Final answer:
To classify a new data point x using the 1-nearest-neighbor method, we compare the distances between x and the two given patterns. The class of the pattern closest to x is assigned to x.
Step-by-step explanation:
The question asks for the classification of a new data point x belonging to the range [0,1] using the 1-nearest-neighbor method based on two given patterns. The two patterns are located at coordinates (0.4, ω1) and (0.6, ω2), representing different classes.
To determine the class of x, we find which of the two given patterns is closer to x in terms of Euclidean distance. The pattern that is nearest to x will determine its class.
1-nearest-neighbor is a simple algorithm used in machine learning for classification. It operates on the principle of assigning the class of the nearest training example to the new point. Therefore, if you are given a new data point x and you need to predict its class, you will identify which of the existing patterns is closest to x and use that pattern's class as the prediction for x.
In the provided question, if x were, for example, 0.5, it would be equidistant from both patterns and could be assigned to either class ω1 or ω2. If x were closer to 0.4, it would be classified as ω1. Conversely, if x were nearer to 0.6, its class would be ω2.