Unsupervised Learning - Kmeans Week 11 Challenge

Calculating similarity for categorical data involves different approaches compared to numerical data. Here are some common methods for measuring similarity between categorical variables:

^{1. Hamming Distance}

Hamming distance measures the number of positions at which the corresponding elements are different. It is used when the data is categorical, and the variables are of equal length.

• Formula: $\text{Hamming Distance}={\sum }_{i=1}^n\text{I}(x_i\mathrm{\ne }{y}_i)$
• Where:
  • $x_i$and $y_i$ are the values at position $i$i in the two strings.
  • $\text{I}$is an indicator function that equals 1 if the condition is true and 0 otherwise.

^{2. Jaccard Similarity}

Jaccard similarity measures the proportion of shared attributes between two sets.

• Formula: $\text{Jaccard Similarity} = \frac{|A \cap B|}{|A \cup B|}$​
• Where:
  • $A$ and $B$ are sets of attributes.
  • $|A \cap B|$ is the number of common attributes.
  • $|A \cup B|$ is the number of total unique attributes.

^{3. Cosine Similarity}

Cosine similarity measures the cosine of the angle between two vectors. For categorical data, you typically convert categories into binary vectors.

• Formula: $\text{Cosine Similarity} = \frac{A \cdot B}{\|A\| \|B\|}$​
• Where:
  • $A$ and $B$ are vectors representing the categorical attributes.
  • $\cdot$ is the dot product.
  • $\| \cdot \|$ denotes vector norm.

^{4. Matching Coefficient}

The matching coefficient measures the similarity by counting the number of matching attributes between two categorical records.

• Formula: $\text{Matching Coefficient} = \frac{\text{Number of Matching Attributes}}{\text{Total Number of Attributes}}$​

^{5. Dice's Coefficient}

Dice's coefficient is similar to Jaccard but gives more weight to matches.

• Formula: $\text{Dice's Coefficient} = \frac{2 \cdot |A \cap B|}{|A| + |B|}$​
• Where:
  • $|A|$ and $|B|$ are the sizes of sets $A$ and $B$, respectively.

^{6. Kullback-Leibler Divergence}

Used for comparing probability distributions, it can also be applied to categorical data by treating them as probability distributions.

• Formula: $D_{KL}(P \| Q) = \sum_{i} P(i) \log \frac{P(i)}{Q(i)}$​
• Where:
• $P$ and $Q$ are probability distributions over categorical attributes.

Explanations and Business Insights

Customer Segmentation:

Clusters: The clusters represent different segments of customers based on their car features.

Insight: For example, one cluster might represent customers who prefer high-end cars with high horsepower, while another might represent budget-conscious customers who prioritize fuel efficiency.

Product Positioning:

Analysis: By examining the average features in each cluster, you can understand how different car features are valued.

Insight: You might find that one cluster values high engine size and horsepower, indicating a preference for performance cars.

Marketing Strategies:

Strategy: Tailor marketing campaigns to each cluster's preferences.

Insight: High-end car features can be highlighted in campaigns targeting clusters that value luxury, while fuel efficiency can be emphasized for budget-focused clusters.

Inventory Management:

Inventory: Adjust stock based on cluster preferences.

Insight: If a cluster with a large market share prefers cars with high horsepower, ensure adequate inventory of performance models.

Example Output

Elbow Method Plot:

Helps determine the optimal number of clusters by plotting the distortion score against the number of clusters.

Cluster Summary:

Shows average feature values for each cluster, helping to profile each customer segment.

Scatter Plots:

Visualize how clusters differ based on features like MPG City vs. Horsepower and Weight vs. Engine Size.

Silhouette Score:

Indicates how well-separated the clusters are. A higher score means better-defined clusters.