{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy.linalg import svd\n",
    "from sklearn.datasets import load_iris\n",
    "from sklearn.decomposition import PCA as skPCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation 1\n",
    "- based on svd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PCA():\n",
    "    def __init__(self, n_components=2):\n",
    "        self.n_components = n_components\n",
    "\n",
    "    def fit(self, X):\n",
    "        U, S, V = svd(X, full_matrices=False)\n",
    "        self.components_ = V[:self.n_components]\n",
    "        self.explained_variance_ratio_ = np.square(S[:self.n_components]) / np.sum(np.square(S))\n",
    "        return self\n",
    "\n",
    "    def transform(self, X):\n",
    "        return np.dot(X, self.components_.T)\n",
    "\n",
    "    def inverse_transform(self, X):\n",
    "        return np.dot(X, self.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, _ = load_iris(return_X_y=True)\n",
    "X -= np.mean(X, axis=0)\n",
    "pca1 = PCA().fit(X)\n",
    "Xt1 = pca1.transform(X)\n",
    "Xinv1 = pca1.inverse_transform(Xt1)\n",
    "pca2 = skPCA(n_components=2).fit(X)\n",
    "Xt2 = pca2.transform(X)\n",
    "Xinv2 = pca2.inverse_transform(Xt2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(pca1.components_.shape[0]):\n",
    "    assert np.allclose(pca1.components_[i], pca2.components_[i]) or np.allclose(pca1.components_[i], -pca2.components_[i])\n",
    "assert np.allclose(pca1.explained_variance_ratio_, pca2.explained_variance_ratio_)\n",
    "for i in range(Xt1.shape[1]):\n",
    "    assert np.allclose(Xt1[:, i], Xt2[:, i]) or np.allclose(Xt1[:, i], -Xt2[:, i])\n",
    "assert np.allclose(Xinv1, Xinv2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation 2\n",
    "- based on svd\n",
    "- center the dataset before svd\n",
    "- similar to scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PCA():\n",
    "    def __init__(self, n_components=2):\n",
    "        self.n_components = n_components\n",
    "\n",
    "    def fit(self, X):\n",
    "        self.mean_ = np.mean(X, axis=0)\n",
    "        X_train = X - self.mean_\n",
    "        U, S, V = svd(X_train, full_matrices=False)\n",
    "        self.components_ = V[:self.n_components]\n",
    "        self.explained_variance_ratio_ = np.square(S[:self.n_components]) / np.sum(np.square(S))\n",
    "        return self\n",
    "\n",
    "    def transform(self, X):\n",
    "        X_train = X - self.mean_\n",
    "        return np.dot(X_train, self.components_.T)\n",
    "\n",
    "    def inverse_transform(self, X):\n",
    "        return np.dot(X, self.components_) + self.mean_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, _ = load_iris(return_X_y=True)\n",
    "pca1 = PCA().fit(X)\n",
    "Xt1 = pca1.transform(X)\n",
    "Xinv1 = pca1.inverse_transform(Xt1)\n",
    "pca2 = skPCA(n_components=2).fit(X)\n",
    "Xt2 = pca2.transform(X)\n",
    "Xinv2 = pca2.inverse_transform(Xt2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(pca1.components_.shape[0]):\n",
    "    assert np.allclose(pca1.components_[i], pca2.components_[i]) or np.allclose(pca1.components_[i], -pca2.components_[i])\n",
    "assert np.allclose(pca1.explained_variance_ratio_, pca2.explained_variance_ratio_)\n",
    "for i in range(Xt1.shape[1]):\n",
    "    assert np.allclose(Xt1[:, i], Xt2[:, i]) or np.allclose(Xt1[:, i], -Xt2[:, i])\n",
    "assert np.allclose(Xinv1, Xinv2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation 3\n",
    "- based on covariance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PCA():\n",
    "    def __init__(self, n_components=2):\n",
    "        self.n_components = n_components\n",
    "\n",
    "    def fit(self, X):\n",
    "        covmat = np.cov(X, rowvar=False)\n",
    "        eigval, eigvec = np.linalg.eig(covmat)\n",
    "        idx = eigval.argsort()[::-1]\n",
    "        self.components_ = eigvec[idx[:self.n_components]]\n",
    "        self.explained_variance_ratio_ = np.square(eigval[idx[:self.n_components]]) / np.sum(np.square(eigval))\n",
    "        return self\n",
    "\n",
    "    def transform(self, X):\n",
    "        return np.dot(X, self.components_.T)\n",
    "\n",
    "    def inverse_transform(self, X):\n",
    "        return np.dot(X, self.components_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, _ = load_iris(return_X_y=True)\n",
    "X -= np.mean(X, axis=0)\n",
    "pca1 = PCA().fit(X)\n",
    "Xt1 = pca1.transform(X)\n",
    "Xinv1 = pca1.inverse_transform(Xt1)\n",
    "pca2 = skPCA(n_components=2).fit(X)\n",
    "Xt2 = pca2.transform(X)\n",
    "Xinv2 = pca2.inverse_transform(Xt2)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}