Mallows' L2 distance in some multivariate methods and its application to histogram-type data

Košmelj, Katarina (author), Billard, Lynne (author)

Mallowsʼ L2 distance allows for decomposition of total inertia into within and between inertia according to Huygens theorem. It can be decomposed into three terms: the location term, the spread term and the shape term; a simple and straightforward proof of this theorem is presented. These characteristics are very helpful in the interpretation of the results for some distance-based methods, such as clustering by k-means and classical multidimensional scaling. For histogram-type data, Mallowsʼ L2 distance is preferable because its calculation is simple, even when the number and length of the histogramsʼ subintervals differ. An illustration of its use on population pyramids for 14 East European countries in the period 1995-2015 is presented. The results provide an insight into the information that this distance can extract from a complex dataset.

• Language: English
• Keywords: statistične metode, statistika, klaster analiza, Mallows L2 razdalja, večrazsežnostno lestvičenje, MDS
• Work type: Not categorized
• Typology: 1.01 - Original Scientific Article
• Organization: BF - Biotechnical Faculty
• Year: 2012
• Number of pages: Str. 107-118
• Numbering: Vol. 9, no. 2
• PID: 20.500.12556/RUL-44466
• UDC: 303
• ISSN on article: 1854-0023
• COBISS.SI-ID: 7389561
• Publication date in RUL: 10.07.2015

Record is a part of a journal

• Title: Advances in methodology and statistics
• Shortened title: Metodol. zv.
• Publisher: Fakulteta za družbene vede
• ISSN: 1854-0023
• COBISS.SI-ID: 215795712