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Sequential pattern mining is a topic of data mining concerned with finding statistically relevant patterns between data examples where the values are delivered in a sequence. [ 1 ] [ 2 ] It is usually presumed that the values are discrete, and thus time series mining is closely related, but usually considered a different activity.
A simple and inefficient way to see where one string occurs inside another is to check at each index, one by one. First, we see if there is a copy of the needle starting at the first character of the haystack; if not, we look to see if there's a copy of the needle starting at the second character of the haystack, and so forth.
Thus, if we have a vector containing elements (2, 5, 7, 3, 8, 6, 4, 1), and we want to create an array slice from the 3rd to the 6th items, we get (7, 3, 8, 6). In programming languages that use a 0-based indexing scheme, the slice would be from index 2 to 5. Reducing the range of any index to a single value effectively eliminates that index.
In the random-access machine commonly used in algorithm analysis, a simple algorithm that scans the indexes in input order and swaps whenever the scan encounters an index whose reversal is a larger number would perform a linear number of data moves. [10] However, computing the reversal of each index may take a non-constant number of steps.
The fundamental idea behind array programming is that operations apply at once to an entire set of values. This makes it a high-level programming model as it allows the programmer to think and operate on whole aggregates of data, without having to resort to explicit loops of individual scalar operations.
The indexing expression for a 1-based index would then be ′ +. Hence, the efficiency benefit at run time of zero-based indexing is not inherent, but is an artifact of the decision to represent an array with the address of its first element rather than the address of the fictitious zeroth element.
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In this case the estimate of {x(t)} is defined to be a sequence of values which maximize the functional P ( x ) = p ( x ∣ r ) , {\displaystyle P(x)=p(x\mid r),} where p ( x | r ) denotes the conditional joint probability density function of the underlying series { x ( t )} given that the observed series has taken the values { r ( t )}.