Distance Measures. Two main distance measures were introduced in this report, namely Euclidean and Mahalanobis based measures. These measures were used for both classification purposes, and for creating decision boundaries within the height and width based models. There are numerous alternative distance measures for use in this type of situation. Some of the more famous include Manhattan distance, Chebyshev distance (computationally cheap but less accurate than Euclidean distance), Minkowski distance (of a set order), Quadratic distance (which is computationally very expensive) and Canberra distance (which is normally only used for nonnegative values). Euclidean distance was introduced in this report based on its simplicity, and ease of use. Comparable techniques, such as Manhattan distance could have been used; however, measures such as these add complexity without adding any significant advantages to the measurement process (Manhattan distance is similar measure to Euclidean distance using absolute values). Beyond this, while Xxxxxxxxx distance takes the direct (Pythagorean) distance between two points (hypotenuse), Manhattan distance (sometimes known as city block distance) takes the distance of the other sides of the triangle, making it unusable for modelbased classification: Figure 7.2 – Operation of Manhattan or City Block Measure It is also known that Xxxxxxxxx distance of order m = 1 is the same as using the Manhattan distance. If m= 2, the distance returned is the same as using Euclidean distance. As the order increases, the measure tends towards the Chebyshev result. From this, it can be seen that many of the popular distance measures are connected or similar. Therefore, use of the Euclidean measure is adequate for this project. One of the few measurement techniques that operate on a rather unique system is Mahalanobis distance. Based on covariance matrix values, it allows models to use the clustering information from class measurements, and thus provides a more applicable measurement and decision boundary creation system than many others provide for model based distance matching. This was the main reason for its inclusion within this project.
