watex.analysis.total_variance_ratio#

watex.analysis.total_variance_ratio(X, view=False)[source]#

Compute the total variance ratio.

Is the ratio of an eigenvalues \(\lambda_j\), as simply the fraction of and eigen value, \(\lambda_j\) and the total sum of the eigen values as:

\[\text{explained_variance_ratio}= \frac{\lambda_j}{\sum{j=1}^{d} \lambda_j}\]

Using numpy cumsum function, we can then calculate the cumulative sum of explained variance which can be plot if plot is set to True via matplotlib set function.

Parameters

  • X (Nd-array, shape(M, N)) – Array of training set with M examples and N-features

  • view (bool, default {'False'}) – give an overview of the total explained variance.

Returns

cum_var_exp – Cumulative sum of variance total explained.

Return type

array-like

Examples

>>> from watex.analysis import total_variance_ratio
>>> # Use the X value in the example of `extract_pca` function
>>> cum_var = total_variance_ratio(X, view=True)
>>> cum_var
... array([0.26091916, 0.44042728, 0.57625294, 0.69786032, 0.80479823,
       0.89379712, 0.97474381, 1.        ])