# Import libraries necessary for this project
import numpy as np
import pandas as pd
from IPython.display import display # Allows the use of display() for DataFrames

# Import supplementary visualizations code visuals.py
import visuals as vs

# Pretty display for notebooks
%matplotlib inline

# Load the wholesale customers dataset
try:
    data = pd.read_csv("customers.csv")
    data.drop(['Region', 'Channel'], axis = 1, inplace = True)
    print "Wholesale customers dataset has {} samples with {} features each.".format(*data.shape)
except:
    print "Dataset could not be loaded. Is the dataset missing?"

"""
Explanation: Machine Learning Engineer Nanodegree
Unsupervised Learning
Project: Creating Customer Segments
Welcome to the third project of the Machine Learning Engineer Nanodegree! In this notebook, some template code has already been provided for you, and it will be your job to implement the additional functionality necessary to successfully complete this project. Sections that begin with 'Implementation' in the header indicate that the following block of code will require additional functionality which you must provide. Instructions will be provided for each section and the specifics of the implementation are marked in the code block with a 'TODO' statement. Please be sure to read the instructions carefully!
In addition to implementing code, there will be questions that you must answer which relate to the project and your implementation. Each section where you will answer a question is preceded by a 'Question X' header. Carefully read each question and provide thorough answers in the following text boxes that begin with 'Answer:'. Your project submission will be evaluated based on your answers to each of the questions and the implementation you provide.  

Note: Code and Markdown cells can be executed using the Shift + Enter keyboard shortcut. In addition, Markdown cells can be edited by typically double-clicking the cell to enter edit mode.

Getting Started
In this project, you will analyze a dataset containing data on various customers' annual spending amounts (reported in monetary units) of diverse product categories for internal structure. One goal of this project is to best describe the variation in the different types of customers that a wholesale distributor interacts with. Doing so would equip the distributor with insight into how to best structure their delivery service to meet the needs of each customer.
The dataset for this project can be found on the UCI Machine Learning Repository. For the purposes of this project, the features 'Channel' and 'Region' will be excluded in the analysis — with focus instead on the six product categories recorded for customers.
Run the code block below to load the wholesale customers dataset, along with a few of the necessary Python libraries required for this project. You will know the dataset loaded successfully if the size of the dataset is reported.
End of explanation
"""


# Display a description of the dataset
display(data.describe())


"""
Explanation: Data Exploration
In this section, you will begin exploring the data through visualizations and code to understand how each feature is related to the others. You will observe a statistical description of the dataset, consider the relevance of each feature, and select a few sample data points from the dataset which you will track through the course of this project.
Run the code block below to observe a statistical description of the dataset. Note that the dataset is composed of six important product categories: 'Fresh', 'Milk', 'Grocery', 'Frozen', 'Detergents_Paper', and 'Delicatessen'. Consider what each category represents in terms of products you could purchase.
End of explanation
"""


# TODO: Select three indices of your choice you wish to sample from the dataset

#print data.nlargest(5,'Delicatessen')
#print data.nlargest(5,'Fresh')
#print data.nlargest(5, 'Grocery')
#indices = [183,181,85]
indices = [23,125,333]
# Create a DataFrame of the chosen samples
samples = pd.DataFrame(data.loc[indices], columns = data.keys()).reset_index(drop = True)
print "Chosen samples of wholesale customers dataset:"
display(samples)


"""
Explanation: Implementation: Selecting Samples
To get a better understanding of the customers and how their data will transform through the analysis, it would be best to select a few sample data points and explore them in more detail. In the code block below, add three indices of your choice to the indices list which will represent the customers to track. It is suggested to try different sets of samples until you obtain customers that vary significantly from one another.
End of explanation
"""


from matplotlib import pyplot
#analyze density of the data
data.plot(kind='density', subplots=True, layout=(4,4), sharex=False, legend=True,
fontsize=1)
pyplot.show()
#analyze boxplots
data.plot(kind='box', subplots=True, layout=(4,4), sharex=False, sharey=False,
fontsize=8)
pyplot.show()
#analyze scatterplot for cross correlation
import seaborn as sns
sns.set()
sns.pairplot(data)
#Looks like Detergents_paper is correlated with Grocery. Let's see if we can predict "Detergents_Paper" based on all other features
# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature

new_data = data.copy()
new_data.drop(['Detergents_Paper'], axis = 1, inplace = True)
X = new_data.values
Y = data['Detergents_Paper'].values

from sklearn.tree import DecisionTreeRegressor
from sklearn.model_selection import train_test_split

validation_size = 0.25
seed = 7

# TODO: Split the data into training and testing sets using the given feature as the target
X_train, X_validation, Y_train, Y_validation = train_test_split(X, Y,
test_size=validation_size, random_state=seed)

# TODO: Create a decision tree regressor and fit it to the training set
regressor = DecisionTreeRegressor(random_state=seed)
regressor = regressor.fit(X_train, Y_train)

# TODO: Report the score of the prediction using the testing set
from sklearn.metrics import r2_score
Y_pred = regressor.predict(X_validation)

score =  r2_score(Y_validation, Y_pred)

n = float(len(Y_validation))
print "sample size n is: ", n
k=float(len(new_data.columns))
print "no of independant variables is: ", k
print "R^2 score is: ", score
r2adj = float(1-(n-1)/(n-k-1)*(1-score))

print "Adjusted R^2 is: ", r2adj


"""
Explanation: Question 1
Consider the total purchase cost of each product category and the statistical description of the dataset above for your sample customers.
What kind of establishment (customer) could each of the three samples you've chosen represent?
Hint: Examples of establishments include places like markets, cafes, and retailers, among many others. Avoid using names for establishments, such as saying "McDonalds" when describing a sample customer as a restaurant.
Answer:
The first establishment is like a "cafe/deli" in downntown / business district that people converge for lunch and go back to work with a little bit of grocery. It is #2 in Delicatessen sales (Deliberately excluded the top one *index 183*. It's value of 47943 is more than 17 times the standard deviation from the mean)
The second establishment is possibly a chain grocery store that focuses on "Fresh Produce". In my hometown there is one whose name starts with 'Mei...". It is #2 in Fresh sales (Deliberately excluded the top one *index 183*. It's value of 112151 is more than 7 times the standard deviation from the mean)
The third establishment is an exceptional regular grocery that ranks #2 on grocery. (Deliberately excluded the top ranker  *index 85*. It's value of 92780 is more than 9 times the standard deviation from the mean)
If we consider gaussian distribution of these *features*, the top rankers in each category are much more than 3 times standard deviation away from the mean and hence likely outlier. Just to be safe, they have not been selected.
Implementation: Feature Relevance
One interesting thought to consider is if one (or more) of the six product categories is actually relevant for understanding customer purchasing. That is to say, is it possible to determine whether customers purchasing some amount of one category of products will necessarily purchase some proportional amount of another category of products? We can make this determination quite easily by training a supervised regression learner on a subset of the data with one feature removed, and then score how well that model can predict the removed feature.
In the code block below, you will need to implement the following:
 - Assign new_data a copy of the data by removing a feature of your choice using the DataFrame.drop function.
 - Use sklearn.cross_validation.train_test_split to split the dataset into training and testing sets.
   - Use the removed feature as your target label. Set a test_size of 0.25 and set a random_state.
 - Import a decision tree regressor, set a random_state, and fit the learner to the training data.
 - Report the prediction score of the testing set using the regressor's score function.
End of explanation
"""


# Produce a scatter matrix for each pair of features in the data
pd.scatter_matrix(data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');

"""
Explanation: Question 2
Which feature did you attempt to predict? What was the reported prediction score? Is this feature is necessary for identifying customers' spending habits?
Hint: The coefficient of determination, R^2, is scored between 0 and 1, with 1 being a perfect fit. A negative R^2 implies the model fails to fit the data.
Answer:
I attempted to predict the sales of Detergents_Paper.
I had noticed that Seaborn pairplot should a nice correlation between Detergents_paper and Grocery.
The R^2 score I got was .6953
Is this good enough?
I computed adjusted R^2 as 0.6806
Adjusted R^2 or r2adj=1−(n−1)/(n−p−1)(1−R^2) where n is samples (in this case 110) and k is the number of independent variables (or number of features which in this case 5). 
This suggests that this was a reasonable fit. However I would not want to be emphatic about it without evaluating standard error of the regression 
Visualize Feature Distributions
To get a better understanding of the dataset, we can construct a scatter matrix of each of the six product features present in the data. If you found that the feature you attempted to predict above is relevant for identifying a specific customer, then the scatter matrix below may not show any correlation between that feature and the others. Conversely, if you believe that feature is not relevant for identifying a specific customer, the scatter matrix might show a correlation between that feature and another feature in the data. Run the code block below to produce a scatter matrix.
End of explanation
"""


print "Numerically the mutual correlation numbers between these features are:","\n"
display(data.corr())

"""
Explanation: Question 3
Are there any pairs of features which exhibit some degree of correlation? Does this confirm or deny your suspicions about the relevance of the feature you attempted to predict? How is the data for those features distributed?
Hint: Is the data normally distributed? Where do most of the data points lie?
End of explanation
"""


# TODO: Scale the data using the natural logarithm
log_data = np.log(data)

# TODO: Scale the sample data using the natural logarithm
log_samples = np.log(samples)

# Produce a scatter matrix for each pair of newly-transformed features
pd.scatter_matrix(log_data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');

#also adding the correlation values in tabular form
display(log_data.corr())

"""
Explanation: Answer:
The plot suggests a strong linear correlation between Grocery and Detergents_Paper.
In fact I chose to drop Detergents_Paper on the basis of similar Seaborn plot. This plot confirms my suspician that Detergents_Paper as a feature could be dropped without much loss of information
The data is non-gaussian. It is heavily biased i.e. the maxima is closer to zero with a long tail asymptotic to x-axis away from origin. In other words the data frequency peaks to a maximum fairly close to zero and then peters down back slowly towards the max value of each feature
If mean > mode (i.e. 50 percetile mark) then the data is called right-skewed and if mean < mode then the data is called left-skewed. By that definition all our data is right skewed (although the maxima are to the left closer to origin)
Some models may require the data to be normalized for the model to perform well (As an example: As the name suggests Gaussian NB model expects the data distribution to be gaussian and not not skewed)
Right-skewed data can be normalized using transforms like roots or logarithms or reciprocals.
Left-skewed data can be normalized using transforms like squares or cubes or higher powers
Ref: http://fmwww.bc.edu/repec/bocode/t/transint.html
Data Preprocessing
In this section, you will preprocess the data to create a better representation of customers by performing a scaling on the data and detecting (and optionally removing) outliers. Preprocessing data is often times a critical step in assuring that results you obtain from your analysis are significant and meaningful.
Implementation: Feature Scaling
If data is not normally distributed, especially if the mean and median vary significantly (indicating a large skew), it is most often appropriate to apply a non-linear scaling — particularly for financial data. One way to achieve this scaling is by using a Box-Cox test, which calculates the best power transformation of the data that reduces skewness. A simpler approach which can work in most cases would be applying the natural logarithm.
In the code block below, you will need to implement the following:
 - Assign a copy of the data to log_data after applying logarithmic scaling. Use the np.log function for this.
 - Assign a copy of the sample data to log_samples after applying logarithmic scaling. Again, use np.log.
End of explanation
"""


# Display the log-transformed sample data

display(log_samples)

"""
Explanation: Note to myself
The correlation between Detergents_Paper and Grocery got softened to 0.796398 from 0.924641. This means Grocery alone will not sufficiently explain spend of Detergents_Paper and for that reason Detergents_Paper should not be dropped as a dimensionality reduction exercise.
Observation
After applying a natural logarithm scaling to the data, the distribution of each feature should appear much more normal. For any pairs of features you may have identified earlier as being correlated, observe here whether that correlation is still present (and whether it is now stronger or weaker than before).
Run the code below to see how the sample data has changed after having the natural logarithm applied to it.
End of explanation
"""


# For each feature find the data points with extreme high or low values
outliers = []
for feature in log_data.keys():
    
    # TODO: Calculate Q1 (25th percentile of the data) for the given feature
    Q1 = np.percentile(log_data.loc[:, feature], 25)
    
    # TODO: Calculate Q3 (75th percentile of the data) for the given feature
    Q3 = np.percentile(log_data.loc[:, feature], 75)
    
    # TODO: Use the interquartile range to calculate an outlier step (1.5 times the interquartile range)
    step = 1.5 * (Q3 - Q1)
    
    # Display the outliers
    print "Data points considered outliers for the feature '{}':".format(feature)
    
    #display(log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))])
##    print log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))].index
    
# OPTIONAL: Select the indices for data points you wish to remove

    outliers.append(list(log_data[~((log_data[feature] >= Q1 - step) & (log_data[feature] <= Q3 + step))].index))

# Remove the outliers, if any were specified
flat=reduce(lambda x,y: x+y,outliers)
print "Outliers with duplicates: \n", flat
#remove duplicates from flat list as
flat2=list(set(flat))
#identify the duplicates:
dupes =[]
for stuff in flat2:
    if flat.count(stuff)>1:
        dupes.append(stuff)
print "Duplicate indexes have been these: ", dupes
print "Outliers with duplicates removed: \n",flat2
print "No of outliers: ",len(flat2)
print "No of data rows before outliers removal: ", len(log_data)
good_data = log_data.drop(log_data.index[flat2]).reset_index(drop = True)
print "No of data rows after outliers removal: ", len(good_data)
outliers=flat2

"""
Explanation: Implementation: Outlier Detection
Detecting outliers in the data is extremely important in the data preprocessing step of any analysis. The presence of outliers can often skew results which take into consideration these data points. There are many "rules of thumb" for what constitutes an outlier in a dataset. Here, we will use Tukey's Method for identfying outliers: An outlier step is calculated as 1.5 times the interquartile range (IQR). A data point with a feature that is beyond an outlier step outside of the IQR for that feature is considered abnormal.
In the code block below, you will need to implement the following:
 - Assign the value of the 25th percentile for the given feature to Q1. Use np.percentile for this.
 - Assign the value of the 75th percentile for the given feature to Q3. Again, use np.percentile.
 - Assign the calculation of an outlier step for the given feature to step.
 - Optionally remove data points from the dataset by adding indices to the outliers list.
NOTE: If you choose to remove any outliers, ensure that the sample data does not contain any of these points!
Once you have performed this implementation, the dataset will be stored in the variable good_data.
End of explanation
"""


from sklearn.decomposition import PCA

#good_data=log_data #This was done to get an idea what happens when so called outliers are not removed

# TODO: Apply PCA by fitting the good data with the same number of dimensions as features
pca = PCA(n_components=6)
pca.fit(good_data)

# TODO: Transform log_samples using the PCA fit above
pca_samples = pca.transform(log_samples)


# Generate PCA results plot
pca_results = vs.pca_results(good_data, pca)

"""
Explanation: Question 4
Are there any data points considered outliers for more than one feature based on the definition above? Should these data points be removed from the dataset? If any data points were added to the outliers list to be removed, explain why. 
Answer:
There were 5 unique outlier rows that appeared more than once in the ouliers list. See:
Outliers with duplicates: 
[65, 66, 81, 95, 96, 128, 171, 193, 218, 304, 305, 338, 353, 355, 357, 412, 86, 98, 154, 356, 75, 154, 38, 57, 65, 145, 175, 264, 325, 420, 429, 439, 75, 161, 66, 109, 128, 137, 142, 154, 183, 184, 187, 203, 233, 285, 289, 343]
Outliers with duplicates removed: 
[128, 193, 264, 137, 142, 145, 154, 412, 285, 161, 420, 38, 171, 429, 175, 304, 305, 439, 184, 57, 187, 65, 66, 203, 325, 289, 75, 81, 338, 86, 343, 218, 95, 96, 353, 98, 355, 356, 357, 233, 109, 183]
They were removed from the outliers to leave only a single instance of them in the final list of outliers. Since Python Dicts are ordered with python's own hash-table logic, removal process of a outlier based on an index may well remove a good observation.
Feature Transformation
In this section you will use principal component analysis (PCA) to draw conclusions about the underlying structure of the wholesale customer data. Since using PCA on a dataset calculates the dimensions which best maximize variance, we will find which compound combinations of features best describe customers.
Implementation: PCA
Now that the data has been scaled to a more normal distribution and has had any necessary outliers removed, we can now apply PCA to the good_data to discover which dimensions about the data best maximize the variance of features involved. In addition to finding these dimensions, PCA will also report the explained variance ratio of each dimension — how much variance within the data is explained by that dimension alone. Note that a component (dimension) from PCA can be considered a new "feature" of the space, however it is a composition of the original features present in the data.
In the code block below, you will need to implement the following:
 - Import sklearn.decomposition.PCA and assign the results of fitting PCA in six dimensions with good_data to pca.
 - Apply a PCA transformation of log_samples using pca.transform, and assign the results to pca_samples.
End of explanation
"""


import pandas as pd
display(pca_results)
print "Cumulative Explained variance for added dimension in model looks like this:"
display(pd.DataFrame(pca_results['Explained Variance']).cumsum())

"""
Explanation: Question 5
How much variance in the data is explained in total by the first and second principal component? What about the first four principal components? Using the visualization provided above, discuss what the first four dimensions best represent in terms of customer spending.
Hint: A positive increase in a specific dimension corresponds with an increase of the positive-weighted features and a decrease of the negative-weighted features. The rate of increase or decrease is based on the indivdual feature weights.
End of explanation
"""


# Display sample log-data after having a PCA transformation applied

display(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))

"""
Explanation: Answer:
The first two principal components explain 72.52% of the variance
The first four explain 92.79% of the variance.
Consider the Dimensions as a composite of our features Fresh, Milk, Grocery, Frozen, Detergents_Paper and Delicatessen multiplies by their weights and summed together.In the table above you can see weights assigned to each feature to build each dimension.
Dimension1 = -0.0976Fresh+0.4109Milk+0.4511Grocery-0.1280Frozen+0.7595Detergents_Paper+0.1579Delicatesse
Now since first four dimensions explain 92.79 we can work using the four dimensions. 
What is the advantage? I am still using all 6 features to compute the dimensions. The advantage of the 4 dimensions proposed by PCA is that I can work with much lesser data (lesser observations).
If I look at Dimension 1 which has coefficients 0.759, 0.4109 and 0.4511 for Detergents_Paper, Milk and Grocery respectively a data point farther along this dimension declares itself as a Retail store (not Deli or Restaurant or a cafe). Dimension 2 has coefficients 0.6300, 0.6008 and 0.4634 for Frozen, Fresh and Delicatessen features. A data-point farther along the Dimension 2 is screaming itself to be a Deli / Restaurant. Dimension 3 has 0.5422 and -0.7452 as coefficients for Delicatessen and Fresh features. A datapoint farther along this dimension can be generally loosely labeled as a Cakeshop or a Coffeeshop or a Cafe maybe?
Observation
Run the code below to see how the log-transformed sample data has changed after having a PCA transformation applied to it in six dimensions. Observe the numerical value for the first four dimensions of the sample points. Consider if this is consistent with your initial interpretation of the sample points.
End of explanation
"""


# TODO: Apply PCA by fitting the good data with only two dimensions
pca = PCA(n_components=2)
pca.fit(good_data)

# TODO: Transform the good data using the PCA fit above
reduced_data = pca.transform(good_data)

# TODO: Transform log_samples using the PCA fit above
pca_samples = pca.transform(log_samples)

# Create a DataFrame for the reduced data
reduced_data = pd.DataFrame(reduced_data, columns = ['Dimension 1', 'Dimension 2'])


"""
Explanation: Implementation: Dimensionality Reduction
When using principal component analysis, one of the main goals is to reduce the dimensionality of the data — in effect, reducing the complexity of the problem. Dimensionality reduction comes at a cost: Fewer dimensions used implies less of the total variance in the data is being explained. Because of this, the cumulative explained variance ratio is extremely important for knowing how many dimensions are necessary for the problem. Additionally, if a signifiant amount of variance is explained by only two or three dimensions, the reduced data can be visualized afterwards.
In the code block below, you will need to implement the following:
 - Assign the results of fitting PCA in two dimensions with good_data to pca.
 - Apply a PCA transformation of good_data using pca.transform, and assign the results to reduced_data.
 - Apply a PCA transformation of log_samples using pca.transform, and assign the results to pca_samples.
End of explanation
"""


# Display sample log-data after applying PCA transformation in two dimensions
display(pd.DataFrame(np.round(pca_samples, 4), columns = ['Dimension 1', 'Dimension 2']).head())

"""
Explanation: Observation
Run the code below to see how the log-transformed sample data has changed after having a PCA transformation applied to it using only two dimensions. Observe how the values for the first two dimensions remains unchanged when compared to a PCA transformation in six dimensions.
End of explanation
"""


# Create a biplot
vs.biplot(good_data, reduced_data, pca)

"""
Explanation: Visualizing a Biplot
A biplot is a scatterplot where each data point is represented by its scores along the principal components. The axes are the principal components (in this case Dimension 1 and Dimension 2). In addition, the biplot shows the projection of the original features along the components. A biplot can help us interpret the reduced dimensions of the data, and discover relationships between the principal components and original features.
Run the code cell below to produce a biplot of the reduced-dimension data.
End of explanation
"""


import warnings
warnings.filterwarnings("ignore", category=DeprecationWarning) 

from sklearn.mixture import GMM
from sklearn.metrics import silhouette_score
# TODO: Apply your clustering algorithm of choice to the reduced data
cluster_list = [2, 3, 4, 5]
cluster_matrix=[]
for n_clusters in cluster_list:
    clusterer = GMM(n_components=n_clusters).fit(reduced_data)
    # TODO: Predict the cluster for each data point
    preds = clusterer.predict(reduced_data)

    # TODO: Find the cluster centers
    centers = clusterer.means_

    # TODO: Predict the cluster for each transformed sample data point
    sample_preds = clusterer.predict(pca_samples)

    # TODO: Calculate the mean silhouette coefficient for the number of clusters chosen
    score = silhouette_score(reduced_data, preds, metric='mahalanobis')
    print "The average silhouette score is ", score, " for ", n_clusters, " clusters"
    cluster_matrix.append([n_clusters,preds, centers,sample_preds, score])
    if n_clusters == :
        centers_2=centers
        preds_2=preds
        sample_preds_2=sample_preds

df = pd.DataFrame(cluster_matrix, columns=['N_clusters',"preds","centers","sample_preds","score"])
print "The best score is for " ,int(df.loc[df['score']==df['score'].max()]['N_clusters']), " clusters"
#resetting values of parametrs for the next section:
preds = preds_2
centers= centers_2
sample_preds=sample_preds_2
gmm_centers = centers
gmm_sample_preds=sample_preds

"""
Explanation: Observation
Once we have the original feature projections (in red), it is easier to interpret the relative position of each data point in the scatterplot. For instance, a point the lower right corner of the figure will likely correspond to a customer that spends a lot on 'Milk', 'Grocery' and 'Detergents_Paper', but not so much on the other product categories. 
From the biplot, which of the original features are most strongly correlated with the first component? What about those that are associated with the second component? Do these observations agree with the pca_results plot you obtained earlier?
Clustering
In this section, you will choose to use either a K-Means clustering algorithm or a Gaussian Mixture Model clustering algorithm to identify the various customer segments hidden in the data. You will then recover specific data points from the clusters to understand their significance by transforming them back into their original dimension and scale. 
Question 6
What are the advantages to using a K-Means clustering algorithm? What are the advantages to using a Gaussian Mixture Model clustering algorithm? Given your observations about the wholesale customer data so far, which of the two algorithms will you use and why?
Answer:
K-Means clustering algorithm
* Advantages are that 1: Easy to understand and implement. 2: Works well in practice.
* Disadvantages are that that 1: It may converge to a local optimum. 2: It is susceptible to outliers.
 Gaussian Mixture Model clustering algorithm
* Advantages are that 1: It allows Soft assignment of points in the bordering area (equi-distant) and may belong to more than one cluster with associated probability 2: It affords flexibility that K-Means does not for the border area points. Thus these points will be guarantteed memebrship to atleast one cluster
* Disadvantages are that that 1: Computational difficulties 2: Domain Knowledge required to determine number of clusters and their initial placements
My preference would be GMM since it will provide dual membership to customers and it will give me a break in understanding my customers better
Implementation: Creating Clusters
Depending on the problem, the number of clusters that you expect to be in the data may already be known. When the number of clusters is not known a priori, there is no guarantee that a given number of clusters best segments the data, since it is unclear what structure exists in the data — if any. However, we can quantify the "goodness" of a clustering by calculating each data point's silhouette coefficient. The silhouette coefficient for a data point measures how similar it is to its assigned cluster from -1 (dissimilar) to 1 (similar). Calculating the mean silhouette coefficient provides for a simple scoring method of a given clustering.
In the code block below, you will need to implement the following:
 - Fit a clustering algorithm to the reduced_data and assign it to clusterer.
 - Predict the cluster for each data point in reduced_data using clusterer.predict and assign them to preds.
 - Find the cluster centers using the algorithm's respective attribute and assign them to centers.
 - Predict the cluster for each sample data point in pca_samples and assign them sample_preds.
 - Import sklearn.metrics.silhouette_score and calculate the silhouette score of reduced_data against preds.
   - Assign the silhouette score to score and print the result.
End of explanation
"""


# Display the results of the clustering from implementation
vs.cluster_results(reduced_data, preds, centers, pca_samples)


"""
Explanation: Question 7
Report the silhouette score for several cluster numbers you tried. Of these, which number of clusters has the best silhouette score? 
Answer:
I tried test upto 5 clusters (ignoring the trivial 1 cluster)
The results are as listed above: (I am not pasting them below because they change after every run of the prior cells)
The best score is for  2  clusters (This observation has not changed for each run of the prior cells)
(Interestingly if the outliers were not removed the best score is for 3 clusters)
GMM Cluster Visualization
Once you've chosen the optimal number of clusters for your clustering algorithm using the scoring metric above, you can now visualize the results by executing the code block below. Note that, for experimentation purposes, you are welcome to adjust the number of clusters for your clustering algorithm to see various visualizations. The final visualization provided should, however, correspond with the optimal number of clusters.
End of explanation
"""


# TODO: Inverse transform the centers

model_centers = (['GMM',gmm_centers],['K-Means',kmeans_centers])

for stuff in model_centers:
    log_centers = pca.inverse_transform(stuff[1])

# TODO: Exponentiate the centers
    true_centers = np.exp(log_centers)

# Display the true centers
    segments = ['Segment {}'.format(i) for i in range(0,len(stuff[1]))]
    true_centers = pd.DataFrame(np.round(true_centers), columns = data.keys())
    true_centers.index = segments
    print "For model: ",stuff[0]
    display(true_centers)
   

### Question 8
Consider the total purchase cost of each product category for the representative data points above, and reference the statistical description of the dataset at the beginning of this project. *What set of establishments could each of the customer segments represent?*  
**Hint:** A customer who is assigned to `'Cluster X'` should best identify with the establishments represented by the feature set of `'Segment X'`.

"""
Explanation: Repeat the process above for K-Means
import warnings
warnings.filterwarnings("ignore", category=DeprecationWarning) 
from sklearn.cluster import KMeans
from sklearn.metrics import silhouette_score
TODO: Apply your clustering algorithm of choice to the reduced data
cluster_list = [2, 3, 4, 5]
cluster_matrix=[]
for n_clusters in cluster_list:
    clusterer = KMeans(n_clusters=n_clusters).fit(reduced_data)
    # TODO: Predict the cluster for each data point
    preds = clusterer.predict(reduced_data)
# TODO: Find the cluster centers
centers = clusterer.cluster_centers_

# TODO: Predict the cluster for each transformed sample data point
sample_preds = clusterer.predict(pca_samples)

# TODO: Calculate the mean silhouette coefficient for the number of clusters chosen
score = silhouette_score(reduced_data, preds, metric='euclidean')
print "The average silhouette score is ", score, " for ", n_clusters, " clusters"
cluster_matrix.append([n_clusters,preds, centers,sample_preds, score])
if n_clusters == 2:
    centers_2=centers
    preds_2=preds
    sample_preds_2=sample_preds

df = pd.DataFrame(cluster_matrix, columns=['N_clusters',"preds","centers","sample_preds","score"])
print "The best score is for " ,int(df.loc[df['score']==df['score'].max()]['N_clusters']), " clusters"
resetting values of parametrs for the next section:
preds = preds_2
centers= centers_2
kmeans_centers = centers
sample_preds=sample_preds_2
kmeans_sample_preds=sample_preds
print "GMM centers :", gmm_centers
print "\n"
print "KMeans centers :", kmeans_centers
The best score is:
Here also I tried test upto 5 clusters (ignoring the trivial 1 cluster)
The results are  as shown above: (I am not copy-pasting them here because they keep changing after every run of this and prior cells)
The best score is for  2  clusters
(interestingly if the outliers are not removed best score is still for 2 clusters)
k-Means Cluster Visualization
vs.cluster_results(reduced_data, preds, centers, pca_samples)
Implementation: Data Recovery
Each cluster present in the visualization above has a central point. These centers (or means) are not specifically data points from the data, but rather the averages of all the data points predicted in the respective clusters. For the problem of creating customer segments, a cluster's center point corresponds to the average customer of that segment. Since the data is currently reduced in dimension and scaled by a logarithm, we can recover the representative customer spending from these data points by applying the inverse transformations.
In the code block below, you will need to implement the following:
 - Apply the inverse transform to centers using pca.inverse_transform and assign the new centers to log_centers.
 - Apply the inverse function of np.log to log_centers using np.exp and assign the true centers to true_centers.
End of explanation
"""


# Display the predictions
model_sample_preds = (['GMM',gmm_sample_preds],['KMeans',kmeans_sample_preds])
for stuff in model_sample_preds:
    print "For model", stuff[0], ":"
    for i, pred in enumerate(stuff[1]):
        print "Sample point", i, "predicted to be in Cluster", pred
    print ""    

"""
Explanation: Answer:
Let's consider the data described by pandas when we started this exercise:
The means for Fresh, Milk, Grocery, Frozen, Detergents_Paper and Delicatessen were 12000,5796.265909,7951,3071,2881 and 1524.
Segment 0 is more likely a restaurent / deli / high-end grocery (since they sell more than mean of delicatessen...but also more than mean of Detergents_Paper)
Thus Segment 1 is more like a retail / grocery shop (They are closer to the mean of Fresh produce)
Question 9
For each sample point, which customer segment from Question 8 best represents it? Are the predictions for each sample point consistent with this?
Run the code block below to find which cluster each sample point is predicted to be.
End of explanation
"""


# Display the clustering results based on 'Channel' data
import renders as rs

rs.channel_results(reduced_data, outliers, pca_samples)

"""
Explanation: Answer:
Interestingly both models have my samples in the "two-clusters-discrimination" similarly!
My sample points were a reflection of three establishments local to my home town. My Sample 0 was a downtown Deli which also sells grocery of many kind. 
My Sample 1 is a grocery store that prides itself for being focused on Fresh produce.
My Sample 2 is big on grocery (may also be big on Detergents / Tissues / Bath tissue etc.
So cluster 0 looks like a Restaurent / Deli / Grocery that wants to act like a cafe or deli
Cluster 1 is more like a Fresh produce / Grocery / retailer
Conclusion
In this final section, you will investigate ways that you can make use of the clustered data. First, you will consider how the different groups of customers, the customer segments, may be affected differently by a specific delivery scheme. Next, you will consider how giving a label to each customer (which segment that customer belongs to) can provide for additional features about the customer data. Finally, you will compare the customer segments to a hidden variable present in the data, to see whether the clustering identified certain relationships.
Question 10
Companies will often run A/B tests when making small changes to their products or services to determine whether making that change will affect its customers positively or negatively. The wholesale distributor is considering changing its delivery service from currently 5 days a week to 3 days a week. However, the distributor will only make this change in delivery service for customers that react positively. How can the wholesale distributor use the customer segments to determine which customers, if any, would react positively to the change in delivery service?
Hint: Can we assume the change affects all customers equally? How can we determine which group of customers it affects the most?
Answer:
We have seen that data points that are farther along Dimension-1 are ones who can be generally called Retail outlets because they are strong on Detergents_Paper, Milk and Grocery. The data points farther along Dimension 2 are outlets that can be generally call Deli, Restaurents, Cafes. Their emphasis is on Freshness. Knowing this the retailers closer to Dimension-1 axis and farther from the origin (showing very distinct retailness) are likely to be open to the reduced frequecy of the deliveries. If any trials of reduced delivery frequecy under the A/B were to be conducted start with some of the customers around whom I have marked a circle in the lower right quadrant in the graphic below:
<img src="files/My_guess.png">
Question 11
Additional structure is derived from originally unlabeled data when using clustering techniques. Since each customer has a customer segment it best identifies with (depending on the clustering algorithm applied), we can consider 'customer segment' as an engineered feature for the data. Assume the wholesale distributor recently acquired ten new customers and each provided estimates for anticipated annual spending of each product category. Knowing these estimates, the wholesale distributor wants to classify each new customer to a customer segment to determine the most appropriate delivery service.
How can the wholesale distributor label the new customers using only their estimated product spending and the customer segment data?
Hint: A supervised learner could be used to train on the original customers. What would be the target variable?
Answer:
~~~We did not discus possibility of combining the total spend on fresh + milk + grocery etc. and using that as a feature. If that feature was cosnidered to be significant and useful over the other features (so that the total spend alone could explain large chubk of the variance) then we stand a reasonable chance in fitting the customer into clusters as diffrentiated by the total spend/budget would dictate.~~~
We see that the customers can be classified in two clusters meaningfully. But we had no meaningful names for the clusters merely Cluster 0 and Cluster 1. But when we label these clusters as Retailers and Deli/Restaurents/Cafe`s they add insight to the data that we did not have. Let's add these cluster labels to the dataset once the classification takes place. 
Now there are pop-and-mom retailers and pop-and-mom Delis/Restaurents/Cafes. There are also big retailers as well as big Delis/Restaurents/Cafes. Hence we add a feature called total spend (which is sum total of all the m.u.s in Grocery, Milk, Fresh...etc..). The math computation is quite trivial
Now we could chain that data into another supervised learner to find newer clusters based on the total spend and original cluster labels so that they fit into a matrix. One such simple matrix could be as represented in the graphics below:
<img src="files/My_guess2.png">
Let's call this variable (another label) called sub-segment. This is how the data transformation would look like:
Unlabeled data ==> Labeled data with total spend added ==>Data only with labels and total spend==>Classification of sub-segments (for example Big bucks retailer or Small and Medium Deli) Now the wholesale distributor can design a customized delivery service for all existing customers and also for the 10 new customers (for whom only their market segment label and their total annual spend is known)
A simple k-NN classifier will take the market segment labels and total annual spend as input vectors and provide sub-segment labels like Small and Medium Retailer
Visualizing Underlying Distributions
At the beginning of this project, it was discussed that the 'Channel' and 'Region' features would be excluded from the dataset so that the customer product categories were emphasized in the analysis. By reintroducing the 'Channel' feature to the dataset, an interesting structure emerges when considering the same PCA dimensionality reduction applied earlier to the original dataset.
Run the code block below to see how each data point is labeled either 'HoReCa' (Hotel/Restaurant/Cafe) or 'Retail' the reduced space. In addition, you will find the sample points are circled in the plot, which will identify their labeling.
End of explanation
"""


