Separating positive and negative example with a straight line that is as far as possible from both positive and negative examples, a median that maximizes the space between positive and negative examples.
Constraints are applied to build a support vector(u) and define a constant b that allow to sort positive examples from negative ones. The width of a “street” between the positive and negative values is maximized.
Going through the algebra, the resulting equation show that the optimization depends only on the dot product of pair of samples.
The decision rule that defines if a sample is positive or negative only depends on the dot product of the sample vector and the unknown vector.
No local maximum
Such support vector algorithm can be proven to be evolving in a convex space, meaning that it will never be blocked at a local maximum.
The algorithm cannot find a median between data which cannot be linearly separable. A transformation can however be applied to the space to reorganize the samples so that they can be linearly separable. Certain transformations can however create an over fitting model that becomes useless by only sorting the example data.
A detection mechanism generates a vector of features. These features are converted in a vector of values that is compared to a library of possibilities to find the closest match in order to recognize patterns, objects, etc.
Method: Standard objects (ex: electric covers) are positioned in a space according to recognizable characteristics (ex: size, hole size). Decision boundaries between the standards are then established in the space to define areas of attribution to a nearest neighbor. Objects are then sorted according to which area the belong to.
Another method of sorting objects (ex: newspaper articles) to recognize could be to compare the angle of their vectors in the space with the vectors of the standard objects.
In the case of a robotic arm, instead of solving equations of angles at the joints which cannot be implemented in real life, due to friction and wear, a table of values is gathered at each position during a learning phase. During the working phase, the closest set of values from the table is used to complete the task.
Spread: Values can be concentrated in the space making it difficult to discern objects. Solution: norm the data using statistical analysis.
Subject matter: make sure to measure values that do actually make a difference between objects, not values that generate confusing results.
Relevancy: use data that is relevant to the matter at hand, not just any data that is independent from the target results.