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Linear algebra operations, Dimensionality reduction and some other mi…
…nor changes (#81) * Lineer Algebra operations * Covariance * PCA and KernelPCA * Tests for PCA, Eigenvalues and Covariance * KernelPCA update * KernelPCA and its test * KernelPCA and its test * MatrixTest, KernelPCA and PCA tests * Readme update * Readme update
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| Original file line number | Diff line number | Diff line change |
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| <?php | ||
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| declare(strict_types=1); | ||
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| namespace Phpml\DimensionReduction; | ||
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| use Phpml\Math\Distance\Euclidean; | ||
| use Phpml\Math\Distance\Manhattan; | ||
| use Phpml\Math\Matrix; | ||
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| class KernelPCA extends PCA | ||
| { | ||
| const KERNEL_RBF = 1; | ||
| const KERNEL_SIGMOID = 2; | ||
| const KERNEL_LAPLACIAN = 3; | ||
| const KERNEL_LINEAR = 4; | ||
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| /** | ||
| * Selected kernel function | ||
| * | ||
| * @var int | ||
| */ | ||
| protected $kernel; | ||
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| /** | ||
| * Gamma value used by the kernel | ||
| * | ||
| * @var float | ||
| */ | ||
| protected $gamma; | ||
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| /** | ||
| * Original dataset used to fit KernelPCA | ||
| * | ||
| * @var array | ||
| */ | ||
| protected $data; | ||
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| /** | ||
| * Kernel principal component analysis (KernelPCA) is an extension of PCA using | ||
| * techniques of kernel methods. It is more suitable for data that involves | ||
| * vectors that are not linearly separable<br><br> | ||
| * Example: <b>$kpca = new KernelPCA(KernelPCA::KERNEL_RBF, null, 2, 15.0);</b> | ||
| * will initialize the algorithm with an RBF kernel having the gamma parameter as 15,0. <br> | ||
| * This transformation will return the same number of rows with only <i>2</i> columns. | ||
| * | ||
| * @param int $kernel | ||
| * @param float $totalVariance Total variance to be preserved if numFeatures is not given | ||
| * @param int $numFeatures Number of columns to be returned | ||
| * @param float $gamma Gamma parameter is used with RBF and Sigmoid kernels | ||
| * | ||
| * @throws \Exception | ||
| */ | ||
| public function __construct(int $kernel = self::KERNEL_RBF, $totalVariance = null, $numFeatures = null, $gamma = null) | ||
| { | ||
| $availableKernels = [self::KERNEL_RBF, self::KERNEL_SIGMOID, self::KERNEL_LAPLACIAN, self::KERNEL_LINEAR]; | ||
| if (! in_array($kernel, $availableKernels)) { | ||
| throw new \Exception("KernelPCA can be initialized with the following kernels only: Linear, RBF, Sigmoid and Laplacian"); | ||
| } | ||
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| parent::__construct($totalVariance, $numFeatures); | ||
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| $this->kernel = $kernel; | ||
| $this->gamma = $gamma; | ||
| } | ||
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| /** | ||
| * Takes a data and returns a lower dimensional version | ||
| * of this data while preserving $totalVariance or $numFeatures. <br> | ||
| * $data is an n-by-m matrix and returned array is | ||
| * n-by-k matrix where k <= m | ||
| * | ||
| * @param array $data | ||
| * | ||
| * @return array | ||
| */ | ||
| public function fit(array $data) | ||
| { | ||
| $numRows = count($data); | ||
| $this->data = $data; | ||
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| if ($this->gamma === null) { | ||
| $this->gamma = 1.0 / $numRows; | ||
| } | ||
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| $matrix = $this->calculateKernelMatrix($this->data, $numRows); | ||
| $matrix = $this->centerMatrix($matrix, $numRows); | ||
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| list($this->eigValues, $this->eigVectors) = $this->eigenDecomposition($matrix, $numRows); | ||
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| $this->fit = true; | ||
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| return Matrix::transposeArray($this->eigVectors); | ||
| } | ||
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| /** | ||
| * Calculates similarity matrix by use of selected kernel function<br> | ||
| * An n-by-m matrix is given and an n-by-n matrix is returned | ||
| * | ||
| * @param array $data | ||
| * @param int $numRows | ||
| * | ||
| * @return array | ||
| */ | ||
| protected function calculateKernelMatrix(array $data, int $numRows) | ||
| { | ||
| $kernelFunc = $this->getKernel(); | ||
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| $matrix = []; | ||
| for ($i=0; $i < $numRows; $i++) { | ||
| for ($k=0; $k < $numRows; $k++) { | ||
| if ($i <= $k) { | ||
| $matrix[$i][$k] = $kernelFunc($data[$i], $data[$k]); | ||
| } else { | ||
| $matrix[$i][$k] = $matrix[$k][$i]; | ||
| } | ||
| } | ||
| } | ||
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| return $matrix; | ||
| } | ||
|
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| /** | ||
| * Kernel matrix is centered in its original space by using the following | ||
| * conversion: | ||
| * | ||
| * K′ = K − N.K − K.N + N.K.N where N is n-by-n matrix filled with 1/n | ||
| * | ||
| * @param array $matrix | ||
| * @param int $n | ||
| */ | ||
| protected function centerMatrix(array $matrix, int $n) | ||
| { | ||
| $N = array_fill(0, $n, array_fill(0, $n, 1.0/$n)); | ||
| $N = new Matrix($N, false); | ||
| $K = new Matrix($matrix, false); | ||
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| // K.N (This term is repeated so we cache it once) | ||
| $K_N = $K->multiply($N); | ||
| // N.K | ||
| $N_K = $N->multiply($K); | ||
| // N.K.N | ||
| $N_K_N = $N->multiply($K_N); | ||
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| return $K->subtract($N_K) | ||
| ->subtract($K_N) | ||
| ->add($N_K_N) | ||
| ->toArray(); | ||
| } | ||
|
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| /** | ||
| * Returns the callable kernel function | ||
| * | ||
| * @return \Closure | ||
| */ | ||
| protected function getKernel() | ||
| { | ||
| switch ($this->kernel) { | ||
| case self::KERNEL_LINEAR: | ||
| // k(x,y) = xT.y | ||
| return function ($x, $y) { | ||
| return Matrix::dot($x, $y)[0]; | ||
| }; | ||
| case self::KERNEL_RBF: | ||
| // k(x,y)=exp(-γ.|x-y|) where |..| is Euclidean distance | ||
| $dist = new Euclidean(); | ||
| return function ($x, $y) use ($dist) { | ||
| return exp(-$this->gamma * $dist->sqDistance($x, $y)); | ||
| }; | ||
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| case self::KERNEL_SIGMOID: | ||
| // k(x,y)=tanh(γ.xT.y+c0) where c0=1 | ||
| return function ($x, $y) { | ||
| $res = Matrix::dot($x, $y)[0] + 1.0; | ||
| return tanh($this->gamma * $res); | ||
| }; | ||
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| case self::KERNEL_LAPLACIAN: | ||
| // k(x,y)=exp(-γ.|x-y|) where |..| is Manhattan distance | ||
| $dist = new Manhattan(); | ||
| return function ($x, $y) use ($dist) { | ||
| return exp(-$this->gamma * $dist->distance($x, $y)); | ||
| }; | ||
| } | ||
| } | ||
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| /** | ||
| * @param array $sample | ||
| * | ||
| * @return array | ||
| */ | ||
| protected function getDistancePairs(array $sample) | ||
| { | ||
| $kernel = $this->getKernel(); | ||
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| $pairs = []; | ||
| foreach ($this->data as $row) { | ||
| $pairs[] = $kernel($row, $sample); | ||
| } | ||
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| return $pairs; | ||
| } | ||
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| /** | ||
| * @param array $pairs | ||
| * | ||
| * @return array | ||
| */ | ||
| protected function projectSample(array $pairs) | ||
| { | ||
| // Normalize eigenvectors by eig = eigVectors / eigValues | ||
| $func = function ($eigVal, $eigVect) { | ||
| $m = new Matrix($eigVect, false); | ||
| $a = $m->divideByScalar($eigVal)->toArray(); | ||
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| return $a[0]; | ||
| }; | ||
| $eig = array_map($func, $this->eigValues, $this->eigVectors); | ||
|
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| // return k.dot(eig) | ||
| return Matrix::dot($pairs, $eig); | ||
| } | ||
|
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| /** | ||
| * Transforms the given sample to a lower dimensional vector by using | ||
| * the variables obtained during the last run of <code>fit</code>. | ||
| * | ||
| * @param array $sample | ||
| * | ||
| * @return array | ||
| */ | ||
| public function transform(array $sample) | ||
| { | ||
| if (!$this->fit) { | ||
| throw new \Exception("KernelPCA has not been fitted with respect to original dataset, please run KernelPCA::fit() first"); | ||
| } | ||
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| if (is_array($sample[0])) { | ||
| throw new \Exception("KernelPCA::transform() accepts only one-dimensional arrays"); | ||
| } | ||
|
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| $pairs = $this->getDistancePairs($sample); | ||
|
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| return $this->projectSample($pairs); | ||
| } | ||
| } |
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