Unsupervised Learning - Kmeans Week 11 Challenge

1. How does similarity is calculated if data is categorical in nature

1. Hamming Distance

• Used when categorical variables are binary (0/1, Yes/No, True/False).

• It calculates the number of positions at which two strings of equal length are different.

• Formula:

  $$d(x, y) = \sum_{i=1}^{n} I(x_i \neq y_i)$$d(x,y)=i=1∑n​I(xi​=yi​)

  where $I(x_i \neq y_i)$I(xi​=yi​) is 1 if $x_i \neq y_i$xi​=yi​, otherwise 0.

2. Jaccard Similarity

• Used for categorical variables, especially nominal data (e.g., colors, product categories).

• Measures the ratio of common elements to total unique elements.

• Formula:

  $$J(A, B) = \frac{|A \cap B|}{|A \cup B|}$$J(A,B)=∣A∪B∣∣A∩B∣​

• Example: If A = {red, blue, green} and B = {blue, green, yellow}, then

  $$J(A, B) = \frac{2}{4} = 0.5$$J(A,B)=42​=0.5

3. Simple Matching Coefficient (SMC)

• Similar to Jaccard but includes both matches (1-1 and 0-0) in similarity calculation.

• Formula:

  $$SMC = \frac{a + d}{a + b + c + d}$$SMC=a+b+c+da+d​

  where:

  • $a$a = Number of attributes where both objects have 1 (Yes-Yes)

  • $d$d = Number of attributes where both objects have 0 (No-No)

  • $b$b, $c$c = Number of mismatches

4. Gower’s Similarity Coefficient

• Works for mixed data types (numerical + categorical).

• Computes similarity for each feature separately and averages them.

5. One-Hot Encoding + Cosine Similarity

• Convert categorical data into binary vectors using one-hot encoding.

• Compute cosine similarity between vectors:

  $$\cos(\theta) = \frac{A \cdot B}{\|A\| \|B\|}$$cos(θ)=∥A∥∥B∥A⋅B​

6. Levenshtein Distance (Edit Distance)

• Measures similarity between strings by counting minimum operations (insert, delete, replace) to convert one string into another.

2. Implement K-means for “Car dataset” and come up with the business insights

📊 METRICS USED

We extracted and cleaned multiple car specifications, then engineered some key features:

1. Mileage (kmpl or km/kg)

• Extracted from ARAI_Certified_Mileage, Highway_Mileage, and City_Mileage.

• Higher mileage = more fuel efficiency.

2. Power & Torque

• Cleaned using regex from strings like "100 bhp @ 4000 rpm".

• Indicates engine strength and pulling capacity.

3. Ex-Showroom Price (₹)

• Cleaned by removing symbols and converted to float.

• Proxy for affordability and segment.

4. Number of Airbags & Safety Rating

• Measures passenger safety.

• Included in scoring and purchasing capacity.

5. Composite Score

• Normalized features and computed average score for ranking cars.

• Inverted price since low price is more desirable.

6. Cluster (KMeans)

• Cars were grouped using KMeans clustering based on normalized features:

  • "Ex-Showroom_Price", "Mileage", "Power", "Torque", "Number_of_Airbags"

• PCA was used for 2D visualization of clusters.

7. Purchasing Capacity

• Proxy indicator = 0.6 * Price + 0.2 * Power + 0.2 * Number_of_Airbags

• Used for evaluating affordability by cluster.

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📈 GRAPHS AND VISUALIZATIONS

1. Top 10 Cars by Composite Score

• Displayed cars ranked using normalized metrics.

• Helped identify value-for-money cars with balance between performance, safety, and price.

2. KMeans Cluster Plot (PCA1 vs PCA2)

• Each car visualized in 2D space after PCA dimensionality reduction.

• Clusters show natural groupings like:

  • Cluster 0: Budget & fuel-efficient

  • Cluster 1: Mid-range all-rounders

  • Cluster 2: Premium/high-performance

  • Cluster 3: Luxury/flagship models

3. Cluster Pie Chart

• Distribution of cars by cluster.

• Showed which cluster has the most cars (e.g., mid-range dominating).

4. Sales by Make

• Bar chart showing how many cars are sold for each car brand.

• Helpful to see brand popularity (e.g., Maruti, Hyundai leading).

5. Purchasing Capacity by Cluster (Pie Chart)

• Visualized which cluster contributes most to total purchasing capacity.

• Luxury/premium clusters contribute more even with fewer cars.

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✅ CONCLUSIONS

1. Mileage vs Power Tradeoff

• Budget cars have high mileage but low power.

• Premium cars sacrifice mileage for performance.

2. Cluster Insights

• Majority cars fall in mid-range/budget segment (Clusters 0 and 1).

• Cluster 3 has fewer cars but significantly higher purchasing power.

3. Top Performing Cars

• Some mid-price cars (e.g., from Hyundai, Maruti) scored high due to a good balance of features, safety, and price.

4. Brand Popularity

• Brands like Maruti Suzuki and Hyundai have higher representation, suggesting market penetration.

5. Feature-Rich Cars Don't Always Mean High Score

• Overpriced vehicles with imbalanced features scored lower.

• Normalization helped avoid skewing scores by high price.