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

Let the mean feature vectors of three classes be $\{15,-17\},\{17,15\}$, and $\{-16,16\}$. Let the test vectors be $\{18,-16\},\{18,14\}$, and $\{-16,16\}$. Find the three discriminant functions of the three classes. Classify the test vectors.

Key Concepts

Feature Vectors

Feature vectors are sets of numerical values that represent the characteristics or attributes of an object or observation in a multi-dimensional space. They form the fundamental input for many classification and pattern recognition algorithms, allowing for the mathematical manipulation and comparison of different observations.

Euclidean Distance

Euclidean distance is a metric that measures the direct straight-line distance between two points in space. In classification tasks, it is often used to assess the similarity between an input data point and class means, where a smaller distance implies a higher likelihood of the point belonging to that class.

Classification

Classification is the process of assigning observations to one of several predefined categories based on their features. It involves processes like calculating discriminant functions and distances, and then using these computations to determine which class a given input vector is most likely to belong to.

Discriminant Functions

Discriminant functions are mathematical tools used to decide which class an observation should be assigned to. They typically quantize the similarity between an input feature vector and each class's model parameters, often by measuring distances or evaluating likelihoods, allowing the classifier to assign the observation to the class with the highest score.

Nearest Mean Classifier

The nearest mean classifier is a simple classification method that assigns a data point to the class whose mean (or centroid) is closest to it according to a distance metric, usually the Euclidean distance. This method assumes that the class means provide a good representation of the data distribution within each class.

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