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Maximum Likelihood classifier β how it works and its main assumption?
Plain English (default view) β short, conversational, lightly seasoned with science
Picture each land-cover class (forest, water, city) as a **fuzzy cloud floating in spectral space**. Max Likelihood asks the question: > *"Which cloud is this pixel most likely sitting inside?"* Crucially, it considers each cloud's **shape** (covariance), not just its center. Min Distance only looks at the center β it's like deciding which city you're closest to without checking which one's borders you're inside. That's why ML usually wins on accuracy: it understands a tightly-grouped class is more confident, while a wide loose class lets in more variety.
π¬ Scientific / formula (revealed on click) β markdown + $$β¦$$ ok
For each pixel, compute the **probability** it belongs to each class. Assign to the **most likely** class. - **Key assumption:** each class is **multivariate Gaussian** (each band normally distributed inside the class). - Uses the class **mean AND covariance matrix** β thatβs how it accounts for class shape, not just position. - **Strength:** most accurate of the four decision rules when classes are well-sampled and bands are roughly normal. - **Weakness:** needs enough training samples to estimate covariance; fails on non-Gaussian classes. - **Bayesian variant (Hord 1982):** supply per-class prior probabilities instead of assuming equal priors.
π‘ Mnemonic / memory aid (shown on hover)
ML uses **mean + covariance**, not just the mean. Min Distance ignores shape (just the mean). Mahalanobis adds shape. Max Likelihood adds priors on top. The full discriminant formula lives in the long-form review β the *concept* lives here.
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