PCA_theory_practise.ipynb

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      "name": "PCA_theory_practise",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/RaminParker/PrincipalComponentAnalysis_PCA/blob/master/PCA_theory_practise.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2dErh9zq7cbq",
        "colab_type": "text"
      },
      "source": [
        "# Principal Component Analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QdUaq6kCJckn",
        "colab_type": "text"
      },
      "source": [
        "**PCA:** method for reducing the dimensionality of data.\n",
        "\n",
        "**What is it doing:** Data with m-columns (features) is projected into a subspace with m or fewer columns."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gMtXsByt7aR_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from numpy import array\n",
        "from numpy import mean\n",
        "from numpy import cov\n",
        "from numpy.linalg import eig\n",
        "\n",
        "\n",
        "from numpy import array\n",
        "from sklearn.decomposition import PCA\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns; sns.set()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sYZbGbg-H4Tm",
        "colab_type": "text"
      },
      "source": [
        "## Manually Calculate Principal Component Analysis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mVakHR408KDw",
        "colab_type": "text"
      },
      "source": [
        "Define the data of the dataset\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gur2kEGk7mqg",
        "colab_type": "code",
        "outputId": "3dccf0a8-43c7-41cf-f823-6877b889476c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A = array([[90, 60, 90], [90, 90, 30], [60, 60,60], [60, 60, 90], [30, 30, 30]])\n",
        "print(A)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[90 60 90]\n",
            " [90 90 30]\n",
            " [60 60 60]\n",
            " [60 60 90]\n",
            " [30 30 30]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cFfB91f-8sTB",
        "colab_type": "text"
      },
      "source": [
        "Calculate the mean of each column:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3-qcfnCq8l4I",
        "colab_type": "code",
        "outputId": "41c31064-9fa2-4b08-e75d-0292f38da321",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "M=A.mean(0)\n",
        "print(M)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[66. 60. 60.]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3rb1rkibG9UM",
        "colab_type": "text"
      },
      "source": [
        "Center columns by subtracting column means"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7o9pld787k7X",
        "colab_type": "code",
        "outputId": "5ad8f0e0-9051-454c-c49f-779c07e5844e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "C=A-M\n",
        "print(C)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 24.   0.  30.]\n",
            " [ 24.  30. -30.]\n",
            " [ -6.   0.   0.]\n",
            " [ -6.   0.  30.]\n",
            " [-36. -30. -30.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3kPm1HH5GuIl",
        "colab_type": "text"
      },
      "source": [
        "Calculate variance-covariance matrix (cross-covariance matrix) of centered matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tVEb5IhM_QIV",
        "colab_type": "code",
        "outputId": "b7206e5b-5a95-4fdc-9a0d-0b160d5d217f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "V=cov(C.T)\n",
        "V\n",
        "print('NumPy cross-covariance matrix: \\n%s' %V)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "NumPy cross-covariance matrix: \n",
            "[[630. 450. 225.]\n",
            " [450. 450.   0.]\n",
            " [225.   0. 900.]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "s6bxrI13OwD5",
        "colab_type": "text"
      },
      "source": [
        "If you don't want to use the pre-defined function:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V7JEyzwBOp2y",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# mean_vec = np.mean(A, axis=0)\n",
        "# cov_mat = (A - mean_vec).T.dot((A - mean_vec)) / (A.shape[0]-1)\n",
        "# print('Cross-covariance matrix \\n%s' %cov_mat)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A6-p7jRUImyQ",
        "colab_type": "text"
      },
      "source": [
        "Obtain the eigenvalues and eigenvectors of the cross-covariance matrix:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0Qqv7kDN9wAy",
        "colab_type": "code",
        "outputId": "139a4d31-7e2d-44b9-b15e-d44d4060d074",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "eigenvalues, eigenvectors = eig(V)\n",
        "\n",
        "print(eigenvalues)\n",
        "print()\n",
        "print(eigenvectors)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[  56.02457535 1137.5874413   786.38798335]\n",
            "\n",
            "[[ 0.6487899  -0.65580225 -0.3859988 ]\n",
            " [-0.74104991 -0.4291978  -0.51636642]\n",
            " [-0.17296443 -0.62105769  0.7644414 ]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vHw5ZumoQZok",
        "colab_type": "text"
      },
      "source": [
        "Choose the *k* eigenvectors that correspond to the *k* largest eigenvalues (where *k* is the number of dimensions of the new feature subspace) --> then you get the **projection matrix**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JWwlWb5dI0-T",
        "colab_type": "text"
      },
      "source": [
        "**Projection onto the new feature space:** The eigenvectors and eigenvalues are taken as the principal components and singular values and used to project the original data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ykHvHHdIT0g1",
        "colab_type": "code",
        "outputId": "0beea7be-f6fb-49f1-8afb-36e5d6e4736e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "Y=C.dot(eigenvectors)\n",
        "print(Y)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[ 10.3820247  -34.37098481  13.66927088]\n",
            " [ -1.47160698  -9.98345733 -47.68820559]\n",
            " [ -3.89273939   3.93481353   2.31599277]\n",
            " [ -9.08167225 -14.69691716  25.24923474]\n",
            " [  4.06399392  55.11654576   6.45370719]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vSDvrtU-JWbd",
        "colab_type": "text"
      },
      "source": [
        "## Automatically Calculate Principal Component Analysis"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CFfAUrvjJuk_",
        "colab_type": "code",
        "outputId": "4ce4f0e5-5a5b-4c78-aac8-38ce4c0c79c7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "A = array([[90, 60, 90], [90, 90, 30], [60, 60,60], [60, 60, 90], [30, 30, 30]])\n",
        "print(A)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[90 60 90]\n",
            " [90 90 30]\n",
            " [60 60 60]\n",
            " [60 60 90]\n",
            " [30 30 30]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6w0dtWoTLYcB",
        "colab_type": "text"
      },
      "source": [
        "Create PCA object"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XDowdhJcLBJ_",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "pca=PCA(n_components=3)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QyGK7IKILfXR",
        "colab_type": "text"
      },
      "source": [
        "Fit on data:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "BreCPau4LjiS",
        "colab_type": "code",
        "outputId": "e878540e-5237-41df-8ec5-7d40c72cf56b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "pca.fit(A)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(copy=True, iterated_power='auto', n_components=3, random_state=None,\n",
              "  svd_solver='auto', tol=0.0, whiten=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 78
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7dG9YT7zLsNJ",
        "colab_type": "text"
      },
      "source": [
        "Get values (meaning see example below):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RmYof0HILqoJ",
        "colab_type": "code",
        "outputId": "98c349c1-38be-4ab6-d6e1-0f025775ff9c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 85
        }
      },
      "source": [
        "print(pca.components_) # number of components to keep\n",
        "print()\n",
        "print(pca.explained_variance_)  # The amount of variance explained by each of the selected components."
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.94446029 -0.32862557]\n",
            " [-0.32862557  0.94446029]]\n",
            "\n",
            "[0.7625315 0.0184779]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5UNHGdhBJFdS",
        "colab_type": "text"
      },
      "source": [
        " Transform data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fxJPz6yWMBVp",
        "colab_type": "code",
        "outputId": "0608e85b-8c43-4e29-ef13-8eef8bfba20a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 102
        }
      },
      "source": [
        "B = pca.transform(A)\n",
        "print(B)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-34.37098481 -13.66927088  10.3820247 ]\n",
            " [ -9.98345733  47.68820559  -1.47160698]\n",
            " [  3.93481353  -2.31599277  -3.89273939]\n",
            " [-14.69691716 -25.24923474  -9.08167225]\n",
            " [ 55.11654576  -6.45370719   4.06399392]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hXVfAZD7ZDqa",
        "colab_type": "text"
      },
      "source": [
        "## More usefull example\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wpr7VoaBifxI",
        "colab_type": "text"
      },
      "source": [
        "**Credit goes to:** Jake VanderPlas\n",
        "\n",
        "The Jupyter notebook version of the Python Data Science Handbook  is available on GitHub. If you find this content useful, please consider supporting the work by buying the book!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UNP5Ud4BZMur",
        "colab_type": "code",
        "outputId": "c11f595c-a0ff-49f2-b64a-0bd474ceacbb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "rng = np.random.RandomState(1)\n",
        "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
        "plt.scatter(X[:, 0], X[:, 1])\n",
        "plt.axis('equal');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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qa//85z+jvLwcZWVlePXVV+HzSZ9VTERExok7HEpKSrBhwwZUVFREfd2FCxfw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\nVbl0+VAweCUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7A49mryMbL6X",
        "colab_type": "text"
      },
      "source": [
        "Fit matrix"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bh9E5IzwZYMB",
        "colab_type": "code",
        "outputId": "ccefa5c5-0d26-4465-f2c3-0b8f0732f196",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "pca = PCA(n_components=2)\n",
        "pca.fit(X)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
              "  svd_solver='auto', tol=0.0, whiten=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-_25-TE9bRce",
        "colab_type": "text"
      },
      "source": [
        "Get values:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bp5dOmHgZgOz",
        "colab_type": "code",
        "outputId": "95215703-8a1f-4d06-a166-b25743d08efd",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "print(pca.components_)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[-0.94446029 -0.32862557]\n",
            " [-0.32862557  0.94446029]]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uRdUM9hLZnnC",
        "colab_type": "code",
        "outputId": "590870ae-c2ef-46a9-87fa-1272e0ec1f85",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "print(pca.explained_variance_)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[0.7625315 0.0184779]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V_cvNSh2bZhA",
        "colab_type": "text"
      },
      "source": [
        "See what these numbers mean:\n",
        "\n",
        "\n",
        "*  \"components\" defines the direction of the vector\n",
        "*   \"explained variance\" defines the squared-length of the vector\n",
        "\n",
        "**Note:** length of the vector is an indication of how \"important\" that axis is in describing the distribution of the data —more precisely, it is a measure of the variance of the data when projected onto that axis\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zGXUxoSUZqqD",
        "colab_type": "code",
        "outputId": "8005fdaf-c9ca-4dd9-a423-20e8b1a648d2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "def draw_vector(v0, v1, ax=None):\n",
        "    ax = ax or plt.gca()\n",
        "    arrowprops=dict(arrowstyle='->',\n",
        "                    linewidth=2,\n",
        "                    shrinkA=0, shrinkB=0)\n",
        "    ax.annotate('', v1, v0, arrowprops=arrowprops)\n",
        "\n",
        "# plot data\n",
        "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
        "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
        "    v = vector * 3 * np.sqrt(length)\n",
        "    draw_vector(pca.mean_, pca.mean_ + v)\n",
        "plt.axis('equal');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mLntd7nLS6fZl0yYN18NxfQxNoVxztkRBnO1M3hzEjrba8XhFAUVRpv5fIZOJUyyu/A1i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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ea1ZrLSRcI5n",
        "colab_type": "text"
      },
      "source": [
        "The projection of each data point onto the principal axes are the **\"principal components\"** of the data."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "iY0Rdb_jZtci",
        "colab_type": "code",
        "outputId": "c7f42f57-a38c-42f0-b590-2a70e9603ba2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 495
        }
      },
      "source": [
        "rng = np.random.RandomState(1)\n",
        "X = np.dot(rng.rand(2, 2), rng.randn(2, 200)).T\n",
        "pca = PCA(n_components=2, whiten=True)\n",
        "pca.fit(X)\n",
        "\n",
        "fig, ax = plt.subplots(1, 2, figsize=(16, 6))\n",
        "fig.subplots_adjust(left=0.0625, right=0.95, wspace=0.1)\n",
        "\n",
        "# plot data\n",
        "ax[0].scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
        "for length, vector in zip(pca.explained_variance_, pca.components_):\n",
        "    v = vector * 3 * np.sqrt(length)\n",
        "    draw_vector(pca.mean_, pca.mean_ + v, ax=ax[0])\n",
        "ax[0].axis('equal');\n",
        "ax[0].set(xlabel='x', ylabel='y', title='input')\n",
        "\n",
        "# plot principal components\n",
        "X_pca = pca.transform(X)\n",
        "ax[1].scatter(X_pca[:, 0], X_pca[:, 1], alpha=0.2)\n",
        "draw_vector([0, 0], [0, 3], ax=ax[1])\n",
        "draw_vector([0, 0], [3, 0], ax=ax[1])\n",
        "ax[1].axis('equal')\n",
        "ax[1].set(xlabel='component 1', ylabel='component 2',\n",
        "          title='principal components',\n",
        "          xlim=(-5, 5), ylim=(-3, 3.1))\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(-3, 3.1),\n",
              " Text(0, 0.5, 'component 2'),\n",
              " (-5, 5),\n",
              " Text(0.5, 0, 'component 1'),\n",
              " Text(0.5, 1.0, 'principal components')]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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bqEsMua0uUWUxc4SIiGpevWdFFJsJUsrsoBNbPDaaLVu2YO3atVi5ciXeeust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\ngKD2H0cgITf+5u/XAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 1152x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d0eNg5GPfStX",
        "colab_type": "text"
      },
      "source": [
        "## PCA as dimensionality reduction\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "j8KzsFyiikP3",
        "colab_type": "text"
      },
      "source": [
        "**Credit goes to:** Jake VanderPlas\n",
        "\n",
        "The Jupyter notebook version of the Python Data Science Handbook  is available on GitHub. If you find this content useful, please consider supporting the work by buying the book!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u42Udv8Dei4f",
        "colab_type": "code",
        "outputId": "1ef89463-5017-497d-ebba-e72d40915fbb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 51
        }
      },
      "source": [
        "pca = PCA(n_components=1)\n",
        "pca.fit(X)\n",
        "X_pca = pca.transform(X)\n",
        "print(\"original shape:   \", X.shape)\n",
        "print(\"transformed shape:\", X_pca.shape)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "original shape:    (200, 2)\n",
            "transformed shape: (200, 1)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Z_z-WXcfhOo",
        "colab_type": "text"
      },
      "source": [
        "The transformed data has been reduced to a single dimension. \n",
        "\n",
        "Plot reduced data it along with the original data:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GJyJCQSDfXmw",
        "colab_type": "code",
        "outputId": "e7a1e2e9-67b7-4374-feda-cf61473930cc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 274
        }
      },
      "source": [
        "X_new = pca.inverse_transform(X_pca)\n",
        "plt.scatter(X[:, 0], X[:, 1], alpha=0.2)\n",
        "plt.scatter(X_new[:, 0], X_new[:, 1], alpha=0.8)\n",
        "plt.axis('equal');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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W5U6769lcTVCVM5QbogFQJp5ELH8DnmzeJp0vEgvrnLehAQ+F0UyBC0f/g5bX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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0jefQrMuf9YE",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "*   Light points: original data\n",
        "*   Orange points: projected data\n",
        "\n",
        "\n",
        "Dimensionality reduction --> the information along the least important principal axis or axes is **removed**, leaving only the component(s) of the data with the **highest variance**."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aMxKJV2GfsWi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}