PCA Lab practice scripts.ipynb

{
    "cells": [
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "This notebook is designed to run in a IBM Watson Studio default runtime (NOT the Watson Studio Apache Spark Runtime as the default runtime with 1 vCPU is free of charge). Therefore, we install Apache Spark in local mode for test purposes only. Please don't use it in production.\n\nIn case you are facing issues, please read the following two documents first:\n\nhttps://github.com/IBM/skillsnetwork/wiki/Environment-Setup\n\nhttps://github.com/IBM/skillsnetwork/wiki/FAQ\n\nThen, please feel free to ask:\n\nhttps://coursera.org/learn/machine-learning-big-data-apache-spark/discussions/all\n\nPlease make sure to follow the guidelines before asking a question:\n\nhttps://github.com/IBM/skillsnetwork/wiki/FAQ#im-feeling-lost-and-confused-please-help-me\n\n\nIf running outside Watson Studio, this should work as well. In case you are running in an Apache Spark context outside Watson Studio, please remove the Apache Spark setup in the first notebook cells."
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": "from IPython.display import Markdown, display\ndef printmd(string):\n    display(Markdown('# <span style=\"color:red\">'+string+'</span>'))\n\n\nif ('sc' in locals() or 'sc' in globals()):\n    printmd('<<<<<!!!!! It seems that you are running in a IBM Watson Studio Apache Spark Notebook. Please run it in an IBM Watson Studio Default Runtime (without Apache Spark) !!!!!>>>>>')\n"
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": "!pip install pyspark==2.4.5"
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": "try:\n    from pyspark import SparkContext, SparkConf\n    from pyspark.sql import SparkSession\nexcept ImportError as e:\n    printmd('<<<<<!!!!! Please restart your kernel after installing Apache Spark !!!!!>>>>>')"
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": "sc = SparkContext.getOrCreate(SparkConf().setMaster(\"local[*]\"))\n\nspark = SparkSession \\\n    .builder \\\n    .getOrCreate()"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "# Exercise 3.2\nWelcome to the last exercise of this course. This is also the most advanced one because it somehow glues everything together you've learned. \n\nThese are the steps you will do:\n- load a data frame from cloudant/ApacheCouchDB\n- perform feature transformation by calculating minimal and maximal values of different properties on time windows (we'll explain what a time windows is later in here)\n- reduce these now twelve dimensions to three using the PCA (Principal Component Analysis) algorithm of SparkML (Spark Machine Learning) => We'll actually make use of SparkML a lot more in the next course\n- plot the dimensionality reduced data set"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Now it is time to grab a PARQUET file and create a dataframe out of it. Using SparkSQL you can handle it like a database. "
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": "!wget https://github.com/IBM/coursera/blob/master/coursera_ds/washing.parquet?raw=true\n!mv washing.parquet?raw=true washing.parquet"
        },
        {
            "cell_type": "code",
            "execution_count": null,
            "metadata": {},
            "outputs": [],
            "source": "df = spark.read.parquet('washing.parquet')\ndf.createOrReplaceTempView('washing')\ndf.show()"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "This is the feature transformation part of this exercise. Since our table is mixing schemas from different sensor data sources we are creating new features. In other word we use existing columns to calculate new ones. We only use min and max for now, but using more advanced aggregations as we've learned in week three may improve the results. We are calculating those aggregations over a sliding window \"w\". This window is defined in the SQL statement and basically reads the table by a one by one stride in direction of increasing timestamp. Whenever a row leaves the window a new one is included. Therefore this window is called sliding window (in contrast to tubling, time or count windows). More on this can be found here: https://flink.apache.org/news/2015/12/04/Introducing-windows.html\n\n"
        },
        {
            "cell_type": "code",
            "execution_count": 2,
            "metadata": {},
            "outputs": [],
            "source": "result = spark.sql(\"\"\"\nSELECT * from (\n    SELECT\n    min(temperature) over w as min_temperature,\n    max(temperature) over w as max_temperature, \n    min(voltage) over w as min_voltage,\n    max(voltage) over w as max_voltage,\n    min(flowrate) over w as min_flowrate,\n    max(flowrate) over w as max_flowrate,\n    min(frequency) over w as min_frequency,\n    max(frequency) over w as max_frequency,\n    min(hardness) over w as min_hardness,\n    max(hardness) over w as max_hardness,\n    min(speed) over w as min_speed,\n    max(speed) over w as max_speed\n    FROM washing \n    WINDOW w AS (ORDER BY ts ROWS BETWEEN CURRENT ROW AND 10 FOLLOWING) \n)\nWHERE min_temperature is not null \nAND max_temperature is not null\nAND min_voltage is not null\nAND max_voltage is not null\nAND min_flowrate is not null\nAND max_flowrate is not null\nAND min_frequency is not null\nAND max_frequency is not null\nAND min_hardness is not null\nAND min_speed is not null\nAND max_speed is not null   \n\"\"\")"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Since this table contains null values also our window might contain them. In case for a certain feature all values in that window are null we obtain also null. As we can see here (in my dataset) this is the case for 9 rows."
        },
        {
            "cell_type": "code",
            "execution_count": 3,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": "7"
                    },
                    "execution_count": 3,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": "df.count()-result.count()"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Now we import some classes from SparkML. PCA for the actual algorithm. Vectors for the data structure expected by PCA and VectorAssembler to transform data into these vector structures."
        },
        {
            "cell_type": "code",
            "execution_count": 4,
            "metadata": {},
            "outputs": [],
            "source": "from pyspark.ml.feature import PCA\nfrom pyspark.ml.linalg import Vectors\nfrom pyspark.ml.feature import VectorAssembler"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Let's define a vector transformation helper class which takes all our input features (result.columns) and created one additional column called \"features\" which contains all our input features as one single column wrapped in \"DenseVector\" objects"
        },
        {
            "cell_type": "code",
            "execution_count": 5,
            "metadata": {},
            "outputs": [],
            "source": "assembler = VectorAssembler(inputCols=result.columns, outputCol=\"features\")"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Now we actually transform the data, note that this is highly optimized code and runs really fast in contrast if we had implemented it."
        },
        {
            "cell_type": "code",
            "execution_count": 6,
            "metadata": {},
            "outputs": [],
            "source": "features = assembler.transform(result)"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Let's have a look at how this new additional column \"features\" looks like:"
        },
        {
            "cell_type": "code",
            "execution_count": 7,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": "[DenseVector([81.0, 100.0, 221.0, 223.0, 11.0, 11.0, 68.0, 76.0, 71.0, 78.0, 1033.0, 1033.0]),\n DenseVector([81.0, 100.0, 221.0, 223.0, 11.0, 11.0, 68.0, 76.0, 72.0, 78.0, 1033.0, 1033.0]),\n DenseVector([81.0, 100.0, 221.0, 223.0, 11.0, 11.0, 68.0, 76.0, 72.0, 80.0, 1033.0, 1033.0]),\n DenseVector([81.0, 100.0, 222.0, 223.0, 11.0, 11.0, 68.0, 74.0, 72.0, 80.0, 1033.0, 1046.0]),\n DenseVector([81.0, 100.0, 222.0, 223.0, 11.0, 11.0, 68.0, 74.0, 73.0, 80.0, 1033.0, 1046.0]),\n DenseVector([80.0, 94.0, 222.0, 223.0, 11.0, 11.0, 68.0, 74.0, 73.0, 80.0, 1033.0, 1046.0]),\n DenseVector([80.0, 94.0, 222.0, 236.0, 11.0, 11.0, 68.0, 74.0, 73.0, 80.0, 1046.0, 1046.0]),\n DenseVector([80.0, 94.0, 222.0, 236.0, 11.0, 11.0, 68.0, 74.0, 73.0, 80.0, 1046.0, 1046.0]),\n DenseVector([80.0, 94.0, 222.0, 236.0, 11.0, 11.0, 71.0, 74.0, 73.0, 80.0, 1046.0, 1046.0]),\n DenseVector([80.0, 94.0, 222.0, 236.0, 11.0, 11.0, 71.0, 74.0, 73.0, 80.0, 1046.0, 1046.0])]"
                    },
                    "execution_count": 7,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": "features.rdd.map(lambda r : r.features).take(10)"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Since the source data set has been prepared as a list of DenseVectors we can now apply PCA. Note that the first line again only prepares the algorithm by finding the transformation matrices (fit method)"
        },
        {
            "cell_type": "code",
            "execution_count": 8,
            "metadata": {},
            "outputs": [],
            "source": "pca = PCA(k=3, inputCol=\"features\", outputCol=\"pcaFeatures\")\nmodel = pca.fit(features)"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Now we can actually transform the data. Let's have a look at the first 20 rows"
        },
        {
            "cell_type": "code",
            "execution_count": 9,
            "metadata": {},
            "outputs": [
                {
                    "name": "stdout",
                    "output_type": "stream",
                    "text": "+-----------------------------------------------------------+\n|pcaFeatures                                                |\n+-----------------------------------------------------------+\n|[1459.9789705814187,-18.745237781780922,70.78430794796873] |\n|[1459.995481828676,-19.11343146165273,70.72738871425986]   |\n|[1460.0895843561282,-20.969471062922928,70.75630600322052] |\n|[1469.6993929419532,-20.403124647615513,62.013569674880955]|\n|[1469.7159041892107,-20.771318327487293,61.95665044117209] |\n|[1469.7128317338704,-20.790751117222456,61.896106678330966]|\n|[1478.3530264572928,-20.294557029728722,71.67550104809607] |\n|[1478.3530264572928,-20.294557029728722,71.67550104809607] |\n|[1478.3686036138165,-20.260626897636314,71.63355353606426] |\n|[1478.3686036138165,-20.260626897636314,71.63355353606426] |\n|[1483.5412027684088,-20.006222577501354,66.82710394284209] |\n|[1483.5171090223353,-20.867020421583753,66.86707301954084] |\n|[1483.4224268542928,-19.87574823665505,66.93027077913985]  |\n|[1483.4224268542928,-19.87574823665505,66.93027077913985]  |\n|[1488.103073547271,-19.311848573386925,72.1626182636411]   |\n|[1488.1076926849646,-19.311945711095063,72.27621605605316] |\n|[1488.0135901575127,-17.455906109824838,72.2472987670925]  |\n|[1488.026374556614,-17.47632766649086,72.2214703423]       |\n|[1465.1644738447062,-17.50333829280811,47.06072898272612]  |\n|[1465.1644738447062,-17.50333829280811,47.06072898272612]  |\n+-----------------------------------------------------------+\nonly showing top 20 rows\n\n"
                }
            ],
            "source": "result_pca = model.transform(features).select(\"pcaFeatures\")\nresult_pca.show(truncate=False)"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "So we obtained three completely new columns which we can plot now. Let run a final check if the number of rows is the same."
        },
        {
            "cell_type": "code",
            "execution_count": 10,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "text/plain": "2051"
                    },
                    "execution_count": 10,
                    "metadata": {},
                    "output_type": "execute_result"
                }
            ],
            "source": "result_pca.count()"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Cool, this works as expected. Now we obtain a sample and read each of the three columns into a python list"
        },
        {
            "cell_type": "code",
            "execution_count": 26,
            "metadata": {},
            "outputs": [],
            "source": "rdd = result_pca.rdd.sample(False,0.8)"
        },
        {
            "cell_type": "code",
            "execution_count": 27,
            "metadata": {},
            "outputs": [],
            "source": "x = rdd.map(lambda a : a.pcaFeatures).map(lambda a : a[0]).collect()"
        },
        {
            "cell_type": "code",
            "execution_count": 28,
            "metadata": {},
            "outputs": [],
            "source": "y = rdd.map(lambda a : a.pcaFeatures).map(lambda a : a[1]).collect()"
        },
        {
            "cell_type": "code",
            "execution_count": 29,
            "metadata": {},
            "outputs": [],
            "source": "z = rdd.map(lambda a : a.pcaFeatures).map(lambda a : a[2]).collect()"
        },
        {
            "cell_type": "markdown",
            "metadata": {},
            "source": "Finally we plot the three lists and name each of them as dimension 1-3 in the plot"
        },
        {
            "cell_type": "code",
            "execution_count": 30,
            "metadata": {},
            "outputs": [
                {
                    "data": {
                        "image/png": 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\n",
                        "text/plain": "<Figure size 432x288 with 1 Axes>"
                    },
                    "metadata": {
                        "needs_background": "light"
                    },
                    "output_type": "display_data"
                }
            ],
            "source": "%matplotlib inline\nimport matplotlib.pyplot as plt\nfrom mpl_toolkits.mplot3d import Axes3D\n\n\nfig = plt.figure()\nax = fig.add_subplot(111, projection='3d')\n\n\n\n\nax.scatter(x,y,z, c='r', marker='o')\n\nax.set_xlabel('dimension1')\nax.set_ylabel('dimension2')\nax.set_zlabel('dimension3')\n\nplt.show()"
        },
        {
            "cell_type": "markdown",
            "metadata": {
                "collapsed": true
            },
            "source": "Congratulations, we are done! We can see two clusters in the data set. We can also see a third cluster which either can be outliers or a real cluster. In the next course we will actually learn how to compute clusters automatically. For now we know that the data indicates that there are two semi-stable states of the machine and sometime we see some anomalies since those data points don't fit into one of the two clusters."
        }
    ],
    "metadata": {
        "kernelspec": {
            "display_name": "Python 3.6 with Spark",
            "language": "python3",
            "name": "python36"
        },
        "language_info": {
            "codemirror_mode": {
                "name": "ipython",
                "version": 3
            },
            "file_extension": ".py",
            "mimetype": "text/x-python",
            "name": "python",
            "nbconvert_exporter": "python",
            "pygments_lexer": "ipython3",
            "version": "3.6.8"
        }
    },
    "nbformat": 4,
    "nbformat_minor": 1
}