Strong classification

Consider the sign language domain. What if, when we record the original data, each stream corresponds not to a single sign, but to a sentence (i.e. a sequence) of signs? Then there would not be a simple association of one stream to a class, but from a stream to a sequence of classes. This would be an example of a strong classification problem.

A formal definition of strong classification is a modification of the definition of weak classification: Rather than have a function $\mathit{class}(S)$, we have a function $\mathit{classseq}(S)$ which has the following type:

$$\mathit{classseq}(S): \mathit{SS} \rightarrow \mathit{CL}^+$$

In other words, $\ensuremath{\mathit{classseq}}(S)$ returns a sequence of classes for a given stream, rather than a single class.

Our problem can be restated as: given a subset of the function $\mathit{classseq}$ (say $\ensuremath{\mathit{classseq}}_T$), produce a function $\mathit{classseq}_P$ which is a similar to $\mathit{classseq}$ as possible.

If there are $m$ possible classes, and we assume that for each stream, the longest possible class sequence is $n$, then in general there are $\frac{m(m^n-1)}{m-1}$ possible class sequences; because there could be anywhere between 1 and n classes in the class sequence. Theoretically, therefore, the two variants are equivalent; as each sentence could be treated as a single label. This is not practical, of course, and generally, strong temporal classification is harder than weak temporal classification.