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Moments of Low Order

Moments are basic quantitative measures of data set characteristics such as location and dispersion. oneDAL computes the following low order characteristics:

• minimums/maximums

• sums

• means

• sums of squares

• sums of squared differences from the means

• second order raw moments

• variances

• standard deviations

• variations

Details

Given a set \(X\) of \(n\) feature vectors \(x_1 = (x_{11}, \ldots, x_{1p}), \ldots, x_n = (x_{n1}, \ldots, x_{np})\) of dimension \(p\), the problem is to compute the following sample characteristics for each feature in the data set:

Moments of Low Order

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

The following computation modes are available:

• Batch Processing
• Online Processing
• Distributed Processing

Examples

C++ (CPU)Python*

Batch Processing:

• low_order_moms_dense_batch.cpp

• low_order_moms_csr_batch.cpp

Online Processing:

• low_order_moms_dense_online.cpp

• low_order_moms_csr_online.cpp

Distributed Processing:

• low_order_moms_dense_distr.cpp

• low_order_moms_csr_distr.cpp

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