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๐-๐๐๐๐ง๐ฌ ๐๐ฅ๐ฎ๐ฌ๐ญ๐๐ซ๐ข๐ง๐ ๐๐ฑ๐ฉ๐ฅ๐๐ข๐ง๐๐ - ๐๐จ๐ซ ๐๐๐ ๐ข๐ง๐ง๐๐ซ๐ฌ
๐๐ก๐๐ญ ๐ข๐ฌ ๐-๐๐๐๐ง๐ฌ?
Itโs an unsupervised machine learning algorithm that automatically groups your data into K similar clusters without labels. It finds hidden patterns using distance-based similarity.
๐๐ง๐ญ๐ฎ๐ข๐ญ๐ข๐ฏ๐ ๐๐ฑ๐๐ฆ๐ฉ๐ฅ๐:
You run a mall. Your data has:
โบ Age
โบ Annual Income
โบ Spending Score
K-Means can divide customers into:
โคท Budget Shoppers
โคท Mid-Range Customers
โคท High-End Spenders
๐๐จ๐ฐ ๐ข๐ญ ๐ฐ๐จ๐ซ๐ค๐ฌ:
โ Choose the number of clusters K
โก Randomly initialize K centroids
โข Assign each point to its nearest centroid
โฃ Move centroids to the mean of their assigned points
โค Repeat until centroids donโt move (convergence)
๐๐๐ฃ๐๐๐ญ๐ข๐ฏ๐:
Minimize the total squared distance between data points and their cluster centroids
๐ = ฮฃโ๐ฑแตข - ฮผโฑผโยฒ
Where ๐ฑแตข = data point, ฮผโฑผ = cluster center
๐๐จ๐ฐ ๐ญ๐จ ๐ฉ๐ข๐๐ค ๐:
Use the Elbow Method
โคท Plot K vs. total within-cluster variance
โคท The โelbowโ in the curve = ideal number of clusters
๐๐จ๐๐ ๐๐ฑ๐๐ฆ๐ฉ๐ฅ๐ (๐๐๐ข๐ค๐ข๐ญ-๐๐๐๐ซ๐ง):
๐๐๐ฌ๐ญ ๐๐ฌ๐ ๐๐๐ฌ๐๐ฌ:
โคท Customer segmentation
โคท Image compression
โคท Market analysis
โคท Social network analysis
๐๐ข๐ฆ๐ข๐ญ๐๐ญ๐ข๐จ๐ง๐ฌ:
โบ Sensitive to outliers
โบ Requires you to predefine K
โบ Works best with spherical clusters
https://whatsapp.com/channel/0029VaC7Weq29753hpcggW2A๐ฑ
๐๐ก๐๐ญ ๐ข๐ฌ ๐-๐๐๐๐ง๐ฌ?
Itโs an unsupervised machine learning algorithm that automatically groups your data into K similar clusters without labels. It finds hidden patterns using distance-based similarity.
๐๐ง๐ญ๐ฎ๐ข๐ญ๐ข๐ฏ๐ ๐๐ฑ๐๐ฆ๐ฉ๐ฅ๐:
You run a mall. Your data has:
โบ Age
โบ Annual Income
โบ Spending Score
K-Means can divide customers into:
โคท Budget Shoppers
โคท Mid-Range Customers
โคท High-End Spenders
๐๐จ๐ฐ ๐ข๐ญ ๐ฐ๐จ๐ซ๐ค๐ฌ:
โ Choose the number of clusters K
โก Randomly initialize K centroids
โข Assign each point to its nearest centroid
โฃ Move centroids to the mean of their assigned points
โค Repeat until centroids donโt move (convergence)
๐๐๐ฃ๐๐๐ญ๐ข๐ฏ๐:
Minimize the total squared distance between data points and their cluster centroids
๐ = ฮฃโ๐ฑแตข - ฮผโฑผโยฒ
Where ๐ฑแตข = data point, ฮผโฑผ = cluster center
๐๐จ๐ฐ ๐ญ๐จ ๐ฉ๐ข๐๐ค ๐:
Use the Elbow Method
โคท Plot K vs. total within-cluster variance
โคท The โelbowโ in the curve = ideal number of clusters
๐๐จ๐๐ ๐๐ฑ๐๐ฆ๐ฉ๐ฅ๐ (๐๐๐ข๐ค๐ข๐ญ-๐๐๐๐ซ๐ง):
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_)
๐๐๐ฌ๐ญ ๐๐ฌ๐ ๐๐๐ฌ๐๐ฌ:
โคท Customer segmentation
โคท Image compression
โคท Market analysis
โคท Social network analysis
๐๐ข๐ฆ๐ข๐ญ๐๐ญ๐ข๐จ๐ง๐ฌ:
โบ Sensitive to outliers
โบ Requires you to predefine K
โบ Works best with spherical clusters
https://whatsapp.com/channel/0029VaC7Weq29753hpcggW2A
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๐ฃ๐ฟ๐ถ๐ป๐ฐ๐ถ๐ฝ๐ฎ๐น ๐๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐ ๐๐ป๐ฎ๐น๐๐๐ถ๐ (๐ฃ๐๐)
๐ง๐ต๐ฒ ๐๐ฟ๐ ๐ผ๐ณ ๐ฅ๐ฒ๐ฑ๐๐ฐ๐ถ๐ป๐ด ๐๐ถ๐บ๐ฒ๐ป๐๐ถ๐ผ๐ป๐ ๐ช๐ถ๐๐ต๐ผ๐๐ ๐๐ผ๐๐ถ๐ป๐ด ๐๐ป๐๐ถ๐ด๐ต๐๐
๐ช๐ต๐ฎ๐ ๐๐ ๐ฎ๐ฐ๐๐น๐ ๐๐ ๐ฃ๐๐?
โคท ๐ฃ๐๐ is a ๐บ๐ฎ๐๐ต๐ฒ๐บ๐ฎ๐๐ถ๐ฐ๐ฎ๐น ๐๐ฒ๐ฐ๐ต๐ป๐ถ๐พ๐๐ฒ used to transform a ๐ต๐ถ๐ด๐ต-๐ฑ๐ถ๐บ๐ฒ๐ป๐๐ถ๐ผ๐ป๐ฎ๐น dataset into fewer dimensions, while retaining as much ๐๐ฎ๐ฟ๐ถ๐ฎ๐ฏ๐ถ๐น๐ถ๐๐ (๐ถ๐ป๐ณ๐ผ๐ฟ๐บ๐ฎ๐๐ถ๐ผ๐ป) as possible.
โคท Think of it as โ๐ฐ๐ผ๐บ๐ฝ๐ฟ๐ฒ๐๐๐ถ๐ป๐ดโ data, similar to how we reduce the size of an image without losing too much detail.
๐ช๐ต๐ ๐จ๐๐ฒ ๐ฃ๐๐ ๐ถ๐ป ๐ฌ๐ผ๐๐ฟ ๐ฃ๐ฟ๐ผ๐ท๐ฒ๐ฐ๐๐?
โคท ๐ฆ๐ถ๐บ๐ฝ๐น๐ถ๐ณ๐ your data for ๐ฒ๐ฎ๐๐ถ๐ฒ๐ฟ ๐ฎ๐ป๐ฎ๐น๐๐๐ถ๐ and ๐บ๐ผ๐ฑ๐ฒ๐น๐ถ๐ป๐ด
โคท ๐๐ป๐ต๐ฎ๐ป๐ฐ๐ฒ machine learning models by reducing ๐ฐ๐ผ๐บ๐ฝ๐๐๐ฎ๐๐ถ๐ผ๐ป๐ฎ๐น ๐ฐ๐ผ๐๐
โคท ๐ฉ๐ถ๐๐๐ฎ๐น๐ถ๐๐ฒ multi-dimensional data in 2๐ or 3๐ for insights
โคท ๐๐ถ๐น๐๐ฒ๐ฟ ๐ผ๐๐ ๐ป๐ผ๐ถ๐๐ฒ and uncover hidden patterns in your data
๐ง๐ต๐ฒ ๐ฃ๐ผ๐๐ฒ๐ฟ ๐ผ๐ณ ๐ฃ๐ฟ๐ถ๐ป๐ฐ๐ถ๐ฝ๐ฎ๐น ๐๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐๐
โคท The ๐ณ๐ถ๐ฟ๐๐ ๐ฝ๐ฟ๐ถ๐ป๐ฐ๐ถ๐ฝ๐ฎ๐น ๐ฐ๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐ is the direction in which the data varies the most.
โคท Each subsequent component represents the ๐ป๐ฒ๐ ๐ ๐ต๐ถ๐ด๐ต๐ฒ๐๐ ๐ฟ๐ฎ๐๐ฒ of variance, but is ๐ผ๐ฟ๐๐ต๐ผ๐ด๐ผ๐ป๐ฎ๐น (๐๐ป๐ฐ๐ผ๐ฟ๐ฟ๐ฒ๐น๐ฎ๐๐ฒ๐ฑ) to the previous one.
โคท The challenge is selecting how many components to keep based on the ๐๐ฎ๐ฟ๐ถ๐ฎ๐ป๐ฐ๐ฒ they explain.
๐ฃ๐ฟ๐ฎ๐ฐ๐๐ถ๐ฐ๐ฎ๐น ๐๐ ๐ฎ๐บ๐ฝ๐น๐ฒ
1: ๐๐๐๐๐ผ๐บ๐ฒ๐ฟ ๐ฆ๐ฒ๐ด๐บ๐ฒ๐ป๐๐ฎ๐๐ถ๐ผ๐ป
Imagine youโre working on a project to ๐๐ฒ๐ด๐บ๐ฒ๐ป๐ customers for a marketing campaign, with data on spending habits, age, income, and location.
โคท Using ๐ฃ๐๐, you can reduce these four variables into just ๐๐๐ผ ๐ฝ๐ฟ๐ถ๐ป๐ฐ๐ถ๐ฝ๐ฎ๐น ๐ฐ๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐๐ that retain 90% of the variance.
โคท These two new components can then be used for ๐ธ-๐บ๐ฒ๐ฎ๐ป๐ clustering to identify distinct customer groups without dealing with the complexity of all the original variables.
๐ง๐ต๐ฒ ๐ฃ๐๐ ๐ฃ๐ฟ๐ผ๐ฐ๐ฒ๐๐ โ ๐ฆ๐๐ฒ๐ฝ-๐๐-๐ฆ๐๐ฒ๐ฝ
โคท ๐ฆ๐๐ฒ๐ฝ ๐ญ: ๐๐ฎ๐๐ฎ ๐ฆ๐๐ฎ๐ป๐ฑ๐ฎ๐ฟ๐ฑ๐ถ๐๐ฎ๐๐ถ๐ผ๐ป
Ensure your data is on the same scale (e.g., mean = 0, variance = 1).
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฎ: ๐๐ผ๐๐ฎ๐ฟ๐ถ๐ฎ๐ป๐ฐ๐ฒ ๐ ๐ฎ๐๐ฟ๐ถ๐
Calculate how features are correlated.
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฏ: ๐๐ถ๐ด๐ฒ๐ป ๐๐ฒ๐ฐ๐ผ๐บ๐ฝ๐ผ๐๐ถ๐๐ถ๐ผ๐ป
Compute the eigenvectors and eigenvalues to determine the principal components.
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฐ: ๐ฆ๐ฒ๐น๐ฒ๐ฐ๐ ๐๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐๐
Choose the top-k components based on the explained variance ratio.
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฑ: ๐๐ฎ๐๐ฎ ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฎ๐๐ถ๐ผ๐ป
Transform your data onto the new ๐ฃ๐๐ space with fewer dimensions.
๐ช๐ต๐ฒ๐ป ๐ก๐ผ๐ ๐๐ผ ๐จ๐๐ฒ ๐ฃ๐๐
โคท ๐ฃ๐๐ is not suitable when the dataset contains ๐ป๐ผ๐ป-๐น๐ถ๐ป๐ฒ๐ฎ๐ฟ ๐ฟ๐ฒ๐น๐ฎ๐๐ถ๐ผ๐ป๐๐ต๐ถ๐ฝ๐ or ๐ต๐ถ๐ด๐ต๐น๐ ๐๐ธ๐ฒ๐๐ฒ๐ฑ ๐ฑ๐ฎ๐๐ฎ.
โคท For non-linear data, consider ๐ง-๐ฆ๐ก๐ or ๐ฎ๐๐๐ผ๐ฒ๐ป๐ฐ๐ผ๐ฑ๐ฒ๐ฟ๐ instead.
https://whatsapp.com/channel/0029VaC7Weq29753hpcggW2A๐ฑ
๐ง๐ต๐ฒ ๐๐ฟ๐ ๐ผ๐ณ ๐ฅ๐ฒ๐ฑ๐๐ฐ๐ถ๐ป๐ด ๐๐ถ๐บ๐ฒ๐ป๐๐ถ๐ผ๐ป๐ ๐ช๐ถ๐๐ต๐ผ๐๐ ๐๐ผ๐๐ถ๐ป๐ด ๐๐ป๐๐ถ๐ด๐ต๐๐
๐ช๐ต๐ฎ๐ ๐๐ ๐ฎ๐ฐ๐๐น๐ ๐๐ ๐ฃ๐๐?
โคท ๐ฃ๐๐ is a ๐บ๐ฎ๐๐ต๐ฒ๐บ๐ฎ๐๐ถ๐ฐ๐ฎ๐น ๐๐ฒ๐ฐ๐ต๐ป๐ถ๐พ๐๐ฒ used to transform a ๐ต๐ถ๐ด๐ต-๐ฑ๐ถ๐บ๐ฒ๐ป๐๐ถ๐ผ๐ป๐ฎ๐น dataset into fewer dimensions, while retaining as much ๐๐ฎ๐ฟ๐ถ๐ฎ๐ฏ๐ถ๐น๐ถ๐๐ (๐ถ๐ป๐ณ๐ผ๐ฟ๐บ๐ฎ๐๐ถ๐ผ๐ป) as possible.
โคท Think of it as โ๐ฐ๐ผ๐บ๐ฝ๐ฟ๐ฒ๐๐๐ถ๐ป๐ดโ data, similar to how we reduce the size of an image without losing too much detail.
๐ช๐ต๐ ๐จ๐๐ฒ ๐ฃ๐๐ ๐ถ๐ป ๐ฌ๐ผ๐๐ฟ ๐ฃ๐ฟ๐ผ๐ท๐ฒ๐ฐ๐๐?
โคท ๐ฆ๐ถ๐บ๐ฝ๐น๐ถ๐ณ๐ your data for ๐ฒ๐ฎ๐๐ถ๐ฒ๐ฟ ๐ฎ๐ป๐ฎ๐น๐๐๐ถ๐ and ๐บ๐ผ๐ฑ๐ฒ๐น๐ถ๐ป๐ด
โคท ๐๐ป๐ต๐ฎ๐ป๐ฐ๐ฒ machine learning models by reducing ๐ฐ๐ผ๐บ๐ฝ๐๐๐ฎ๐๐ถ๐ผ๐ป๐ฎ๐น ๐ฐ๐ผ๐๐
โคท ๐ฉ๐ถ๐๐๐ฎ๐น๐ถ๐๐ฒ multi-dimensional data in 2๐ or 3๐ for insights
โคท ๐๐ถ๐น๐๐ฒ๐ฟ ๐ผ๐๐ ๐ป๐ผ๐ถ๐๐ฒ and uncover hidden patterns in your data
๐ง๐ต๐ฒ ๐ฃ๐ผ๐๐ฒ๐ฟ ๐ผ๐ณ ๐ฃ๐ฟ๐ถ๐ป๐ฐ๐ถ๐ฝ๐ฎ๐น ๐๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐๐
โคท The ๐ณ๐ถ๐ฟ๐๐ ๐ฝ๐ฟ๐ถ๐ป๐ฐ๐ถ๐ฝ๐ฎ๐น ๐ฐ๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐ is the direction in which the data varies the most.
โคท Each subsequent component represents the ๐ป๐ฒ๐ ๐ ๐ต๐ถ๐ด๐ต๐ฒ๐๐ ๐ฟ๐ฎ๐๐ฒ of variance, but is ๐ผ๐ฟ๐๐ต๐ผ๐ด๐ผ๐ป๐ฎ๐น (๐๐ป๐ฐ๐ผ๐ฟ๐ฟ๐ฒ๐น๐ฎ๐๐ฒ๐ฑ) to the previous one.
โคท The challenge is selecting how many components to keep based on the ๐๐ฎ๐ฟ๐ถ๐ฎ๐ป๐ฐ๐ฒ they explain.
๐ฃ๐ฟ๐ฎ๐ฐ๐๐ถ๐ฐ๐ฎ๐น ๐๐ ๐ฎ๐บ๐ฝ๐น๐ฒ
1: ๐๐๐๐๐ผ๐บ๐ฒ๐ฟ ๐ฆ๐ฒ๐ด๐บ๐ฒ๐ป๐๐ฎ๐๐ถ๐ผ๐ป
Imagine youโre working on a project to ๐๐ฒ๐ด๐บ๐ฒ๐ป๐ customers for a marketing campaign, with data on spending habits, age, income, and location.
โคท Using ๐ฃ๐๐, you can reduce these four variables into just ๐๐๐ผ ๐ฝ๐ฟ๐ถ๐ป๐ฐ๐ถ๐ฝ๐ฎ๐น ๐ฐ๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐๐ that retain 90% of the variance.
โคท These two new components can then be used for ๐ธ-๐บ๐ฒ๐ฎ๐ป๐ clustering to identify distinct customer groups without dealing with the complexity of all the original variables.
๐ง๐ต๐ฒ ๐ฃ๐๐ ๐ฃ๐ฟ๐ผ๐ฐ๐ฒ๐๐ โ ๐ฆ๐๐ฒ๐ฝ-๐๐-๐ฆ๐๐ฒ๐ฝ
โคท ๐ฆ๐๐ฒ๐ฝ ๐ญ: ๐๐ฎ๐๐ฎ ๐ฆ๐๐ฎ๐ป๐ฑ๐ฎ๐ฟ๐ฑ๐ถ๐๐ฎ๐๐ถ๐ผ๐ป
Ensure your data is on the same scale (e.g., mean = 0, variance = 1).
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฎ: ๐๐ผ๐๐ฎ๐ฟ๐ถ๐ฎ๐ป๐ฐ๐ฒ ๐ ๐ฎ๐๐ฟ๐ถ๐
Calculate how features are correlated.
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฏ: ๐๐ถ๐ด๐ฒ๐ป ๐๐ฒ๐ฐ๐ผ๐บ๐ฝ๐ผ๐๐ถ๐๐ถ๐ผ๐ป
Compute the eigenvectors and eigenvalues to determine the principal components.
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฐ: ๐ฆ๐ฒ๐น๐ฒ๐ฐ๐ ๐๐ผ๐บ๐ฝ๐ผ๐ป๐ฒ๐ป๐๐
Choose the top-k components based on the explained variance ratio.
โคท ๐ฆ๐๐ฒ๐ฝ ๐ฑ: ๐๐ฎ๐๐ฎ ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฎ๐๐ถ๐ผ๐ป
Transform your data onto the new ๐ฃ๐๐ space with fewer dimensions.
๐ช๐ต๐ฒ๐ป ๐ก๐ผ๐ ๐๐ผ ๐จ๐๐ฒ ๐ฃ๐๐
โคท ๐ฃ๐๐ is not suitable when the dataset contains ๐ป๐ผ๐ป-๐น๐ถ๐ป๐ฒ๐ฎ๐ฟ ๐ฟ๐ฒ๐น๐ฎ๐๐ถ๐ผ๐ป๐๐ต๐ถ๐ฝ๐ or ๐ต๐ถ๐ด๐ต๐น๐ ๐๐ธ๐ฒ๐๐ฒ๐ฑ ๐ฑ๐ฎ๐๐ฎ.
โคท For non-linear data, consider ๐ง-๐ฆ๐ก๐ or ๐ฎ๐๐๐ผ๐ฒ๐ป๐ฐ๐ผ๐ฑ๐ฒ๐ฟ๐ instead.
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This channels is for Programmers, Coders, Software Engineers.
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1๏ธโฃ Data Science
2๏ธโฃ Machine Learning
3๏ธโฃ Data Visualization
4๏ธโฃ Artificial Intelligence
5๏ธโฃ Data Analysis
6๏ธโฃ Statistics
7๏ธโฃ Deep Learning
8๏ธโฃ programming Languages
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from SQL to pandas.pdf
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#DataScience #SQL #pandas #InterviewPrep #Python #DataAnalysis #CareerGrowth #TechTips #Analytics
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Forwarded from Data Science Machine Learning Data Analysis Books
๐ฃ AI Paper by Hand.pdf
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๐ฃ AI Paper by Hand โ๏ธ
[1] ๐ช๐ต๐ฎ๐ ๐ ๐ฎ๐๐๐ฒ๐ฟ๐ ๐ถ๐ป ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐? ๐ก๐ผ๐ ๐๐น๐น ๐๐๐๐ฒ๐ป๐๐ถ๐ผ๐ป ๐ถ๐ ๐ก๐ฒ๐ฒ๐ฑ๐ฒ๐ฑ
[2] ๐ฃ๐ฟ๐ฒ๐ฑ๐ถ๐ฐ๐๐ถ๐ป๐ด ๐ณ๐ฟ๐ผ๐บ ๐ฆ๐๐ฟ๐ถ๐ป๐ด๐: ๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ ๐ ๐ผ๐ฑ๐ฒ๐น ๐๐บ๐ฏ๐ฒ๐ฑ๐ฑ๐ถ๐ป๐ด๐ ๐ณ๐ผ๐ฟ ๐๐ฎ๐๐ฒ๐๐ถ๐ฎ๐ป ๐ข๐ฝ๐๐ถ๐บ๐ถ๐๐ฎ๐๐ถ๐ผ๐ป
[3] ๐ ๐ข๐๐๐ ๐ฆ๐ช๐๐ฅ๐ ๐ฆ: ๐๐ผ๐น๐น๐ฎ๐ฏ๐ผ๐ฟ๐ฎ๐๐ถ๐๐ฒ ๐ฆ๐ฒ๐ฎ๐ฟ๐ฐ๐ต ๐๐ผ ๐๐ฑ๐ฎ๐ฝ๐ ๐๐๐ ๐๐ ๐ฝ๐ฒ๐ฟ๐๐ ๐๐ถ๐ฎ ๐ฆ๐๐ฎ๐ฟ๐บ ๐๐ป๐๐ฒ๐น๐น๐ถ๐ด๐ฒ๐ป๐ฐ๐ฒ
[4] ๐ง๐๐๐ก๐๐๐ก๐ ๐๐๐ ๐ฆ: ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐น ๐๐ป๐๐๐ฟ๐๐ฐ๐๐ถ๐ผ๐ป ๐๐ผ๐น๐น๐ผ๐๐ถ๐ป๐ด ๐๐ถ๐๐ต ๐ง๐ต๐ผ๐๐ด๐ต๐ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป
[5] ๐ข๐ฝ๐ฒ๐ป๐ฉ๐๐: ๐๐ป ๐ข๐ฝ๐ฒ๐ป-๐ฆ๐ผ๐๐ฟ๐ฐ๐ฒ ๐ฉ๐ถ๐๐ถ๐ผ๐ป-๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ-๐๐ฐ๐๐ถ๐ผ๐ป ๐ ๐ผ๐ฑ๐ฒ๐น
[6] ๐ฅ๐ง-๐ญ: ๐ฅ๐ผ๐ฏ๐ผ๐๐ถ๐ฐ๐ ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ ๐ณ๐ผ๐ฟ ๐ฅ๐ฒ๐ฎ๐น-๐ช๐ผ๐ฟ๐น๐ฑ ๐๐ผ๐ป๐๐ฟ๐ผ๐น ๐๐ ๐ฆ๐ฐ๐ฎ๐น๐ฒ
[7] ฯ๐ฌ: ๐ ๐ฉ๐ถ๐๐ถ๐ผ๐ป-๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ-๐๐ฐ๐๐ถ๐ผ๐ป ๐๐น๐ผ๐ ๐ ๐ผ๐ฑ๐ฒ๐น ๐ณ๐ผ๐ฟ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐น ๐ฅ๐ผ๐ฏ๐ผ๐ ๐๐ผ๐ป๐๐ฟ๐ผ๐น
[8] ๐ฅ๐ฒ๐๐ฟ๐ถ๐ฒ๐๐ฎ๐น๐๐๐๐ฒ๐ป๐๐ถ๐ผ๐ป: ๐๐ฐ๐ฐ๐ฒ๐น๐ฒ๐ฟ๐ฎ๐๐ถ๐ป๐ด ๐๐ผ๐ป๐ด-๐๐ผ๐ป๐๐ฒ๐ ๐ ๐๐๐ ๐๐ป๐ณ๐ฒ๐ฟ๐ฒ๐ป๐ฐ๐ฒ ๐๐ถ๐ฎ ๐ฉ๐ฒ๐ฐ๐๐ผ๐ฟ ๐ฅ๐ฒ๐๐ฟ๐ถ๐ฒ๐๐ฎ๐น
[9] ๐ฃ-๐ฅ๐๐: ๐ฃ๐ฟ๐ผ๐ด๐ฟ๐ฒ๐๐๐ถ๐๐ฒ ๐ฅ๐ฒ๐๐ฟ๐ถ๐ฒ๐๐ฎ๐น ๐๐๐ด๐บ๐ฒ๐ป๐๐ฒ๐ฑ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป ๐๐ผ๐ฟ ๐ฃ๐น๐ฎ๐ป๐ป๐ถ๐ป๐ด ๐ผ๐ป ๐๐บ๐ฏ๐ผ๐ฑ๐ถ๐ฒ๐ฑ ๐๐๐ฒ๐ฟ๐๐ฑ๐ฎ๐ ๐ง๐ฎ๐๐ธ
[10] ๐ฅ๐๐๐: ๐๐ฒ๐ฎ๐ฟ๐ป๐ฒ๐ฑ-๐ฅ๐๐น๐ฒ-๐๐๐ด๐บ๐ฒ๐ป๐๐ฒ๐ฑ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป ๐๐ผ๐ฟ ๐๐ฎ๐ฟ๐ด๐ฒ ๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ ๐ ๐ผ๐ฑ๐ฒ๐น๐
[11] ๐ข๐ป ๐๐ต๐ฒ ๐ฆ๐๐ฟ๐ฝ๐ฟ๐ถ๐๐ถ๐ป๐ด ๐๐ณ๐ณ๐ฒ๐ฐ๐๐ถ๐๐ฒ๐ป๐ฒ๐๐ ๐ผ๐ณ ๐๐๐๐ฒ๐ป๐๐ถ๐ผ๐ป ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ฒ๐ฟ ๐ณ๐ผ๐ฟ ๐ฉ๐ถ๐๐ถ๐ผ๐ป ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐
[12] ๐ ๐ถ๐ ๐๐๐ฟ๐ฒ-๐ผ๐ณ-๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐: ๐ ๐ฆ๐ฝ๐ฎ๐ฟ๐๐ฒ ๐ฎ๐ป๐ฑ ๐ฆ๐ฐ๐ฎ๐น๐ฎ๐ฏ๐น๐ฒ ๐๐ฟ๐ฐ๐ต๐ถ๐๐ฒ๐ฐ๐๐๐ฟ๐ฒ ๐ณ๐ผ๐ฟ ๐ ๐๐น๐๐ถ-๐ ๐ผ๐ฑ๐ฎ๐น ๐๐ผ๐๐ป๐ฑ๐ฎ๐๐ถ๐ผ๐ป ๐ ๐ผ๐ฑ๐ฒ๐น๐
[13]-[14] ๐๐ฑ๐ถ๐ณ๐ ๐ฏ๐: ๐ฆ๐ฐ๐ฎ๐น๐ฎ๐ฏ๐น๐ฒ ๐๐ถ๐ด๐ต-๐ค๐๐ฎ๐น๐ถ๐๐ ๐ฏ๐ ๐๐๐๐ฒ๐ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป
[15] ๐๐๐๐ฒ ๐๐ฎ๐๐ฒ๐ป๐ ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ: ๐ฃ๐ฎ๐๐ฐ๐ต๐ฒ๐ ๐ฆ๐ฐ๐ฎ๐น๐ฒ ๐๐ฒ๐๐๐ฒ๐ฟ ๐ง๐ต๐ฎ๐ป ๐ง๐ผ๐ธ๐ฒ๐ป๐
[16]-[18] ๐๐ฒ๐ฒ๐ฝ๐ฆ๐ฒ๐ฒ๐ธ-๐ฉ๐ฏ (๐ฃ๐ฎ๐ฟ๐ ๐ญ-๐ฏ)
[19] ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐ ๐๐ถ๐๐ต๐ผ๐๐ ๐ก๐ผ๐ฟ๐บ๐ฎ๐น๐ถ๐๐ฎ๐๐ถ๐ผ๐ป
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[1] ๐ช๐ต๐ฎ๐ ๐ ๐ฎ๐๐๐ฒ๐ฟ๐ ๐ถ๐ป ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐? ๐ก๐ผ๐ ๐๐น๐น ๐๐๐๐ฒ๐ป๐๐ถ๐ผ๐ป ๐ถ๐ ๐ก๐ฒ๐ฒ๐ฑ๐ฒ๐ฑ
[2] ๐ฃ๐ฟ๐ฒ๐ฑ๐ถ๐ฐ๐๐ถ๐ป๐ด ๐ณ๐ฟ๐ผ๐บ ๐ฆ๐๐ฟ๐ถ๐ป๐ด๐: ๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ ๐ ๐ผ๐ฑ๐ฒ๐น ๐๐บ๐ฏ๐ฒ๐ฑ๐ฑ๐ถ๐ป๐ด๐ ๐ณ๐ผ๐ฟ ๐๐ฎ๐๐ฒ๐๐ถ๐ฎ๐ป ๐ข๐ฝ๐๐ถ๐บ๐ถ๐๐ฎ๐๐ถ๐ผ๐ป
[3] ๐ ๐ข๐๐๐ ๐ฆ๐ช๐๐ฅ๐ ๐ฆ: ๐๐ผ๐น๐น๐ฎ๐ฏ๐ผ๐ฟ๐ฎ๐๐ถ๐๐ฒ ๐ฆ๐ฒ๐ฎ๐ฟ๐ฐ๐ต ๐๐ผ ๐๐ฑ๐ฎ๐ฝ๐ ๐๐๐ ๐๐ ๐ฝ๐ฒ๐ฟ๐๐ ๐๐ถ๐ฎ ๐ฆ๐๐ฎ๐ฟ๐บ ๐๐ป๐๐ฒ๐น๐น๐ถ๐ด๐ฒ๐ป๐ฐ๐ฒ
[4] ๐ง๐๐๐ก๐๐๐ก๐ ๐๐๐ ๐ฆ: ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐น ๐๐ป๐๐๐ฟ๐๐ฐ๐๐ถ๐ผ๐ป ๐๐ผ๐น๐น๐ผ๐๐ถ๐ป๐ด ๐๐ถ๐๐ต ๐ง๐ต๐ผ๐๐ด๐ต๐ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป
[5] ๐ข๐ฝ๐ฒ๐ป๐ฉ๐๐: ๐๐ป ๐ข๐ฝ๐ฒ๐ป-๐ฆ๐ผ๐๐ฟ๐ฐ๐ฒ ๐ฉ๐ถ๐๐ถ๐ผ๐ป-๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ-๐๐ฐ๐๐ถ๐ผ๐ป ๐ ๐ผ๐ฑ๐ฒ๐น
[6] ๐ฅ๐ง-๐ญ: ๐ฅ๐ผ๐ฏ๐ผ๐๐ถ๐ฐ๐ ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ ๐ณ๐ผ๐ฟ ๐ฅ๐ฒ๐ฎ๐น-๐ช๐ผ๐ฟ๐น๐ฑ ๐๐ผ๐ป๐๐ฟ๐ผ๐น ๐๐ ๐ฆ๐ฐ๐ฎ๐น๐ฒ
[7] ฯ๐ฌ: ๐ ๐ฉ๐ถ๐๐ถ๐ผ๐ป-๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ-๐๐ฐ๐๐ถ๐ผ๐ป ๐๐น๐ผ๐ ๐ ๐ผ๐ฑ๐ฒ๐น ๐ณ๐ผ๐ฟ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐น ๐ฅ๐ผ๐ฏ๐ผ๐ ๐๐ผ๐ป๐๐ฟ๐ผ๐น
[8] ๐ฅ๐ฒ๐๐ฟ๐ถ๐ฒ๐๐ฎ๐น๐๐๐๐ฒ๐ป๐๐ถ๐ผ๐ป: ๐๐ฐ๐ฐ๐ฒ๐น๐ฒ๐ฟ๐ฎ๐๐ถ๐ป๐ด ๐๐ผ๐ป๐ด-๐๐ผ๐ป๐๐ฒ๐ ๐ ๐๐๐ ๐๐ป๐ณ๐ฒ๐ฟ๐ฒ๐ป๐ฐ๐ฒ ๐๐ถ๐ฎ ๐ฉ๐ฒ๐ฐ๐๐ผ๐ฟ ๐ฅ๐ฒ๐๐ฟ๐ถ๐ฒ๐๐ฎ๐น
[9] ๐ฃ-๐ฅ๐๐: ๐ฃ๐ฟ๐ผ๐ด๐ฟ๐ฒ๐๐๐ถ๐๐ฒ ๐ฅ๐ฒ๐๐ฟ๐ถ๐ฒ๐๐ฎ๐น ๐๐๐ด๐บ๐ฒ๐ป๐๐ฒ๐ฑ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป ๐๐ผ๐ฟ ๐ฃ๐น๐ฎ๐ป๐ป๐ถ๐ป๐ด ๐ผ๐ป ๐๐บ๐ฏ๐ผ๐ฑ๐ถ๐ฒ๐ฑ ๐๐๐ฒ๐ฟ๐๐ฑ๐ฎ๐ ๐ง๐ฎ๐๐ธ
[10] ๐ฅ๐๐๐: ๐๐ฒ๐ฎ๐ฟ๐ป๐ฒ๐ฑ-๐ฅ๐๐น๐ฒ-๐๐๐ด๐บ๐ฒ๐ป๐๐ฒ๐ฑ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป ๐๐ผ๐ฟ ๐๐ฎ๐ฟ๐ด๐ฒ ๐๐ฎ๐ป๐ด๐๐ฎ๐ด๐ฒ ๐ ๐ผ๐ฑ๐ฒ๐น๐
[11] ๐ข๐ป ๐๐ต๐ฒ ๐ฆ๐๐ฟ๐ฝ๐ฟ๐ถ๐๐ถ๐ป๐ด ๐๐ณ๐ณ๐ฒ๐ฐ๐๐ถ๐๐ฒ๐ป๐ฒ๐๐ ๐ผ๐ณ ๐๐๐๐ฒ๐ป๐๐ถ๐ผ๐ป ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ฒ๐ฟ ๐ณ๐ผ๐ฟ ๐ฉ๐ถ๐๐ถ๐ผ๐ป ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐
[12] ๐ ๐ถ๐ ๐๐๐ฟ๐ฒ-๐ผ๐ณ-๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐: ๐ ๐ฆ๐ฝ๐ฎ๐ฟ๐๐ฒ ๐ฎ๐ป๐ฑ ๐ฆ๐ฐ๐ฎ๐น๐ฎ๐ฏ๐น๐ฒ ๐๐ฟ๐ฐ๐ต๐ถ๐๐ฒ๐ฐ๐๐๐ฟ๐ฒ ๐ณ๐ผ๐ฟ ๐ ๐๐น๐๐ถ-๐ ๐ผ๐ฑ๐ฎ๐น ๐๐ผ๐๐ป๐ฑ๐ฎ๐๐ถ๐ผ๐ป ๐ ๐ผ๐ฑ๐ฒ๐น๐
[13]-[14] ๐๐ฑ๐ถ๐ณ๐ ๐ฏ๐: ๐ฆ๐ฐ๐ฎ๐น๐ฎ๐ฏ๐น๐ฒ ๐๐ถ๐ด๐ต-๐ค๐๐ฎ๐น๐ถ๐๐ ๐ฏ๐ ๐๐๐๐ฒ๐ ๐๐ฒ๐ป๐ฒ๐ฟ๐ฎ๐๐ถ๐ผ๐ป
[15] ๐๐๐๐ฒ ๐๐ฎ๐๐ฒ๐ป๐ ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ: ๐ฃ๐ฎ๐๐ฐ๐ต๐ฒ๐ ๐ฆ๐ฐ๐ฎ๐น๐ฒ ๐๐ฒ๐๐๐ฒ๐ฟ ๐ง๐ต๐ฎ๐ป ๐ง๐ผ๐ธ๐ฒ๐ป๐
[16]-[18] ๐๐ฒ๐ฒ๐ฝ๐ฆ๐ฒ๐ฒ๐ธ-๐ฉ๐ฏ (๐ฃ๐ฎ๐ฟ๐ ๐ญ-๐ฏ)
[19] ๐ง๐ฟ๐ฎ๐ป๐๐ณ๐ผ๐ฟ๐บ๐ฒ๐ฟ๐ ๐๐ถ๐๐ต๐ผ๐๐ ๐ก๐ผ๐ฟ๐บ๐ฎ๐น๐ถ๐๐ฎ๐๐ถ๐ผ๐ป
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Scientific Visualization: Python + Matplotlib
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