Signals_Processing_for_ML.ipynb

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  "metadata": {
    "colab": {
      "name": "Signals Processing for ML.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "o2TwXDz_p90k",
        "xxPdz7bbZfBw"
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      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/DanielhCarranza/Curso-Deep-Learning/blob/master/Signals_Processing_for_ML.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Neuuo2YGsGb5"
      },
      "source": [
        "# Signal processing for ML"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sl5V-EWcUNWK"
      },
      "source": [
        "## Fast Fourier Transform\n",
        "Fourier analysis is a method for expressing a function as a sum of periodic components, and for recovering the signal from those components. When both the function and its Fourier transform are replaced with discretized counterparts, it is called the discrete Fourier transform (DFT). The DFT has become a mainstay of numerical computing in part because of a very fast algorithm for computing it, called the Fast Fourier Transform (FFT)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pnYEzShUZesP"
      },
      "source": [
        "from scipy.fftpack import fft , ifft, ifftshift\n",
        "\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "from sklearn.preprocessing import StandardScaler, LabelEncoder\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import accuracy_score\n",
        "from sklearn.decomposition import PCA\n",
        "from sklearn.manifold import TSNE\n",
        "\n",
        "\n",
        "from lightgbm import LGBMClassifier\n",
        "from collections import Counter\n",
        "\n",
        "\n",
        "% matplotlib inline"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "oAiEfinuZew2"
      },
      "source": [
        "help(fft)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IYRTFOXhiumO"
      },
      "source": [
        "The real part of the complex value corresponds with the magnitude, and the imaginary part with the phase of the signal. Since we are only interested in the magnitude of the amplitudes, we use `np.abs()`` to take the real part of the frequency spectrum."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JeroOJnaZe1B"
      },
      "source": [
        "def get_Fast_Fourier_Transform(X, T:int, N:int, Fs:int=None):\n",
        "    \"\"\" Fast Fourier Transform \n",
        "    Args:\n",
        "      X: function or signal: array\n",
        "      T: period = 1/Fs\n",
        "      N: Number of sample points\n",
        "      Fs: sampling frequency\n",
        "    Rerturn\n",
        "    frequency_values \n",
        "    fft_values: vector of complex valued frequencies\n",
        "    \"\"\"\n",
        "    if Fs != None:\n",
        "      T=1/Fs\n",
        "      \n",
        "    frequency_values= np.linspace(0,1.0/(2.0*T), N//2) # we divide by 2, because of Nyquist \n",
        "    fft_values_ =fft(X)\n",
        "    fft_values= 2.0/N * np.abs(fft_values_[0:N//2]) # after N//2 the values really doesn't matter \n",
        "    \n",
        "    return frequency_values, fft_values\n",
        "        "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uC0rVFfShjX-"
      },
      "source": [
        "t_n = 10 \n",
        "N = 1000\n",
        "T = t_n / N \n",
        "f_s = 1/T # 100hz sampling frequency"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "M2PZMo7VZe5J"
      },
      "source": [
        "x=np.linspace(0.0, N*T, N)\n",
        "X =np.sin(25.0 * 2.0*np.pi*x) + 0.5*np.sin(40.0 * 2.0*np.pi*x)\n",
        "\n",
        "frequency_values, fft_values= get_Fast_Fourier_Transform(X, T, N)    "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "05C0fswtZe9c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 302
        },
        "outputId": "b012e7bb-feae-43ba-ac87-c40a29bc54e2"
      },
      "source": [
        "plt.plot(frequency_values, fft_values, linestyle='-', color='blue')\n",
        "plt.xlabel('Frequency [Hz]', fontsize=16)\n",
        "plt.ylabel('Amplitude', fontsize=16)\n",
        "plt.title(\"Frequency domain of the signal\", fontsize=16)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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MoSB5plAQSZlCQfJMoSCSMoWC5JlCQSRlCgXJM4WCSMoUCpJnCgURESlRKIikTDUFyTOF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\nQURESv4/rR9egwAiUkUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o2TwXDz_p90k"
      },
      "source": [
        "## Auto-correlation of a Signal\n",
        "The auto-correlation function calculates the correlation of a signal with a time-delayed version of itself. The idea behind it is that if a signal contain a pattern which repeats itself after a time-period of $\\tau$ seconds, there will be a high correlation between the signal and a $\\tau$ sec delayed version of the signal."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bJLkx0ZJp96n"
      },
      "source": [
        "def autocorr(x):\n",
        "    result = np.correlate(x, x, mode='full')\n",
        "    return result[len(result)//2:] "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LyVZlNl1p9_S"
      },
      "source": [
        "def get_autocorr_values(y_values, T, N):\n",
        "    autocorr_values = autocorr(y_values)\n",
        "    x_values = np.array([T * i for i in range(0, N)])\n",
        "    return x_values, autocorr_values"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o4IUuN38p-Ec"
      },
      "source": [
        "t_values, autocorr_values = get_autocorr_values(X, T, N)\n",
        " "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jjPtNgWOsRYg"
      },
      "source": [
        "# def autocorrelation(x):\n",
        "#     xp = ifftshift((x - np.average(x))/np.std(x))\n",
        "#     n, = xp.shape\n",
        "#     xp = np.r_[xp[:n//2], np.zeros_like(xp), xp[n//2:]]\n",
        "#     f = fft(xp)\n",
        "#     p = np.absolute(f)**2\n",
        "#     pi = ifft(p)\n",
        "#     return np.real(pi)[:n//2]/(np.arange(n//2)[::-1]+n//2)\n",
        "# autocorr_values= autocorrelation(X)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "18ruO21rqp1O",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "outputId": "90c67fc4-d26a-4602-c954-c435db76ae68"
      },
      "source": [
        "plt.plot(t_values, autocorr_values, linestyle='-', color='blue')\n",
        "plt.xlabel('time delay [s]')\n",
        "plt.ylabel('Autocorrelation amplitude')\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Autocorrelation amplitude')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 50
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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ti8mpvSE4169cGV0TI3bc0P4Pu02MNTXQu3fn//8rSrZwk4vpGqy9EL8GjgIuDLYpHYSv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\ncyQp8uelAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xxPdz7bbZfBw"
      },
      "source": [
        "## Power Spectral Density \n",
        "Power **spectral density function** (PSD) shows the strength of the variations(energy) as a function of frequency. In other words, it shows at which frequencies variations are strong and at which frequencies variations are weak. The unit of PSD is energy per frequency(width) and you can obtain energy within a specific frequency range by integrating PSD within that frequency range. Computation of PSD is done directly by the method called FFT or computing autocorrelation function\n",
        "\n",
        "\n",
        "Similar to the FFT, it describes the frequency spectrum of a signal. But in addition to the FFT it also takes the power distribution at each frequency (bin) into account. Generally speaking the locations of the peaks in the frequency spectrum will be the same as in the FFT-case, but the height and width of the peaks will differ. The surface below the peaks corresponds with the power distribution at that frequency.\n",
        "\n",
        "*Note:* \n",
        "Power Spectral Density is the Fourier Transform of the autocorrelation function of a signal. First compute the auto correlation function and then compute its Fourier Transform"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZtHgnnNoZfGU"
      },
      "source": [
        "from scipy.signal import welch"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bTPpw-brZfK2"
      },
      "source": [
        "help(welch)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O1lcMMavZfT-"
      },
      "source": [
        "\n",
        "t_n = 10\n",
        "N = 1000\n",
        "T = t_n / N\n",
        "f_s = 1/T\n",
        " \n",
        "x=np.linspace(0.0, N*T, N)\n",
        "X =np.sin(25.0 * 2.0*np.pi*x) + 0.5*np.sin(40.0 * 2.0*np.pi*x)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TjAgrxNYZfYl"
      },
      "source": [
        "f_values, psd_values = welch(X, fs=f_s)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "higMJlQPZfdJ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "b7fe7151-466b-4c56-fce8-b2ab6cca00ac"
      },
      "source": [
        "plt.plot(f_values, psd_values, linestyle='-', color='blue')\n",
        "plt.xlabel('Frequency [Hz]')\n",
        "plt.ylabel('PSD [V**2 / Hz]')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Z4osmsno1cgAHXioJLCFZ7mJwbwK+mbo9WEBZRILRaAHUD7hUElhCkjUK6CkzuwzYAKwH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\n/wFc6LHHM9Jm/AAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cLU8N0mSZfhk"
      },
      "source": [
        "## Statistical parameter estimation and feature extraction\n",
        "\n",
        "\n",
        "We can calculate the FFT, PSD and the auto-correlation of each signal and use the x and y coordinates of the peaks as input for our classifier.\n",
        "\n",
        "![alt text](http://ataspinar.com/wp-content/uploads/2018/01/signal_to_matrix2-1024x638.png)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jrGiTYgnZfl2"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KiZizdQf4k6T"
      },
      "source": [
        "### Dataset Human Activity Recognition with Smartphones\n",
        "This dataset contains measurements done by 30 people between the ages of 19 to 48. The measurements are done with a smartphone placed on the waist while doing one of the following six activities:\n",
        "\n",
        "* walking,\n",
        "* walking upstairs,\n",
        "* walking downstairs,\n",
        "* sitting,\n",
        "* standing or\n",
        "* laying.\n",
        "\n",
        "The measurements are done at a constant rate of 50 Hz. After filtering out the noise, the signals are cut in fixed-width windows of 2.56 sec with an overlap of 1.28 sec. Each signal will therefore have 50 x 2.56 = 128 samples in total.\n",
        "\n",
        "The smartphone measures three-axial linear body acceleration, three-axial linear total acceleration and three-axial angular velocity. So per measurement, the total signal consists of nine components\n",
        "\n",
        "The sensor acceleration signal, which has gravitational and body motion components, was separated using a Butterworth low-pass filter into body acceleration and gravity. The gravitational force is assumed to have only low frequency components, therefore a filter with 0.3 Hz cutoff frequency was used.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dq0A_QGmRB70",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        },
        "outputId": "26b0eb88-afdb-4dde-8aff-468ee3436d05"
      },
      "source": [
        "# upload your kaggle json file\n",
        "!mkdir -p ~/.kaggle\n",
        "!cp kaggle.json ~/.kaggle/\n",
        "! chmod 600 /root/.kaggle/kaggle.json\n",
        "\n",
        "# download dataset \n",
        "# ! kaggle datasets download -d uciml/human-activity-recognition-with-smartphones\n",
        "! unzip human-activity-recognition-with-smartphones.zip"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Archive:  human-activity-recognition-with-smartphones.zip\n",
            "  inflating: test.csv                \n",
            "  inflating: train.csv               \n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5RfTHqvX3sRv"
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "\n",
        "from sklearn.preprocessing import StandardScaler, LabelEncoder\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.metrics import accuracy_score\n",
        "from sklearn.decomposition import PCA\n",
        "from sklearn.manifold import TSNE\n",
        "\n",
        "\n",
        "from lightgbm import LGBMClassifier\n",
        "from collections import Counter\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AjnowfE4Zfqf"
      },
      "source": [
        "train=pd.read_csv('train.csv')\n",
        "test= pd.read_csv('test.csv')\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X2AMxrD0ZfvA",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 270
        },
        "outputId": "f0502c4e-9663-450e-ac36-0aeb043a7ef6"
      },
      "source": [
        "train.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>tBodyAcc-mean()-X</th>\n",
              "      <th>tBodyAcc-mean()-Y</th>\n",
              "      <th>tBodyAcc-mean()-Z</th>\n",
              "      <th>tBodyAcc-std()-X</th>\n",
              "      <th>tBodyAcc-std()-Y</th>\n",
              "      <th>tBodyAcc-std()-Z</th>\n",
              "      <th>tBodyAcc-mad()-X</th>\n",
              "      <th>tBodyAcc-mad()-Y</th>\n",
              "      <th>tBodyAcc-mad()-Z</th>\n",
              "      <th>tBodyAcc-max()-X</th>\n",
              "      <th>...</th>\n",
              "      <th>fBodyBodyGyroJerkMag-kurtosis()</th>\n",
              "      <th>angle(tBodyAccMean,gravity)</th>\n",
              "      <th>angle(tBodyAccJerkMean),gravityMean)</th>\n",
              "      <th>angle(tBodyGyroMean,gravityMean)</th>\n",
              "      <th>angle(tBodyGyroJerkMean,gravityMean)</th>\n",
              "      <th>angle(X,gravityMean)</th>\n",
              "      <th>angle(Y,gravityMean)</th>\n",
              "      <th>angle(Z,gravityMean)</th>\n",
              "      <th>subject</th>\n",
              "      <th>Activity</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.288585</td>\n",
              "      <td>-0.020294</td>\n",
              "      <td>-0.132905</td>\n",
              "      <td>-0.995279</td>\n",
              "      <td>-0.983111</td>\n",
              "      <td>-0.913526</td>\n",
              "      <td>-0.995112</td>\n",
              "      <td>-0.983185</td>\n",
              "      <td>-0.923527</td>\n",
              "      <td>-0.934724</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.710304</td>\n",
              "      <td>-0.112754</td>\n",
              "      <td>0.030400</td>\n",
              "      <td>-0.464761</td>\n",
              "      <td>-0.018446</td>\n",
              "      <td>-0.841247</td>\n",
              "      <td>0.179941</td>\n",
              "      <td>-0.058627</td>\n",
              "      <td>1</td>\n",
              "      <td>STANDING</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.278419</td>\n",
              "      <td>-0.016411</td>\n",
              "      <td>-0.123520</td>\n",
              "      <td>-0.998245</td>\n",
              "      <td>-0.975300</td>\n",
              "      <td>-0.960322</td>\n",
              "      <td>-0.998807</td>\n",
              "      <td>-0.974914</td>\n",
              "      <td>-0.957686</td>\n",
              "      <td>-0.943068</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.861499</td>\n",
              "      <td>0.053477</td>\n",
              "      <td>-0.007435</td>\n",
              "      <td>-0.732626</td>\n",
              "      <td>0.703511</td>\n",
              "      <td>-0.844788</td>\n",
              "      <td>0.180289</td>\n",
              "      <td>-0.054317</td>\n",
              "      <td>1</td>\n",
              "      <td>STANDING</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.279653</td>\n",
              "      <td>-0.019467</td>\n",
              "      <td>-0.113462</td>\n",
              "      <td>-0.995380</td>\n",
              "      <td>-0.967187</td>\n",
              "      <td>-0.978944</td>\n",
              "      <td>-0.996520</td>\n",
              "      <td>-0.963668</td>\n",
              "      <td>-0.977469</td>\n",
              "      <td>-0.938692</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.760104</td>\n",
              "      <td>-0.118559</td>\n",
              "      <td>0.177899</td>\n",
              "      <td>0.100699</td>\n",
              "      <td>0.808529</td>\n",
              "      <td>-0.848933</td>\n",
              "      <td>0.180637</td>\n",
              "      <td>-0.049118</td>\n",
              "      <td>1</td>\n",
              "      <td>STANDING</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.279174</td>\n",
              "      <td>-0.026201</td>\n",
              "      <td>-0.123283</td>\n",
              "      <td>-0.996091</td>\n",
              "      <td>-0.983403</td>\n",
              "      <td>-0.990675</td>\n",
              "      <td>-0.997099</td>\n",
              "      <td>-0.982750</td>\n",
              "      <td>-0.989302</td>\n",
              "      <td>-0.938692</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.482845</td>\n",
              "      <td>-0.036788</td>\n",
              "      <td>-0.012892</td>\n",
              "      <td>0.640011</td>\n",
              "      <td>-0.485366</td>\n",
              "      <td>-0.848649</td>\n",
              "      <td>0.181935</td>\n",
              "      <td>-0.047663</td>\n",
              "      <td>1</td>\n",
              "      <td>STANDING</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.276629</td>\n",
              "      <td>-0.016570</td>\n",
              "      <td>-0.115362</td>\n",
              "      <td>-0.998139</td>\n",
              "      <td>-0.980817</td>\n",
              "      <td>-0.990482</td>\n",
              "      <td>-0.998321</td>\n",
              "      <td>-0.979672</td>\n",
              "      <td>-0.990441</td>\n",
              "      <td>-0.942469</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.699205</td>\n",
              "      <td>0.123320</td>\n",
              "      <td>0.122542</td>\n",
              "      <td>0.693578</td>\n",
              "      <td>-0.615971</td>\n",
              "      <td>-0.847865</td>\n",
              "      <td>0.185151</td>\n",
              "      <td>-0.043892</td>\n",
              "      <td>1</td>\n",
              "      <td>STANDING</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>5 rows × 563 columns</p>\n",
              "</div>"
            ],
            "text/plain": [
              "   tBodyAcc-mean()-X  tBodyAcc-mean()-Y  tBodyAcc-mean()-Z  tBodyAcc-std()-X  \\\n",
              "0           0.288585          -0.020294          -0.132905         -0.995279   \n",
              "1           0.278419          -0.016411          -0.123520         -0.998245   \n",
              "2           0.279653          -0.019467          -0.113462         -0.995380   \n",
              "3           0.279174          -0.026201          -0.123283         -0.996091   \n",
              "4           0.276629          -0.016570          -0.115362         -0.998139   \n",
              "\n",
              "   tBodyAcc-std()-Y  tBodyAcc-std()-Z  tBodyAcc-mad()-X  tBodyAcc-mad()-Y  \\\n",
              "0         -0.983111         -0.913526         -0.995112         -0.983185   \n",
              "1         -0.975300         -0.960322         -0.998807         -0.974914   \n",
              "2         -0.967187         -0.978944         -0.996520         -0.963668   \n",
              "3         -0.983403         -0.990675         -0.997099         -0.982750   \n",
              "4         -0.980817         -0.990482         -0.998321         -0.979672   \n",
              "\n",
              "   tBodyAcc-mad()-Z  tBodyAcc-max()-X    ...     \\\n",
              "0         -0.923527         -0.934724    ...      \n",
              "1         -0.957686         -0.943068    ...      \n",
              "2         -0.977469         -0.938692    ...      \n",
              "3         -0.989302         -0.938692    ...      \n",
              "4         -0.990441         -0.942469    ...      \n",
              "\n",
              "   fBodyBodyGyroJerkMag-kurtosis()  angle(tBodyAccMean,gravity)  \\\n",
              "0                        -0.710304                    -0.112754   \n",
              "1                        -0.861499                     0.053477   \n",
              "2                        -0.760104                    -0.118559   \n",
              "3                        -0.482845                    -0.036788   \n",
              "4                        -0.699205                     0.123320   \n",
              "\n",
              "   angle(tBodyAccJerkMean),gravityMean)  angle(tBodyGyroMean,gravityMean)  \\\n",
              "0                              0.030400                         -0.464761   \n",
              "1                             -0.007435                         -0.732626   \n",
              "2                              0.177899                          0.100699   \n",
              "3                             -0.012892                          0.640011   \n",
              "4                              0.122542                          0.693578   \n",
              "\n",
              "   angle(tBodyGyroJerkMean,gravityMean)  angle(X,gravityMean)  \\\n",
              "0                             -0.018446             -0.841247   \n",
              "1                              0.703511             -0.844788   \n",
              "2                              0.808529             -0.848933   \n",
              "3                             -0.485366             -0.848649   \n",
              "4                             -0.615971             -0.847865   \n",
              "\n",
              "   angle(Y,gravityMean)  angle(Z,gravityMean)  subject  Activity  \n",
              "0              0.179941             -0.058627        1  STANDING  \n",
              "1              0.180289             -0.054317        1  STANDING  \n",
              "2              0.180637             -0.049118        1  STANDING  \n",
              "3              0.181935             -0.047663        1  STANDING  \n",
              "4              0.185151             -0.043892        1  STANDING  \n",
              "\n",
              "[5 rows x 563 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b-jrcrUDEE-m"
      },
      "source": [
        "labels= train.iloc[:,-1]\n",
        "train=  train.iloc[:,:-2]\n",
        "test_labels= test.iloc[:,-1]\n",
        "test=  test.iloc[:,:-2]\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EmljOTip6aSb",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 365
        },
        "outputId": "ea38ea6d-5cff-4edc-9d4b-d0fbecd5bc46"
      },
      "source": [
        "t=np.arange(0,len(train.iloc[:,0]),1)\n",
        "plt.plot(t,train.iloc[:,0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f9a38deb7f0>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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uaXjLum2HvTKcTyqn7rUgZ4sq8JbGqU7d1dU14sOcYx7tQ8yy9/fLvq+2UGLU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\nAelWd3v0Y45iAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 576x396 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JxkMzmQcZfzw",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 153
        },
        "outputId": "aae4367f-da94-4efd-d181-5eef2746a7d8"
      },
      "source": [
        "print(f'Activities {set(labels)} ')\n",
        "labels.value_counts()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Activities {'LAYING', 'WALKING_UPSTAIRS', 'SITTING', 'STANDING', 'WALKING', 'WALKING_DOWNSTAIRS'} \n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LAYING                1407\n",
              "STANDING              1374\n",
              "SITTING               1286\n",
              "WALKING               1226\n",
              "WALKING_UPSTAIRS      1073\n",
              "WALKING_DOWNSTAIRS     986\n",
              "Name: Activity, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 94
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cNlri3mIZf4T",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 607
        },
        "outputId": "fcbaa32c-9df9-4b6f-cce9-3c1fc3bc1e5b"
      },
      "source": [
        "pd.DataFrame.from_dict(Counter([col.split('-')[0].split('(')[0] for col in train.columns]), orient='index').rename(columns={0:'count'}).sort_values('count', ascending=False)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>count</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>fBodyGyro</th>\n",
              "      <td>79</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fBodyAcc</th>\n",
              "      <td>79</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fBodyAccJerk</th>\n",
              "      <td>79</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyAcc</th>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyAccJerk</th>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyGyro</th>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyGyroJerk</th>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tGravityAcc</th>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fBodyBodyGyroJerkMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fBodyBodyGyroMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fBodyBodyAccJerkMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fBodyAccMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyGyroJerkMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyGyroMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyAccJerkMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tGravityAccMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>tBodyAccMag</th>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>angle</th>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                      count\n",
              "fBodyGyro                79\n",
              "fBodyAcc                 79\n",
              "fBodyAccJerk             79\n",
              "tBodyAcc                 40\n",
              "tBodyAccJerk             40\n",
              "tBodyGyro                40\n",
              "tBodyGyroJerk            40\n",
              "tGravityAcc              40\n",
              "fBodyBodyGyroJerkMag     13\n",
              "fBodyBodyGyroMag         13\n",
              "fBodyBodyAccJerkMag      13\n",
              "fBodyAccMag              13\n",
              "tBodyGyroJerkMag         13\n",
              "tBodyGyroMag             13\n",
              "tBodyAccJerkMag          13\n",
              "tGravityAccMag           13\n",
              "tBodyAccMag              13\n",
              "angle                     7"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MsuF0BGnDKpV"
      },
      "source": [
        "### Model without preproccessing"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zr6zEjbgZf9P"
      },
      "source": [
        "from sklearn.ensemble import RandomForestClassifier\n",
        "from sklearn.metrics import classification_report\n",
        " \n",
        "\n",
        "clf = RandomForestClassifier(n_estimators=1000)\n",
        "clf.fit(train, labels)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sG0pVbG6Z3d5"
      },
      "source": [
        "sensor=np.expand_dims(X_test.iloc[0,:],axis=0)\n",
        "predecir_sensor= modelo.predict(sensor)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Yk12igyYaMXz"
      },
      "source": [
        "\n",
        "pred = modelo.predict(X_test)\n",
        "print(classification_report(y_test, pred))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eLWHXmk8LezC"
      },
      "source": [
        "\n",
        "print(\"Accuracy on training set is : {:.4f}\".format(clf.score(train, labels)))\n",
        "print(\"Accuracy on test set is : {:.4f}\".format(clf.score(test, test_labels)))\n",
        "Y_test_pred = clf.predict(test)\n",
        "print(classification_report(test_labels, Y_test_pred))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VVrdpuGDGu10"
      },
      "source": [
        "### Model  with Principal Component Analysis"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nL_aSIeFKH9N"
      },
      "source": [
        "train=pd.read_csv('train.csv')\n",
        "test= pd.read_csv('test.csv')\n",
        "\n",
        "data = pd.concat([train, test], axis=0).reset_index(drop=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-UJmGZkaGBOd"
      },
      "source": [
        "pca_data = data.iloc[:,:-2].copy()\n",
        "labels = data.iloc[:,-1]\n",
        "\n",
        "# Scale data\n",
        "scl = StandardScaler()\n",
        "pca_data = scl.fit_transform(pca_data)\n",
        "\n",
        "# Reduce dimensions (speed up)\n",
        "pca = PCA(n_components=0.9, random_state=3)\n",
        "pca_data = pca.fit_transform(pca_data)\n",
        "\n",
        "\n",
        "# Encode labels \n",
        "enc = LabelEncoder()\n",
        "label_encoded = enc.fit_transform(labels)\n",
        "\n",
        "# Split the data\n",
        "X_train, X_test, y_train, y_test = train_test_split(pca_data, label_encoded, random_state=3)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HPxNLN14NZXr"
      },
      "source": [
        "#### LGBM Classifier with PCA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3aiQSFfoZgC1"
      },
      "source": [
        "# Create the model\n",
        "lgbm = LGBMClassifier(n_estimators=500, random_state=3)\n",
        "lgbm = lgbm.fit(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "87HqcYBEFo5d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "a3f3a22a-ed9b-4bfc-c10a-8fecbceeca19"
      },
      "source": [
        "y_pred=lgbm.predict(X_test)\n",
        "score = accuracy_score(y_true=y_test, y_pred=y_pred)\n",
        "print('Accuracy on testset:\\t{:.4f}\\n'.format(score))\n",
        "print(classification_report(y_test, y_pred))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy on testset:\t0.9553\n",
            "\n",
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.99      0.99      0.99       502\n",
            "           1       0.92      0.87      0.89       443\n",
            "           2       0.89      0.93      0.91       457\n",
            "           3       0.99      0.98      0.99       446\n",
            "           4       0.98      0.97      0.98       343\n",
            "           5       0.96      0.98      0.97       384\n",
            "\n",
            "   micro avg       0.96      0.96      0.96      2575\n",
            "   macro avg       0.96      0.96      0.96      2575\n",
            "weighted avg       0.96      0.96      0.96      2575\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cU5VxcC9NDCu"
      },
      "source": [
        "#### Random Forest Classifier with PCA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uWDpRQXEFo-U",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 272
        },
        "outputId": "c565751d-91c7-4f81-9546-147ed10f5e97"
      },
      "source": [
        "clf = RandomForestClassifier(n_estimators=1000)\n",
        "clf.fit(X_train, y_train)\n",
        "print(\"Accuracy on training set is : {:.4f}\".format(clf.score(X_train, y_train)))\n",
        "print(\"Accuracy on test set is : {:.4f}\".format(clf.score(X_test, y_test)))\n",
        "Y_test_pred = clf.predict(X_test)\n",
        "print(classification_report(y_test, Y_test_pred))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy on training set is : 1.0000\n",
            "Accuracy on test set is : 0.9429\n",
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.98      0.99      0.99       502\n",
            "           1       0.93      0.83      0.88       443\n",
            "           2       0.87      0.94      0.90       457\n",
            "           3       0.97      0.98      0.97       446\n",
            "           4       0.96      0.95      0.95       343\n",
            "           5       0.96      0.97      0.96       384\n",
            "\n",
            "   micro avg       0.94      0.94      0.94      2575\n",
            "   macro avg       0.94      0.94      0.94      2575\n",
            "weighted avg       0.94      0.94      0.94      2575\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cDV1OKWzFpEx"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "584ZvK8xFpKd"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hULdSffihjXH"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}