Principal component analysis, in its standard version, might not be appropriate for the analysis of spatial data. Particularly, the presence of spatial heterogeneity has been recognized as a possible source of misspecification for the derivation of composite indicators using principal component analysis. In recent times, geographically weighted approach to principal component analysis has been used for the treatment of continuous heterogeneity. However, this technique poses problems for the treatment of discrete heterogeneity and the interpretation of the results. The aim of this paper is to present a new approach to consider spatial heterogeneity in principal component analysis by using simulated annealing algorithm. The proposed method is applied for the definition of a composite indicator of local services for 121 municipalities in the province of Rome.

标准版本的主成分分析可能不适用于空间数据分析。特别是，空间异质性的存在已被认为是使用主成分分析推导综合指标的可能错误指定来源。最近，主要成分分析的地理加权方法已被用于处理连续异质性。然而，这种技术对离散异质性的处理和结果的解释提出了问题。本文的目的是通过使用模拟退火算法提出一种在主成分分析中考虑空间异质性的新方法。