Let the mean feature vectors of three classes be...

Let the mean feature vectors of three classes be $\{10,10\},\{-10,-10\}$, and $\{10,-10\}$. Let the test vectors be $\{12,-10\},\{8,9\}$, and $\{-9,-11\}$. Find the three discriminant functions of the three classes. Classify the test vectors.

Key Concepts

Mean Feature Vectors

Mean feature vectors represent the average or expected values of the features for each class. They summarize the central tendency of the data in each class and are used as prototype points to which new observations can be compared. In many classification problems, especially when assuming similar covariance structures, the class mean is a natural representation of the class which facilitates further analysis through distance measures.

Discriminant Functions

Discriminant functions are mathematical formulations used to decide which class a given input belongs to by projecting the input data into a decision space. Each function assigns a score based on the input features, and the class corresponding to the largest (or smallest, depending on formulation) score is chosen. In the context of the minimum distance classifier, these functions are derived from the distance between the input feature vector and the class mean.

Minimum Distance (or Nearest Mean) Classifier

The minimum distance classifier, also known as the nearest mean classifier, is a simple yet powerful method of classification that assigns a test vector to the class whose mean is closest in Euclidean distance (or another distance measure). This method assumes that classes are well represented by their means and that the distance metric effectively captures the similarity between the test vector and class prototypes.

Classification Decision Rule

The classification decision rule is the process by which the calculated discriminant function values for each class are compared, and the class with the best (typically highest or lowest based on formulation) score is selected for the test vector. This rule is fundamental in pattern recognition, ensuring that each test sample is assigned to the most appropriate class based on computed distances or probabilities.

Transcript

Please give Ace some feedback