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𝐊-𝐌𝐞𝐚𝐧𝐬 𝐂𝐥𝐮𝐬𝐭𝐞𝐫𝐢𝐧𝐠 𝐄𝐱𝐩𝐥𝐚𝐢𝐧𝐞𝐝 - 𝐟𝐨𝐫 𝐛𝐞𝐠𝐢𝐧𝐧𝐞𝐫𝐬

𝐖𝐡𝐚𝐭 𝐢𝐬 𝐊-𝐌𝐞𝐚𝐧𝐬?
It’s an unsupervised machine learning algorithm that automatically groups your data into K similar clusters without labels. It finds hidden patterns using distance-based similarity.

𝐈𝐧𝐭𝐮𝐢𝐭𝐢𝐯𝐞 𝐞𝐱𝐚𝐦𝐩𝐥𝐞:
You run a mall. Your data has:
› Age
› Annual Income
› Spending Score

K-Means can divide customers into:
⤷ Budget Shoppers
⤷ Mid-Range Customers
⤷ High-End Spenders

𝐇𝐨𝐰 𝐢𝐭 𝐰𝐨𝐫𝐤𝐬:
① Choose the number of clusters K
② Randomly initialize K centroids
③ Assign each point to its nearest centroid
④ Move centroids to the mean of their assigned points
⑤ Repeat until centroids don’t move (convergence)

𝐎𝐛𝐣𝐞𝐜𝐭𝐢𝐯𝐞:
Minimize the total squared distance between data points and their cluster centroids
𝐉 = Σ‖𝐱ᵢ - μⱼ‖²
Where 𝐱ᵢ = data point, μⱼ = cluster center

𝐇𝐨𝐰 𝐭𝐨 𝐩𝐢𝐜𝐤 𝐊:
Use the Elbow Method
⤷ Plot K vs. total within-cluster variance
⤷ The “elbow” in the curve = ideal number of clusters

𝐂𝐨𝐝𝐞 𝐄𝐱𝐚𝐦𝐩𝐥𝐞 (𝐒𝐜𝐢𝐤𝐢𝐭-𝐋𝐞𝐚𝐫𝐧):

from sklearn.cluster import KMeans
X = [[1, 2], [1, 4], [1, 0], [10, 2], [10, 4], [10, 0]]
model = KMeans(n_clusters=2, random_state=0)
model.fit(X)
print(model.labels_)
print(model.cluster_centers_)

𝐁𝐞𝐬𝐭 𝐔𝐬𝐞 𝐂𝐚𝐬𝐞𝐬:
⤷ Customer segmentation
⤷ Image compression
⤷ Market analysis
⤷ Social network analysis

𝐋𝐢𝐦𝐢𝐭𝐚𝐭𝐢𝐨𝐧𝐬:
› Sensitive to outliers
› Requires you to predefine K
› Works best with spherical clusters

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𝗣𝗿𝗶𝗻𝗰𝗶𝗽𝗮𝗹 𝗖𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁 𝗔𝗻𝗮𝗹𝘆𝘀𝗶𝘀 (𝗣𝗖𝗔)
𝗧𝗵𝗲 𝗔𝗿𝘁 𝗼𝗳 𝗥𝗲𝗱𝘂𝗰𝗶𝗻𝗴 𝗗𝗶𝗺𝗲𝗻𝘀𝗶𝗼𝗻𝘀 𝗪𝗶𝘁𝗵𝗼𝘂𝘁 𝗟𝗼𝘀𝗶𝗻𝗴 𝗜𝗻𝘀𝗶𝗴𝗵𝘁𝘀

𝗪𝗵𝗮𝘁 𝗘𝘅𝗮𝗰𝘁𝗹𝘆 𝗜𝘀 𝗣𝗖𝗔?
⤷ 𝗣𝗖𝗔 is a 𝗺𝗮𝘁𝗵𝗲𝗺𝗮𝘁𝗶𝗰𝗮𝗹 𝘁𝗲𝗰𝗵𝗻𝗶𝗾𝘂𝗲 used to transform a 𝗵𝗶𝗴𝗵-𝗱𝗶𝗺𝗲𝗻𝘀𝗶𝗼𝗻𝗮𝗹 dataset into fewer dimensions, while retaining as much 𝘃𝗮𝗿𝗶𝗮𝗯𝗶𝗹𝗶𝘁𝘆 (𝗶𝗻𝗳𝗼𝗿𝗺𝗮𝘁𝗶𝗼𝗻) as possible.
⤷ Think of it as “𝗰𝗼𝗺𝗽𝗿𝗲𝘀𝘀𝗶𝗻𝗴” data, similar to how we reduce the size of an image without losing too much detail.

𝗪𝗵𝘆 𝗨𝘀𝗲 𝗣𝗖𝗔 𝗶𝗻 𝗬𝗼𝘂𝗿 𝗣𝗿𝗼𝗷𝗲𝗰𝘁𝘀?
⤷ 𝗦𝗶𝗺𝗽𝗹𝗶𝗳𝘆 your data for 𝗲𝗮𝘀𝗶𝗲𝗿 𝗮𝗻𝗮𝗹𝘆𝘀𝗶𝘀 and 𝗺𝗼𝗱𝗲𝗹𝗶𝗻𝗴
⤷ 𝗘𝗻𝗵𝗮𝗻𝗰𝗲 machine learning models by reducing 𝗰𝗼𝗺𝗽𝘂𝘁𝗮𝘁𝗶𝗼𝗻𝗮𝗹 𝗰𝗼𝘀𝘁
⤷ 𝗩𝗶𝘀𝘂𝗮𝗹𝗶𝘇𝗲 multi-dimensional data in 2𝗗 or 3𝗗 for insights
⤷ 𝗙𝗶𝗹𝘁𝗲𝗿 𝗼𝘂𝘁 𝗻𝗼𝗶𝘀𝗲 and uncover hidden patterns in your data

𝗧𝗵𝗲 𝗣𝗼𝘄𝗲𝗿 𝗼𝗳 𝗣𝗿𝗶𝗻𝗰𝗶𝗽𝗮𝗹 𝗖𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁𝘀
⤷ The 𝗳𝗶𝗿𝘀𝘁 𝗽𝗿𝗶𝗻𝗰𝗶𝗽𝗮𝗹 𝗰𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁 is the direction in which the data varies the most.
⤷ Each subsequent component represents the 𝗻𝗲𝘅𝘁 𝗵𝗶𝗴𝗵𝗲𝘀𝘁 𝗿𝗮𝘁𝗲 of variance, but is 𝗼𝗿𝘁𝗵𝗼𝗴𝗼𝗻𝗮𝗹 (𝘂𝗻𝗰𝗼𝗿𝗿𝗲𝗹𝗮𝘁𝗲𝗱) to the previous one.
⤷ The challenge is selecting how many components to keep based on the 𝘃𝗮𝗿𝗶𝗮𝗻𝗰𝗲 they explain.

𝗣𝗿𝗮𝗰𝘁𝗶𝗰𝗮𝗹 𝗘𝘅𝗮𝗺𝗽𝗹𝗲

1: 𝗖𝘂𝘀𝘁𝗼𝗺𝗲𝗿 𝗦𝗲𝗴𝗺𝗲𝗻𝘁𝗮𝘁𝗶𝗼𝗻
Imagine you’re working on a project to 𝘀𝗲𝗴𝗺𝗲𝗻𝘁 customers for a marketing campaign, with data on spending habits, age, income, and location.
⤷ Using 𝗣𝗖𝗔, you can reduce these four variables into just 𝘁𝘄𝗼 𝗽𝗿𝗶𝗻𝗰𝗶𝗽𝗮𝗹 𝗰𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁𝘀 that retain 90% of the variance.
⤷ These two new components can then be used for 𝗸-𝗺𝗲𝗮𝗻𝘀 clustering to identify distinct customer groups without dealing with the complexity of all the original variables.

𝗧𝗵𝗲 𝗣𝗖𝗔 𝗣𝗿𝗼𝗰𝗲𝘀𝘀 — 𝗦𝘁𝗲𝗽-𝗕𝘆-𝗦𝘁𝗲𝗽
⤷ 𝗦𝘁𝗲𝗽 𝟭: 𝗗𝗮𝘁𝗮 𝗦𝘁𝗮𝗻𝗱𝗮𝗿𝗱𝗶𝘇𝗮𝘁𝗶𝗼𝗻
Ensure your data is on the same scale (e.g., mean = 0, variance = 1).
⤷ 𝗦𝘁𝗲𝗽 𝟮: 𝗖𝗼𝘃𝗮𝗿𝗶𝗮𝗻𝗰𝗲 𝗠𝗮𝘁𝗿𝗶𝘅
Calculate how features are correlated.
⤷ 𝗦𝘁𝗲𝗽 𝟯: 𝗘𝗶𝗴𝗲𝗻 𝗗𝗲𝗰𝗼𝗺𝗽𝗼𝘀𝗶𝘁𝗶𝗼𝗻
Compute the eigenvectors and eigenvalues to determine the principal components.
⤷ 𝗦𝘁𝗲𝗽 𝟰: 𝗦𝗲𝗹𝗲𝗰𝘁 𝗖𝗼𝗺𝗽𝗼𝗻𝗲𝗻𝘁𝘀
Choose the top-k components based on the explained variance ratio.
⤷ 𝗦𝘁𝗲𝗽 𝟱: 𝗗𝗮𝘁𝗮 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗮𝘁𝗶𝗼𝗻
Transform your data onto the new 𝗣𝗖𝗔 space with fewer dimensions.

𝗪𝗵𝗲𝗻 𝗡𝗼𝘁 𝘁𝗼 𝗨𝘀𝗲 𝗣𝗖𝗔
⤷ 𝗣𝗖𝗔 is not suitable when the dataset contains 𝗻𝗼𝗻-𝗹𝗶𝗻𝗲𝗮𝗿 𝗿𝗲𝗹𝗮𝘁𝗶𝗼𝗻𝘀𝗵𝗶𝗽𝘀 or 𝗵𝗶𝗴𝗵𝗹𝘆 𝘀𝗸𝗲𝘄𝗲𝗱 𝗱𝗮𝘁𝗮.
⤷ For non-linear data, consider 𝗧-𝗦𝗡𝗘 or 𝗮𝘂𝘁𝗼𝗲𝗻𝗰𝗼𝗱𝗲𝗿𝘀 instead.

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