Trimmed object projections: a nonparametric robust latent-structure decomposition method

A new nonparametric latent-structure decomposition method based on object projections is developed in this paper. First, the distances from the median centre point are determined for every object. After normalisation to unit length, the summed absolute values of the projections (direction cosines) of all objects onto every object are calculated. Contributions from objects with distances from the median centre point above a threshold are down-weighted in the calculation of the summed absolute value of projections. The first principal object is selected as the one with maximum summed projections. The corresponding normalised trimmed principal object is then constructed by adding to the principal object the other objects weighted by the squares of their projections onto the principal object. The projection from objects with distances larger than the selected threshold are down-weighted. The scores of every object are obtained by projecting on this trimmed principal object. The procedure can be repeated after removing the contribution from the first trimmed principal object to obtain the next one. The trimmed principal objects provide robust principal components, i.e. components that are resistant to outliers. The method is simple and easily comprehensible with light calculations.