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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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9 machine learning concepts for ML engineers!

(explained as visually as possible)

Here's a recap of several visual summaries posted in the Daily Dose of Data Science newsletter.

1️⃣ 4 strategies for Multi-GPU Training.

- Training at scale? Learn these strategies to maximize efficiency and minimize model training time.
- Read here: https://lnkd.in/gmXF_PgZ

2️⃣ 4 ways to test models in production

- While testing a model in production might sound risky, ML teams do it all the time, and it isn’t that complicated.
- Implemented here: https://lnkd.in/g33mASMM

3️⃣ Training & inference time complexity of 10 ML algorithms

Understanding the run time of ML algorithms is important because it helps you:
- Build a core understanding of an algorithm.
- Understand the data-specific conditions to use the algorithm
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4️⃣ Regression & Classification Loss Functions.

- Get a quick overview of the most important loss functions and when to use them.
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5️⃣ Transfer Learning, Fine-tuning, Multitask Learning, and Federated Learning.

- The holy grail of advanced learning paradigms, explained visually.
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6️⃣ 15 Pandas to Polars to SQL to PySpark Translations.

- The visual will help you build familiarity with four popular frameworks for data analysis and processing.
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- A must-have visual guide to interpret and communicate your data effectively.
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Understand and categorize dataset variables for better feature engineering.
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- The ultimate cheat sheet for fast, efficient numerical computing in Python.
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𝗪𝗵𝘆 𝗘𝘃𝗲𝗿𝘆 𝗔𝘀𝗽𝗶𝗿𝗶𝗻𝗴 𝗗𝗮𝘁𝗮 𝗘𝗻𝗴𝗶𝗻𝗲𝗲𝗿 𝗦𝗵𝗼𝘂𝗹𝗱 𝗟𝗲𝗮𝗿𝗻 𝗣𝘆𝗦𝗽𝗮𝗿𝗸

If you’re working with large datasets, tools like Pandas can hit limits fast. That’s where 𝗣𝘆𝗦𝗽𝗮𝗿𝗸 comes in—designed to scale effortlessly across big data workloads.

𝗪𝗵𝗮𝘁 𝗶𝘀 𝗣𝘆𝗦𝗽𝗮𝗿𝗸?
PySpark is the Python API for Apache Spark—a powerful engine for distributed data processing. It's widely used to build scalable ETL pipelines and handle millions of records efficiently.

𝗪𝗵𝘆 𝗣𝘆𝗦𝗽𝗮𝗿𝗸 𝗜𝘀 𝗮 𝗠𝘂𝘀𝘁-𝗛𝗮𝘃𝗲 𝗳𝗼𝗿 𝗗𝗮𝘁𝗮 𝗘𝗻𝗴𝗶𝗻𝗲𝗲𝗿𝘀:
✔️ Scales to handle massive datasets
✔️ Designed for distributed computing
✔️ Blends SQL with Python for flexible logic
✔️ Perfect for building end-to-end ETL pipelines
✔️ Supports integrations like Hive, Kafka, and Delta Lake

𝗤𝘂𝗶𝗰𝗸 𝗘𝘅𝗮𝗺𝗽𝗹𝗲:

from pyspark.sql import SparkSession

spark = SparkSession.builder.appName("Example").getOrCreate() 
df = spark.read.csv("data.csv", header=True, inferSchema=True) 
df.filter(df["age"] > 30).show()

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🐼 "Comparison Between SQL and pandas" – A Handy Reference Guide

⚡️ As a data scientist, I often found myself switching back and forth between SQL and pandas during technical interviews. I was confident answering questions in SQL but sometimes struggled to translate the same logic into pandas – and vice versa.

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[1] 𝗪𝗵𝗮𝘁 𝗠𝗮𝘁𝘁𝗲𝗿𝘀 𝗶𝗻 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿𝘀? 𝗡𝗼𝘁 𝗔𝗹𝗹 𝗔𝘁𝘁𝗲𝗻𝘁𝗶𝗼𝗻 𝗶𝘀 𝗡𝗲𝗲𝗱𝗲𝗱

[2] 𝗣𝗿𝗲𝗱𝗶𝗰𝘁𝗶𝗻𝗴 𝗳𝗿𝗼𝗺 𝗦𝘁𝗿𝗶𝗻𝗴𝘀: 𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲 𝗠𝗼𝗱𝗲𝗹 𝗘𝗺𝗯𝗲𝗱𝗱𝗶𝗻𝗴𝘀 𝗳𝗼𝗿 𝗕𝗮𝘆𝗲𝘀𝗶𝗮𝗻 𝗢𝗽𝘁𝗶𝗺𝗶𝘇𝗮𝘁𝗶𝗼𝗻

[3] 𝗠𝗢𝗗𝗘𝗟 𝗦𝗪𝗔𝗥𝗠𝗦: 𝗖𝗼𝗹𝗹𝗮𝗯𝗼𝗿𝗮𝘁𝗶𝘃𝗲 𝗦𝗲𝗮𝗿𝗰𝗵 𝘁𝗼 𝗔𝗱𝗮𝗽𝘁 𝗟𝗟𝗠 𝗘𝘅𝗽𝗲𝗿𝘁𝘀 𝘃𝗶𝗮 𝗦𝘄𝗮𝗿𝗺 𝗜𝗻𝘁𝗲𝗹𝗹𝗶𝗴𝗲𝗻𝗰𝗲

[4] 𝗧𝗛𝗜𝗡𝗞𝗜𝗡𝗚 𝗟𝗟𝗠𝗦: 𝗚𝗲𝗻𝗲𝗿𝗮𝗹 𝗜𝗻𝘀𝘁𝗿𝘂𝗰𝘁𝗶𝗼𝗻 𝗙𝗼𝗹𝗹𝗼𝘄𝗶𝗻𝗴 𝘄𝗶𝘁𝗵 𝗧𝗵𝗼𝘂𝗴𝗵𝘁 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻

[5] 𝗢𝗽𝗲𝗻𝗩𝗟𝗔: 𝗔𝗻 𝗢𝗽𝗲𝗻-𝗦𝗼𝘂𝗿𝗰𝗲 𝗩𝗶𝘀𝗶𝗼𝗻-𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲-𝗔𝗰𝘁𝗶𝗼𝗻 𝗠𝗼𝗱𝗲𝗹

[6] 𝗥𝗧-𝟭: 𝗥𝗼𝗯𝗼𝘁𝗶𝗰𝘀 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿 𝗳𝗼𝗿 𝗥𝗲𝗮𝗹-𝗪𝗼𝗿𝗹𝗱 𝗖𝗼𝗻𝘁𝗿𝗼𝗹 𝗔𝘁 𝗦𝗰𝗮𝗹𝗲

[7] π𝟬: 𝗔 𝗩𝗶𝘀𝗶𝗼𝗻-𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲-𝗔𝗰𝘁𝗶𝗼𝗻 𝗙𝗹𝗼𝘄 𝗠𝗼𝗱𝗲𝗹 𝗳𝗼𝗿 𝗚𝗲𝗻𝗲𝗿𝗮𝗹 𝗥𝗼𝗯𝗼𝘁 𝗖𝗼𝗻𝘁𝗿𝗼𝗹

[8] 𝗥𝗲𝘁𝗿𝗶𝗲𝘃𝗮𝗹𝗔𝘁𝘁𝗲𝗻𝘁𝗶𝗼𝗻: 𝗔𝗰𝗰𝗲𝗹𝗲𝗿𝗮𝘁𝗶𝗻𝗴 𝗟𝗼𝗻𝗴-𝗖𝗼𝗻𝘁𝗲𝘅𝘁 𝗟𝗟𝗠 𝗜𝗻𝗳𝗲𝗿𝗲𝗻𝗰𝗲 𝘃𝗶𝗮 𝗩𝗲𝗰𝘁𝗼𝗿 𝗥𝗲𝘁𝗿𝗶𝗲𝘃𝗮𝗹

[9] 𝗣-𝗥𝗔𝗚: 𝗣𝗿𝗼𝗴𝗿𝗲𝘀𝘀𝗶𝘃𝗲 𝗥𝗲𝘁𝗿𝗶𝗲𝘃𝗮𝗹 𝗔𝘂𝗴𝗺𝗲𝗻𝘁𝗲𝗱 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻 𝗙𝗼𝗿 𝗣𝗹𝗮𝗻𝗻𝗶𝗻𝗴 𝗼𝗻 𝗘𝗺𝗯𝗼𝗱𝗶𝗲𝗱 𝗘𝘃𝗲𝗿𝘆𝗱𝗮𝘆 𝗧𝗮𝘀𝗸

[10] 𝗥𝘂𝗔𝗚: 𝗟𝗲𝗮𝗿𝗻𝗲𝗱-𝗥𝘂𝗹𝗲-𝗔𝘂𝗴𝗺𝗲𝗻𝘁𝗲𝗱 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻 𝗙𝗼𝗿 𝗟𝗮𝗿𝗴𝗲 𝗟𝗮𝗻𝗴𝘂𝗮𝗴𝗲 𝗠𝗼𝗱𝗲𝗹𝘀

[11] 𝗢𝗻 𝘁𝗵𝗲 𝗦𝘂𝗿𝗽𝗿𝗶𝘀𝗶𝗻𝗴 𝗘𝗳𝗳𝗲𝗰𝘁𝗶𝘃𝗲𝗻𝗲𝘀𝘀 𝗼𝗳 𝗔𝘁𝘁𝗲𝗻𝘁𝗶𝗼𝗻 𝗧𝗿𝗮𝗻𝘀𝗳𝗲𝗿 𝗳𝗼𝗿 𝗩𝗶𝘀𝗶𝗼𝗻 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿𝘀

[12] 𝗠𝗶𝘅𝘁𝘂𝗿𝗲-𝗼𝗳-𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿𝘀: 𝗔 𝗦𝗽𝗮𝗿𝘀𝗲 𝗮𝗻𝗱 𝗦𝗰𝗮𝗹𝗮𝗯𝗹𝗲 𝗔𝗿𝗰𝗵𝗶𝘁𝗲𝗰𝘁𝘂𝗿𝗲 𝗳𝗼𝗿 𝗠𝘂𝗹𝘁𝗶-𝗠𝗼𝗱𝗮𝗹 𝗙𝗼𝘂𝗻𝗱𝗮𝘁𝗶𝗼𝗻 𝗠𝗼𝗱𝗲𝗹𝘀

[13]-[14] 𝗘𝗱𝗶𝗳𝘆 𝟯𝗗: 𝗦𝗰𝗮𝗹𝗮𝗯𝗹𝗲 𝗛𝗶𝗴𝗵-𝗤𝘂𝗮𝗹𝗶𝘁𝘆 𝟯𝗗 𝗔𝘀𝘀𝗲𝘁 𝗚𝗲𝗻𝗲𝗿𝗮𝘁𝗶𝗼𝗻

[15] 𝗕𝘆𝘁𝗲 𝗟𝗮𝘁𝗲𝗻𝘁 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿: 𝗣𝗮𝘁𝗰𝗵𝗲𝘀 𝗦𝗰𝗮𝗹𝗲 𝗕𝗲𝘁𝘁𝗲𝗿 𝗧𝗵𝗮𝗻 𝗧𝗼𝗸𝗲𝗻𝘀

[16]-[18] 𝗗𝗲𝗲𝗽𝗦𝗲𝗲𝗸-𝗩𝟯 (𝗣𝗮𝗿𝘁 𝟭-𝟯)

[19] 𝗧𝗿𝗮𝗻𝘀𝗳𝗼𝗿𝗺𝗲𝗿𝘀 𝘄𝗶𝘁𝗵𝗼𝘂𝘁 𝗡𝗼𝗿𝗺𝗮𝗹𝗶𝘇𝗮𝘁𝗶𝗼𝗻

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Best Statistics Notes ✅

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Scientific Visualization: Python + Matplotlib

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📕 Mastering NumPy – From Basics to Advanced

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