sigma采样工作原理

### Sigma Sampling Working Principle In the context provided by the reference material, sigma (Σ) refers to a mathematical operation that computes the sum of differences between consecutive sample values within a dataset. Specifically, it involves calculating the first-order difference between each pair of adjacent samples \(X_i\) and \(X_{i-1}\). The formula can be expressed as follows: \[ \Sigma = \sum_{i=1}^{N-1} |X_i - X_{i-1}| \] Here, \(N\) denotes the total number of samples in the dataset[^1]. This computation quantifies the variability or fluctuation present in the signal due to changes in sampling rates. The process works by iterating through all pairs of successive elements in the sampled data set and accumulating their absolute differences into one final summation result. Such an approach provides insight into how much variation exists from point-to-point across time-series-like datasets where temporal ordering matters significantly. Additionally, while not directly related but still relevant under broader computational sciences topics such as those mentioned regarding collaborative filtering systems [^3], deep learning techniques including model training strategies over train/dev/test splits which were highlighted earlier too might also utilize similar principles when analyzing sequential patterns found inside large-scale information repositories like text corpora processed via neural networks architectures designed specifically towards handling linguistic structures effectively per another source discussing advancements made possible thanks largely because these methods have improved dramatically even compared against results achieved merely couple years prior before current state-of-the-art implementations came about today.[^2][^4]. ```python def calculate_sigma_sampling(data): """ Calculate the sigma sampling based on given definition. Parameters: data (list): List of numerical sample points Returns: float: Summation of first-difference magnitudes """ n = len(data) if n < 2: return 0 # Not enough data for calculation sigma_sum = sum(abs(data[i] - data[i-1]) for i in range(1, n)) return sigma_sum ```