"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.hist(dataset['Months_on_book']);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The above figure shows more normal distributed variable. The biggest number of customers (~3500) have 36 months on booking. More investigation can be conducted to understand this output. The biggest number of customers at 36 months can be linked to a company campain 36 months ago or every new customer gets 36 as a default month_on_booking."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 93,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.hist(dataset['Credit_Limit']);"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "The figure shows skewness to the right. Most of the customers have less than 5000 credit limit while smaller number of customers have over this limit. This figure confirms the revealed difference between the medain and the mean of Credit_Limit variable earlier."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Let's show the mean and the median on the histgram."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 94,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(3549.0, 2550, 'Median')"
+ ]
+ },
+ "execution_count": 94,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure(figsize=(10,7))\n",
+ "# Use 30 bins for a better representation for the distribution\n",
+ "plt.hist(dataset['Credit_Limit'], bins=30)\n",
+ "plt.vlines(dataset['Credit_Limit'].mean(), 0, 2500, colors='Black')\n",
+ "plt.vlines(dataset['Credit_Limit'].median(), 0, 2500,colors='Black')\n",
+ "\n",
+ "# Print the mean and median text over the vertical lines\n",
+ "plt.text(dataset['Credit_Limit'].mean()-1000, 2500+50, 'Mean')\n",
+ "plt.text(dataset['Credit_Limit'].median()-1000, 2500+50, 'Median')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Data Transformation: Normalization and Log"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Two ways to transform skewed distribution into more normal one. Normalisation using min-max scaler and using log transformation."
]
},
{
"cell_type": "code",
- "execution_count": 22,
+ "execution_count": 95,
"metadata": {},
"outputs": [],
"source": [
- "dataset['CLIENTNUM'] = [x + 90032 for x in list(range(len(dataset)))]"
+ "# Define a funbction for min-max scaler\n",
+ "def get_normalised_value(column):\n",
+ " max_val = column.max()\n",
+ " min_val = column.min()\n",
+ " y = (column-min_val)/(max_val-min_val)\n",
+ " return y\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Since credit_limit variable is skewed, we will try using the normalisation method to solve the problem. This method will make the values range between 0 and 1."
]
},
{
"cell_type": "code",
- "execution_count": 23,
+ "execution_count": 96,
"metadata": {},
"outputs": [],
"source": [
- "dataset.to_csv('BankChurners_v2.csv', index=False)"
+ "# Create a new column create the normalised value of Credit_Limit\n",
+ "dataset['Credit_Limit_normalised'] = get_normalised_value(dataset['Credit_Limit'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 97,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "0.0\n",
+ "1.0\n",
+ "0.21747744547036094\n",
+ "0.09404220970623714\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Check the min and max values of the new columnn\n",
+ "print(dataset['Credit_Limit_normalised'].min())\n",
+ "print(dataset['Credit_Limit_normalised'].max())\n",
+ "print(dataset['Credit_Limit_normalised'].mean())\n",
+ "print(dataset['Credit_Limit_normalised'].median())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We noticed that the difference between the mean and the median is smaller after the normalisation."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "log from Numpy is used for data transformation of the same variable to compare between the two methods. "
]
},
{
"cell_type": "code",
- "execution_count": null,
+ "execution_count": 98,
"metadata": {},
"outputs": [],
- "source": []
+ "source": [
+ "# Data transformation using log \n",
+ "dataset['Credit_Limit_log']= np.log(dataset['Credit_Limit'])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 99,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "7.271217139609844\n",
+ "10.449178263628198\n",
+ "8.60341207921584\n",
+ "8.422662707570003\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Check the min and max values of the new columnn\n",
+ "print(dataset['Credit_Limit_log'].min())\n",
+ "print(dataset['Credit_Limit_log'].max())\n",
+ "print(dataset['Credit_Limit_log'].mean())\n",
+ "print(dataset['Credit_Limit_log'].median())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "We noticed that the difference between the mean and the median is too small after the log transformation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 100,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "C:\\Users\\alaah\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.10_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python310\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning:\n",
+ "\n",
+ "use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
+ "\n",
+ "C:\\Users\\alaah\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.10_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python310\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning:\n",
+ "\n",
+ "use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
+ "\n",
+ "C:\\Users\\alaah\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.10_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python310\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning:\n",
+ "\n",
+ "use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
+ "\n",
+ "C:\\Users\\alaah\\AppData\\Local\\Packages\\PythonSoftwareFoundation.Python.3.10_qbz5n2kfra8p0\\LocalCache\\local-packages\\Python310\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning:\n",
+ "\n",
+ "use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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