# Customer Segment

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 theShift + Enterkeyboard 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.

```
# 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?"
```

## 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.

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

### 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.

```
# TODO: Select three indices of your choice you wish to sample from the dataset
indices = [10,45,300]
# 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)
```

### 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, delis, wholesale retailers, among many others. Avoid using names for establishments, such as saying *"McDonalds"* when describing a sample customer as a restaurant. You can use the mean values for reference to compare your samples with. The mean values are as follows:

- Fresh: 12000.2977
- Milk: 5796.2
- Grocery: 3071.9
- Detergents_paper: 2881.4
- Delicatessen: 1524.8

Knowing this, how do your samples compare? Does that help in driving your insight into what kind of establishments they might be?

The kind of establishment (customer) that each of the three samples that I have chosen can represent are discussed below:

1) Index 10: After carefully inspecting the sample, this establishment seems to have a higher than average consumption of Grocery (12974 > 3071.9), Detergents_paper (5977 > 2881.4), Delicatessen (1744 > 1524) and Frozen products (4400 > 440). However, it has slightly lower than average values for the rest of the product. For example, in terms of the actual and mean values, this establishment has [Milk (5403, 5796.2), Fresh (3366, 12000.2977)]. Also, the value of Grocery product is way higher than the 75th percentile [12974 > 10655.75] for this customer. Hence, it is clear that this establishment does not deal so much in fresh or perishable products and stock a lot of grocery product. My best bet is that this establishment is a GROCERY SHOP or a MINI SUPERMARKET.

2) Index 45: Looking at the sample, this establishment seems to have a lower than average consumption of fresh products (5181 < 12000.97) and slightly higher than average values for the rest of the product. For example, in terms of the actual and mean values, this establishment has [Milk (22044 > 5796.2), Frozen(1740 > 440), Grocery (21531 > 3071.9), Detergents_paper(7353 > 2881.4), and Delicatessen(4985 > 1524.8)]. Similarly, comparing the value to the 75th percentile, this establishment seems to have an unusually high value for consumption of diary product such as Milk. In fact, the value for milk outweighs the 75th percentile for Milk [22044 > 7190.25]. With all the aforementioned in mind, I would guess that this establishment is most likely a COFFEE SHOP.

3) Index 300: Similarly, this establishment seems to have a lower than average consumption of detergent papers (2662 < 2881.4) and slightly higher than average for the rest of the product. For example, in terms of the actual and mean values, this establishment has [Fresh (16448 > 12000.2977), Frozen(824 > 440), Grocery (6360 > 3071.9), and Milk (6243 > 5796.2)]. After inspecting this figure, I would guess that this establishment is most likely a RESTAURANT.

Generally, Mean and median tend to hide outliers. From the description of the dataset, the data is skewed with large deviation of the mean from the median. Since the data can be easily distorted by outliers, it makes sense to compare the spending with percentile

### 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`

.

- Use the removed feature as your target label. Set a
- 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.

```
from sklearn.cross_validation import train_test_split
from sklearn.tree import DecisionTreeRegressor
# TODO: Make a copy of the DataFrame, using the 'drop' function to drop the given feature
new_data = data.drop(['Frozen'], axis=1)
# TODO: Split the data into training and testing sets(0.25) using the given feature as the target
# Set a random state.
X_train, X_test, y_train, y_test = train_test_split(new_data, data['Frozen'], test_size=0.25, random_state=20)
# TODO: Create a decision tree regressor and fit it to the training set
regressor = DecisionTreeRegressor(random_state=20)
regressor.fit(X_train, y_train)
# TODO: Report the score of the prediction using the testing set
score = regressor.score(X_test, y_test)
score
```

### Question 2¶

- Which feature did you attempt to predict?
- What was the reported prediction score?
- Is this feature 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. If you get a low score for a particular feature, that lends us to beleive that that feature point is hard to predict using the other features, thereby making it an important feature to consider when considering relevance.

1) I attempted to predict Frozen 2) The recorded prediction score was -0.57017510815055528 3) Since we are taking the "Frozen" feature as a label and using the rest of the features to predict it, a negative R^2 means the "Frozen" feature is not correlated with other features. In other words, it conveys information that cannot be derived from other features. Thus the negative R^2 value means the feature can be quite useful.

### 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.

```
# Produce a scatter matrix for each pair of features in the data
from scipy.stats import skew
pd.scatter_matrix(data, alpha = 0.3, figsize = (14,8), diagonal = 'kde');
display(data.corr())
display(skew(data))
```

### Question 3¶

- Using the scatter matrix as a reference, discuss the distribution of the dataset, specifically talk about the normality, outliers, large number of data points near 0 among others. If you need to sepearate out some of the plots individually to further accentuate your point, you may do so as well.
- 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? You can use corr() to get the feature correlations and then visualize them using a heatmap(the data that would be fed into the heatmap would be the correlation values, for eg: `data.corr()`

) to gain further insight.

Skewness is a good measure of whether data is normal distributed. We can measure the skewness by using the scipy.stats.skew(), which results in 0 for normally distributed data. Since we have skewness value > 0, it means positive / right skew, i.e. more weight in the left tail of the distribution. Further, from the visualization of the dataset using the scatter matrix as a reference, I observe that most of the datapoint lies close to the origin (0,0). Hence, I assume some of these datapoints are outliers. The data is not normally distributed based on the visualisation, i.e., some of data seems to be cluttered some specific region. In terms of relationship between the features, I noticed a strong correlation between Detergents_Paper (0.924641) and Grocery. There is a slightly positive correlation between milk and grocery. Actually this confirms my initial suspicion that frozen does not have any noticeable correlation with other features. The data seems skewed and may needs to be scaled.

## 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`

.

```
# 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');
```

### 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.

```
# Display the log-transformed sample data
display(log_samples)
```

### 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`

.

```
# For each feature find the data points with extreme high or low values
for feature in log_data.keys():
# TODO: Calculate Q1 (25th percentile of the data) for the given feature
Q1 = np.percentile(log_data[feature],25)
# TODO: Calculate Q3 (75th percentile of the data) for the given feature
Q3 = np.percentile(log_data[feature],75)
# TODO: Use the interquartile range to calculate an outlier step (1.5 times the interquartile range)
step = (Q3-Q1) * 1.5
# 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))])
# OPTIONAL: Select the indices for data points you wish to remove
outliers = [65, 66,75, 128, 154]
# Remove the outliers, if any were specified
good_data = log_data.drop(log_data.index[outliers]).reset_index(drop = True)
```

### 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.

** Hint: ** If you have datapoints that are outliers in multiple categories think about why that may be and if they warrant removal. Also note how k-means is affected by outliers and whether or not this plays a factor in your analysis of whether or not to remove them.

There are some datapoints considered outliers for more than one feature. For example the following list of datapoints [65, 66,75, 128, 154]. To elaborate; datapoint 65 was an outlier for Frozen and Fresh, similarly, 66 was for Delicatessen and Fresh, 75 for Detergents_Paper and Grocery, 128 for Delicatessen and Fresh, and 154 fir Delicatessen, Milk and Grocery.

Yes, these datapoints should be removed from the dataset. Reason: Removing all the outliers may actually lead to losing some crucial information, however, removing datapoints that appear as outliers in more than one features should not affect the model. In fact, I think it will improve the outcome of the model since those datapoint may not provide any additional information that will benefit the model.

## 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`

.

```
from sklearn.decomposition import PCA
# TODO: Apply PCA by fitting the good data with the same number of dimensions as features
pca = PCA(n_components=6).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)
```

### Question 5¶

- How much variance in the data is explained
**in total** - How much variance in the data is explained by the first four principal components?
- Using the visualization provided above, talk about each dimension and the cumulative variance explained by each, stressing upon which features are well represented by each dimension(both in terms of positive and negative variance explained). 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 individual feature weights.

The variance in the data that is explained by the first principal component is 44.02% and by the second principal component is 27.00% making a total of 71.02%. For the third principal component, it is 12.14% and for the fourth, it is 10.02%. The total is 93.18%. This is the amount of variance explained by the first four principal components.

Observing each of these dimensions, the first dimension shows a high absolute weight on detergents_paper, milk, and grocery. This could represent a retail customer behavior. The second dimension shows a high absolute weight for Fresh, Frozen and Delicatessen. It could represent a fast food restaurant. In dimension 3, it is interesting to observe an inverse correlation between delicatessen and fresh. This shows that spending on fresh is inversely correlated with spending on delicatessen. The positive direction indicates that the customer will be spending higher on "Fresh" and lower on "Delicatessen". The fourth dimension majorly shows the variation between Frozen and Delicatessen. i.e., they are both inversely correlated. Frozen is the highest positive-weighted feature. This implies that it has the highest cummulative variance in the fourth dimension. This could represent bulk buyers of frozen goods.

Since we are more interested in the significant feature weights in these dimensions, it is perfectly acceptable to flip the positive and negative weights, and the result would not affect the discussion. For example, for dimension 1, the predominant spending is on milk, grocery and detergents_paper. Although they all have negative weights, it is the absolute value that matters since the signs of the weights are identical.

### 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.

```
# Display sample log-data after having a PCA transformation applied
display(pd.DataFrame(np.round(pca_samples, 4), columns = pca_results.index.values))
```

### 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`

.

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

### 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.

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

## 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.

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

### 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?

** Hint: ** Think about the differences between hard clustering and soft clustering and which would be appropriate for our dataset.

ADVANTAGES OF K-MEANS CLUSTERING 1) K-means clustering are simple and quite easy to implement 2) The result of the clusters are also easy to understand 3) It is computationally faster than hierarchical clustering if the dataset is huge. O(k n T) where n is the given sample size and T represents the number of iterations.

ADVANTAGES OF GAUSSIAN MIXED MODEL CLUSTERING 1] When compared to K-means, GMM is a lot more flexible in terms of cluster covariance. K-means is actually a special case of GMM in which each cluster’s covariance along all dimensions approaches 0. This implies that a point will get assigned only to the cluster closest to it [1]. 2] Another implication of its covariance structure is that GMM allows for mixed membership of points to clusters. In kmeans, a point belongs to one and only one cluster, whereas in GMM a point belongs to each cluster to a different degree [1].

WHICH ALGORITHM TO USE AND WHY Based on my observation of the wholesale data so far, I am slightly leaning towards using the Gaussian Mixed Model clustering approach. I chose this approach because of the following reasons: flexibility, ability to make non-spherical clusters, and allowing mixed membership of points to clusters. I believe it will be the ideal approach to cluster the dataset. Also, after observing the biplot, I realised that the datapoint can potentially belong to multiple clusters because they are more denser in some regions (soft clustering).

References 1] https://www.quora.com/What-are-the-advantages-to-using-a-Gaussian-Mixture-Model-clustering-algorithm

### 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.

```
from sklearn.mixture import GMM
from sklearn.metrics import silhouette_score
# TODO: Apply your clustering algorithm of choice to the reduced data
clusterer = GMM(n_components=2).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)
display(score)
```

### Question 7¶

- Report the silhouette score for several cluster numbers you tried.
- Of these, which number of clusters has the best silhouette score?

Number of clusters | Silhouette score 2 | 0.4118 3 | 0.3736 4 | 0.3060 5 | 0.2536

The cluster with the best silhouette score is 2 clusters

### 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.

```
# Display the results of the clustering from implementation
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`

.

```
# TODO: Inverse transform the centers
log_centers = pca.inverse_transform(centers)
# TODO: Exponentiate the centers
true_centers = np.exp(log_centers)
# Display the true centers
segments = ['Segment {}'.format(i) for i in range(0,len(centers))]
true_centers = pd.DataFrame(np.round(true_centers), columns = data.keys())
true_centers.index = segments
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(specifically looking at the mean values for the various feature points). 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'`

. Think about what each segment represents in terms their values for the feature points chosen. Reference these values with the mean values to get some perspective into what kind of establishment they represent.

Observing the total purchase cost of each product category, an establishment that is assigned to cluster 0 will most like be a small scale GROCERY or fresh food store. The reason for making this assumption is simple; Segment 0 has significant high value for Fresh (8874.0), Milk (2107), Grocery (2757), Frozen (2064) and relatively low value for detergents_paper (353) and delicatessen (721). Also, these values relative are relatively low when compared to the mean values listed below: However, considering how high the values are relative to each other, I will assume that the organisation is fresh food store.

```
Fresh Milk Grocery Frozen Detergents_Paper Delicatessen
```

mean 12000.297727 5796.265909 7951.277273 3071.931818 2881.493182 1524.870455

A customer that is assigned to segment 1 will most likely identify with a grocery store establishment. Reason: Comparing the relatively high value of grocery (9440) relative to the mean of 7951 and similarly for detergents paper (actual value: 2979, mean value: 2881) and relatively low value for delicatessen when compared to the mean (actual: 910, mean: 1524.87). Using this values as a perspective, I think customer in this region will most be a Restaurant or Coffee shop.

### Question 9¶

- For each sample point, which customer segment from
**Question 8** - 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.

```
# Display the predictions
for i, pred in enumerate(sample_preds):
print "Sample point", i, "predicted to be in Cluster", pred
```

```
display(true_centers)
display(samples)
```

Without running clustering algorithm, and based on my judgment, I think the sample points 0, 1, and 2 should be assigned to cluster 0. Reason: these samples have high values for fresh, milk and groceries compared to the average spending in the dataset. From this spending pattern, I think this establishment is more likely a grocery or low end retail store.

1) Index 10: It is clear that it belongs to segment 0 where spending on grocery is high

2) Index 45: Also, this belongs to segment 0 where spending on grocery and milk is high

3) Index 300: I think this should belong to segment 1 where spending on Fresh is high. However, there is also high spending on milk and grocery and the model correctly placed it in segment 0

After running the clustering algorithm, the sample points are correctly placed in their respective clusters baseed on the spending patterns, i.e., high spending on Fresh, Milk, and Grocery products.

## 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

**to a hidden variable present in the data, to see whether the clustering identified certain relationships.**

*customer segments*### 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?

The wholesale distributor can use the customer segments to determine wish customer would react positively to the change in delivery service by oberving the proportion of features in each segment. For example, customers in segment 0 has high value for Fresh (8874.0), Milk (2107), Grocery (2757), Frozen (2064). These kind of items are perishable and may not be last long before they get spoilt. Hence delaying the delivery date may lead to a negative reaction from the customers. Also, customers in segment 1 have high values for all features except delicatessen. I assume this customer is involved in a grocery store. Since it has a high value for fresh and other products. Delaying the delivery date may also lead to a negative reaction from the customer in this segment.

Therefore, intuitively a change in delivery service will most likely affect both customers. However, this intuition could be wrong. The company could run A/B tests when making these changes to determine whether these changes will affect its customers. The company can select some samples of customer from the two custers, apply the 5 days a week delivery change to these samples and see how they respond relative to the rest of the group. Similarly, the establishment can conduct similar experiment for the 3 days delivery. If a pattern is observed, then the establishment will be able to make an informed decision about the kind of delivery they need to use. This would give a better insight into the significance of changing the delivery service.

### 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

**to determine the most appropriate delivery service.**

*customer segment*- 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?

The wholesale distributor can label the new customer by simply using a supervised learner such as Decision Tree or SVM (as suggested in the hint) to train the data contatining customer segment. Then we can classify the customers into either segment 0 or 1 based on their estimated spending. The target variable will be the estimated spending of these customers.

### 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.

```
# Display the clustering results based on 'Channel' data
vs.channel_results(reduced_data, outliers, pca_samples)
```

### Question 12¶

- How well does the clustering algorithm and number of clusters you've chosen compare to this underlying distribution of Hotel/Restaurant/Cafe customers to Retailer customers?
- Are there customer segments that would be classified as purely 'Retailers' or 'Hotels/Restaurants/Cafes' by this distribution?
- Would you consider these classifications as consistent with your previous definition of the customer segments?

Looking at the visualization, it seems like the number of clusters formed by the algorithm matches quite well with the number of underlying distribution of Hotel/Restaurant/Cafe customers to Retailer customers in the given distribution. However, there are some interflowing around the mid-section of the cluster - which are likely to be the mislabeled datapoint. Further, the algorithm accurately classify some points into segment 0 which most likely represents "Retailers" and segment 1 which most likely represents "Hotels/Restaurants/Cafes". When compared to the clustering algorithms (GMM) and the number of clusters(n=2) that I had chosen, I believe the algorithm did a decent job of segmenting the customers into two distinct segments. Based on the output of the visualization, some customers will be classified as purely Retailers, while some will be classified as a 'Hotels/Restaurants/Cafes' customer. However, there are some fews customers that will be misclassified. I think this classification is relatively consistent with my previous definition of customer segment because it produces similar segmentation result.

Note: Once you have completed all of the code implementations and successfully answered each question above, you may finalize your work by exporting the iPython Notebook as an HTML document. You can do this by using the menu above and navigating to

File -> Download as -> HTML (.html). Include the finished document along with this notebook as your submission.