Manual Derivation Series: Cosine Similarity in Clustering and SVD Exercise
For clustering analysis can man also use cosine similarity except distance.
Manual Derivation Series: Cosine Similarity in Clustering and SVD Exercise
- For clustering analysis can man also use cosine similarity except distance.
Cosine and Distance Exercise
2.Singular Value Decomposition (SVD) represents decomposing any complex linear transformation into three sequential steps: Rotation, Scaling, and Rotation.
Exercise1
Exercise2
- outer product
The first few outer products contain the most significant information (the “signal”), while later terms represent fine details or noise.
Think of the original matrix as a complex image. The outer product sum is like building that image layer by layer:
- The first outer product captures the strongest global pattern (the “skeleton”).
- Subsequent outer products add textures and specific features.
- The final products usually add negligible noise.
In Clustering or NLP, this allows us to reconstruct a “cleaned” version of the data by only summing the most dominant outer products.
Outer an Inner Product
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