shiftsdivided

Shiftsdivided is a data transformation technique used in time-series analysis and scheduling optimization to create a normalized, multi-shift representation of a sequence. It combines the ideas of shifting a data sequence and applying a per-shift division to produce a structured set of blocks that can feed feature extraction, forecasting, or optimization algorithms.

In practice, one selects a shift width s and a number of shifts g. Given a sequence a = (a0, a1, ..., aN−1), the method constructs g shifted views by applying consecutive shifts of size s. Each shifted view is then processed with an element-wise division by a corresponding divisor vector d^(i) for i = 1,...,g. The output is a matrix or tensor where each row (or column) represents a shifted, normalized block. The division step serves to adjust scale across blocks and to emphasize relative changes rather than absolute magnitudes.

Key properties include: the approach preserves local temporal relationships within blocks, introduces controlled cross-shift normalization, and remains compatible with standard machine learning and optimization pipelines when the resulting matrix is flattened or fed into a model.

Applications for shiftsdivided appear in time-series feature engineering, preprocessing for scheduling problems, and data compression within streaming analytics. It is particularly useful when analysts want to capture short-term patterns across multiple contemporaneous shifts while mitigating scale differences between blocks.

Example: with a sequence a = [a0, a1, a2, a3, a4, a5], a chosen shift width s and divisor sets d^(i) for i = 1 to g yield g blocks, each formed from a contiguous sub-sequence of length s and each block divided element-wise by its corresponding divisor vector. See also shifting, block processing, and normalization techniques.