Using this restriction the category points are forced to be on a line. However, this restriction is not sufficient to preserve the order for ordinal attributes or even the relative distance for numerical attributes. Therefore, qk is constrained every ALS iteration to satisfy such restrictions. In the case of ordinal attributes this transformation is done by a weighted monotone regression [9] and in the case of numerical attributes this results in replacing qk by the attribute’s original values xk. A detailed description of the ALS algorithm for NL-PCA can be found in [13, 31, 34]. NL-PCA solutions have a number of advantageous properties that make it very suitable to create maps that contain both products and attribute category values.