What is dimensionality reduction? Explain PCA (Principal Component Analysis).
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Dimensionality reduction is a technique in data science and machine learning used to reduce the number of input variables or features in a dataset while preserving as much important information as possible. High-dimensional data can lead to issues like overfitting, increased computation time, and the curse of dimensionality. Dimensionality reduction helps simplify models, improve performance, and visualize data more easily.
🔍 Principal Component Analysis (PCA):
PCA is a widely used linear dimensionality reduction technique that transforms the original features into a new set of uncorrelated variables called principal components.
How PCA Works:
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Standardize the data (mean = 0, variance = 1).
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Compute the covariance matrix to understand feature relationships.
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Calculate eigenvectors and eigenvalues of the covariance matrix.
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Select principal components: Choose the top components that explain the most variance.
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Project the data onto the new component axes (lower-dimensional space).
📌 Key Points:
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Principal components are linear combinations of the original features.
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The first principal component captures the maximum variance.
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Each subsequent component is orthogonal (uncorrelated) to the previous one and captures the next highest variance.
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PCA helps in visualizing high-dimensional data (e.g., plotting in 2D/3D).
✅ Benefits of PCA:
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Reduces complexity.
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Improves model speed and generalization.
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Removes multicollinearity.
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Helps visualize data clusters or patterns.
In summary, PCA is a powerful technique for reducing the number of features in a dataset while retaining the most significant information, making data analysis and machine learning more efficient.
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