Basic Statistics¶
Basic statistics algorithm computes the following set of quantitative dataset characteristics:
minimums/maximums
sums
means
sums of squares
sums of squared differences from the means
second order raw moments
variances
standard deviations
variations
Operation |
Computational methods |
Programming Interface |
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Mathematical formulation¶
Computing¶
Given a set \(X\) of \(n\) \(p\)-dimensional feature vectors \(x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})\), the problem is to compute the following sample characteristics for each feature in the data set:
Statistic |
Definition |
|---|---|
Minimum |
\(min(j) = \smash{\displaystyle \min_i } \{x_{ij}\}\) |
Maximum |
\(max(j) = \smash{\displaystyle \max_i } \{x_{ij}\}\) |
Sum |
\(s(j) = \sum_i x_{ij}\) |
Sum of squares |
\(s_2(j) = \sum_i x_{ij}^2\) |
Means |
\(m(j) = \frac {s(j)} {n}\) |
Second order raw moment |
\(a_2(j) = \frac {s_2(j)} {n}\) |
Sum of squared difference from the means |
\(\text{SDM}(j) = \sum_i (x_{ij} - m(j))^2\) |
Variance |
\(k_2(j) = \frac {\text{SDM}(j) } {n - 1}\) |
Standard deviation |
\(\text{stdev}(j) = \sqrt {k_2(j)}\) |
Variation coefficient |
\(V(j) = \frac {\text{stdev}(j)} {m(j)}\) |
Computation method: dense¶
The method computes the basic statistics for each feature in the data set.
Programming Interface¶
Refer to API Reference: Basic statistics.
Distributed mode¶
The algorithm supports distributed execution in SMPD mode (only on GPU).