isPositiveInteger = require( '@stdlib/assert/is-positive-integer' ).isPrimitive;
var isMatrixLike = require( '@stdlib/assert/is-matrix-like' );
var isVectorLike = require( '@stdlib/assert/is-vector-like' );
var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
var format = require( '@stdlib/string/format' );
var minstd = require( '@stdlib/random/base/minstd-shuffle' );
var floor = require( '@stdlib/math/base/special/floor' );
var ln = require( '@stdlib/math/base/special/ln' );
var dcopy = require( '@stdlib/blas/base/dcopy' );
var createMatrix = require( './matrix.js' );
var copyMatrix = require( './copy_matrix.js' );
var createVector = require( './vector.js' );
var copyVector = require( './copy_vector.js' );
var validate = require( './validate.js' );
var INIT_DEFAULTS = require( './init_defaults.json' );
var initialization = require( './init.js' );
var statistics = require( './stats.js' );
var incrstatistics = require( './incrstats.js' );
var squaredEuclidean = require( './squared_euclidean.js' );
var squaredCosine = require( './squared_cosine.js' );
var squaredCorrelation = require( './squared_correlation.js' );
var closestCentroid = require( './find_closest_centroid.js' );
var updateCentroid = require( './update_centroid.js' );
var normalize = require( './normalize.js' );
var normalizeMatrix = require( './normalize_matrix.js' );
var standardize = require( './standardize.js' );
var standardizeMatrix = require( './standardize_matrix.js' );
// VARIABLES //
// Number of cluster statistics:
var NSTATS = 4; // [ n_obs, sum_squared_dist, mean_squared_dist, stdev_squared_dist ]
// FUNCTIONS //
/**
* Returns a results object.
*
* @private
* @param {PositiveInteger} k - number of clusters
* @param {PositiveInteger} ndims - number of dimensions
* @returns {Object} results object
*/
function createResults( k, ndims ) {
var out = {};
out.centroids = createMatrix( k, ndims, false ); // high-level
out.stats = createMatrix( k, NSTATS, false ); // high-level
return out;
}
// MAIN //
/**
* Returns an accumulator function which incrementally partitions data into `k` clusters.
*
* @param {(PositiveInteger|ndarray)} k - number of clusters or a `k x ndims` matrix containing initial centroids
* @param {PositiveInteger} [ndims] - number of dimensions (should only be provided if provided a numeric `k` argument)
* @param {Options} [options] - function options
* @param {string} [options.metric="euclidean"] - distance metric
* @param {ArrayLikeObject} [options.init] - method for determining initial centroids
* @param {boolean} [options.normalize=true] - boolean indicating whether to normalize incoming data (only relevant for non-Euclidean distance metrics)
* @param {boolean} [options.copy=true] - boolean indicating whether to copy incoming data to prevent mutation during normalization
* @param {*} [options.seed] - PRNG seed
* @throws {TypeError} first argument must be a positive integer
* @throws {TypeError} second argument must be a positive integer
* @throws {TypeError} options argument must be an object
* @throws {TypeError} must provide valid options
* @throws {RangeError} when using sampling to generate initial centroids, the sample size must be greater than or equal to the number of clusters
* @returns {Function} accumulator function
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var ndarray = require( '@stdlib/ndarray/ctor' );
*
* // Define initial centroid locations:
* var buffer = [
* 0.0, 0.0,
* 1.0, 1.0,
* 1.0, -1.0,
* -1.0, -1.0,
* -1.0, 1.0
* ];
* var shape = [ 5, 2 ];
* var strides = [ 2, 1 ];
* var offset = 0;
* var order = 'row-major';
*
* var centroids = ndarray( 'float64', buffer, shape, strides, offset, order );
*
* // Create a k-means accumulator:
* var accumulator = incrkmeans( centroids );
*
* var out = accumulator();
* // returns {...}
*
* // Create a data vector:
* buffer = new Float64Array( 2 );
* shape = [ 2 ];
* strides = [ 1 ];
*
* var vec = ndarray( 'float64', buffer, shape, strides, offset, order );
*
* // Provide data to the accumulator:
* vec.set( 0, 2.0 );
* vec.set( 1, 1.0 );
*
* out = accumulator( vec );
* // returns {...}
*
* vec.set( 0, -5.0 );
* vec.set( 1, 3.14 );
*
* out = accumulator( vec );
* // returns {...}
*
* // Retrieve the current cluster results:
* out = accumulator();
* // returns {...}
*/
function incrkmeans() {
var clusterstats;
var centroids;
var incrstats;
var options;
var results;
var vcopy;
var stats;
var ndims;
var dist;
var opts;
var init;
var err;
var FLG;
var k;
if ( isMatrixLike( arguments[ 0 ] ) ) {
k = arguments[ 0 ].shape[ 0 ];
ndims = arguments[ 0 ].shape[ 1 ];
centroids = createMatrix( k, ndims, true ); // low-level
centroids = copyMatrix( centroids, arguments[ 0 ] );
if ( arguments.length > 1 ) {
options = arguments[ 1 ];
FLG = true;
}
} else if ( isPositiveInteger( arguments[ 0 ] ) ) {
k = arguments[ 0 ];
ndims = arguments[ 1 ];
if ( !isPositiveInteger( ndims ) ) {
throw new TypeError( format( 'invalid argument. Argument specifying number of dimensions must be a positive integer. Value: `%s`.', ndims ) );
}
if ( arguments.length > 2 ) {
options = arguments[ 2 ];
FLG = true;
}
} else {
throw new TypeError( format( 'invalid argument. First argument must either be a positive integer specifying the number of clusters or a matrix containing initial centroids. Value: `%s`.', arguments[ 0 ] ) );
}
opts = {
'metric': 'euclidean',
'init': INIT_DEFAULTS[ 'kmeans++' ].slice(),
'seed': minstd(),
'normalize': true,
'copy': true
};
opts.init[ 1 ] = k; // Note: this default applies to all initialization methods
opts.init[ 2 ] = 2 + floor( ln( k ) ); // Note: from Arthur's and Vassilvitskii's paper "kmeans++: The Advantages of Careful Seeding" (see conclusion)
if ( FLG ) {
err = validate( opts, options );
if ( err ) {
throw err;
}
}
if ( opts.init[ 1 ] < k ) {
throw new RangeError( format( 'invalid option. First `%s` parameter option must be greater than or equal to the number of clusters. Options: `%f`.', 'init', opts.init[ 1 ] ) );
}
// Initialize a results object:
results = createResults( k, ndims );
// Initialize an internal matrix for tabulating cluster statistics:
stats = createMatrix( k, NSTATS, true ); // low-level
// Initialize an internal cluster statistics accumulator:
clusterstats = statistics( stats, k );
// Initialize metric-related variables...
if ( opts.metric === 'cosine' ) {
dist = squaredCosine;
// Initialize a scratch vector for copying input vectors:
if ( opts.copy ) {
vcopy = createVector( ndims, true ); // low-level
}
} else if ( opts.metric === 'correlation' ) {
dist = squaredCorrelation;
// Initialize an accumulator for computing the mean vector and associated standard deviation along each dimension:
if ( opts.normalize ) {
incrstats = incrstatistics( ndims );
}
// Initialize a scratch vector for copying input vectors:
if ( opts.copy ) {
vcopy = createVector( ndims, true ); // low-level
}
} else {
dist = squaredEuclidean;
}
// Check if we need to compute initial centroids...
if ( centroids === void 0 ) {
// Initialize an internal matrix for storing centroids:
centroids = createMatrix( k, ndims, true ); // low-level
// Initialize an accumulator for computing initial centroids:
init = initialization( centroids, stats, clusterstats, incrstats, dist, opts ); // eslint-disable-line max-len
} else {
// Update cluster results to include the initial centroids (why? so that, even if no data is provided, the `results` object contains the provided centroids):
copyMatrix( results.centroids, centroids );
}
// Attach properties and methods to the accumulator:
setReadOnly( accumulator, 'seed', opts.seed );
setReadOnly( accumulator, 'predict', predict );
return accumulator;
/**
* If provided a data point vector, the accumulator function returns updated cluster results. If not provided a data point vector, the accumulator function returns the current cluster results.
*
* @private
* @param {ndarray} [vec] - data vector
* @throws {TypeError} must provide a 1-dimensional ndarray
* @throws {Error} vector length must match centroid dimensions
* @returns {(Object|null)} cluster results or null
*/
function accumulator( vec ) {
var bool;
var cbuf;
var vbuf;
var sbuf;
var sv;
var sc;
var ov;
var oc;
var v;
var N;
var d;
var c;
if ( arguments.length === 0 ) {
if ( init ) {
return null;
}
return results;
}
v = vec; // Why? We mention `arguments` in the function and perform a subsequent reassignment.
if ( !isVectorLike( v ) ) {
throw new TypeError( format( 'invalid argument. Must provide a one-dimensional ndarray. Value: `%s`.', v ) );
}
if ( v.shape[ 0 ] !== ndims ) {
throw new Error( format( 'invalid argument. Vector length must match centroid dimensions. Expected: `%u``. Actual: `%u``.', ndims, v.shape[ 0 ] ) );
}
// Check if we need to update the data point mean vector...
if ( incrstats ) {
incrstats( v );
}
// Check if we have yet to compute initial centroids...
if ( init ) {
bool = init( v );
if ( bool === false ) {
return null;
}
// De-reference `init` so that it and its internal variables can be garbage collected:
init = void 0;
} else {
// If required by the metric, normalize the data vector...
if ( opts.normalize ) {
if ( opts.metric === 'cosine' ) {
if ( opts.copy ) {
v = copyVector( vcopy, v );
}
normalize( ndims, v.data, v.strides[ 0 ], v.offset );
} else if ( opts.metric === 'correlation' ) {
if ( opts.copy ) {
v = copyVector( vcopy, v );
}
sbuf = incrstats();
// Magic numbers come from knowing that `sbuf` is an interleaved strided array...
standardize( ndims, v.data, v.strides[ 0 ], v.offset, sbuf, 2, 0, sbuf, 2, 1 ); // eslint-disable-line max-len
}
}
cbuf = centroids.data;
sc = centroids.strides[ 0 ];
vbuf = v.data;
sv = v.strides[ 0 ];
ov = v.offset;
// Find the closest centroid by computing the distance from the provided data point to each centroid:
c = closestCentroid( dist, k, ndims, cbuf, sc, 0, vbuf, sv, ov ); // Magic number `0` for offset as we know that the matrix view begins at the first buffer element
// Compute the centroids buffer index offset to point to the closest centroid:
oc = sc * c;
// Update the closest centroid:
N = stats.get( c, 0 ) + 1;
updateCentroid( ndims, N, cbuf, 1, oc, vbuf, sv, ov ); // Magic number `1` as we know that the matrix is row-major single-segment contiguous
// Recompute the distance based on the updated centroid position:
d = dist( ndims, cbuf, 1, oc, vbuf, sv, ov ); // Magic number `1` as we know that the matrix is row-major single-segment contiguous
// Update cluster statistics:
clusterstats( c, d );
}
// Update the results object:
dcopy( centroids.length, centroids.data, 1, results.centroids.data, 1 ); // Magic number `1` as we know that these matrices are row-major single-segment contiguous
dcopy( stats.length, stats.data, 1, results.stats.data, 1 ); // Magic number `1` as we know that these matrices are row-major single-segment contiguous
return results;
}
/**
* Computes data point distances to centroids and returns centroid assignment predictions.
*
* @private
* @param {ndarray} [out] - output vector for storing centroid assignment predictions
* @param {ndarray} X - matrix containing data points (`n x d`, where `n` is the number of data points and `d` is the number of dimensions)
* @throws {TypeError} output argument must be a vector
* @throws {TypeError} must provide a matrix
* @throws {Error} vector length must match number of data points
* @throws {Error} number of matrix columns must match centroid dimensions
* @returns {(ndarray|null)} vector containing centroid (index) predictions or null
*/
function predict( out, X ) {
var xbuf;
var cbuf;
var npts;
var sx1;
var sx2;
var sc;
var ox;
var x;
var o;
var c;
var i;
if ( arguments.length > 1 ) {
if ( !isVectorLike( out ) ) {
throw new TypeError( format( 'invalid argument. Output argument must be a one-dimensional ndarray. Value: `%s`.', out ) );
}
o = out;
x = X;
} else {
x = out;
}
if ( !isMatrixLike( x ) ) {
throw new TypeError( format( 'invalid argument. Must provide a two-dimensional ndarray. Value: `%s`.', x ) );
}
if ( x.shape[ 1 ] !== ndims ) {
throw new Error( format( 'invalid argument. Number of matrix columns must match centroid dimensions. Expected: `%u`. Actual: `%u`.', ndims, x.shape[ 1 ] ) );
}
if ( o === void 0 ) {
o = createVector( x.shape[ 0 ], false ); // high-level
} else if ( o.length !== x.shape[ 0 ] ) {
throw new Error( format( 'invalid argument. Output vector length must match the number of data points. Expected: `%u`. Actual: `%u`.', x.shape[ 0 ], o.length ) );
}
if ( init ) {
return null;
}
npts = x.shape[ 0 ];
// If required by the metric, normalize the data vectors along the dimensions...
if ( opts.normalize ) {
if ( opts.metric === 'cosine' ) {
if ( opts.copy ) {
x = copyMatrix( createMatrix( npts, ndims, true ), x ); // low-level
}
x = normalizeMatrix( x );
} else if ( opts.metric === 'correlation' ) {
if ( opts.copy ) {
x = copyMatrix( createMatrix( npts, ndims, true ), x ); // low-level
}
x = standardizeMatrix( x, incrstats() );
}
}
cbuf = centroids.data;
sc = centroids.strides[ 0 ];
xbuf = x.data;
sx1 = x.strides[ 0 ];
sx2 = x.strides[ 1 ];
ox = x.offset;
// For each data point, find the closest centroid...
for ( i = 0; i < npts; i++ ) {
c = closestCentroid( dist, k, ndims, cbuf, sc, 0, xbuf, sx2, ox ); // Magic number `0` for offset as we know that the matrix view begins at the first buffer element
// Update the output vector:
o.set( i, c );
// Compute the data point buffer index offset to point to the next data point:
ox += sx1;
}
return o;
}
}
// EXPORTS //
module.exports = incrkmeans;
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