An Empirical Study on the Performance of the Distance Metrics

Year 2023, Volume: 23 Issue: 6, 1445 - 1457, 28.12.2023

Fatih Aydın

https://doi.org/10.35414/akufemubid.1325843

Abstract

Metrics are used to measure the distance, similarity, or dissimilarity between two points in a metric space. Metric learning algorithms perform the finding task of data points that are closest or furthest to a query point in m-dimensional metric space. Some metrics take into account the assumption that the whole dimensions are of equal importance, and vice versa. However, this assumption does not incorporate a number of real-world problems that classification algorithms tackle. In this research, the existing information gain, the information gain ratio, and some well-known conventional metrics have been compared by each other. The 1-Nearest Neighbor algorithm taking these metrics as its meta-parameter has been applied to forty-nine benchmark datasets. Only the accuracy rate criterion has been employed in order to quantify the performance of the metrics. The experimental results show that each metric is successful on datasets corresponding to its own domain. In other words, each metric is favorable on datasets overlapping its own assumption. In addition, there also exists incompleteness in classification tasks for metrics just like there is for learning algorithms.

Keywords

Machine learning, Metric learning, Information gain, No free lunch theorems, K-nearest neighbors

Uzaklık Metriklerinin Performansı Üzerine Ampirik Bir Çalışma

Abstract

Metrik, bir metrik uzayda iki nokta arasındaki mesafeyi, benzerliği veya farklılığı ölçmek için kullanılır. Metrik öğrenme algoritmaları, m boyutlu metrik uzayda bir sorgulama noktasına en yakın veya en uzak olan veri noktalarını bulma görevini gerçekleştirir. Bazı metrikler, tüm boyutların eşit öneme sahip olduğu varsayımını dikkate alır ve bunun tersi de geçerlidir. Ancak bu varsayım, sınıflandırma algoritmalarının üstesinden geldiği bazı gerçek dünya problemleriyle örtüşmez. Bu araştırmada; mevcut bilgi kazanımı, bilgi kazanım oranı ve bazı iyi bilinen konvansiyonel metrikler birbirleri ile karşılaştırılmıştır. Bu metrikleri meta parametresi olarak alan 1-En Yakın Komşular algoritması 49 veri kümesine uygulanmıştır. Metriklerin performansını ölçmek için sadece doğruluk oranı ölçütü kullanılmıştır. Deneysel sonuçlar, her metriğin kendi domainine karşılık gelen veri setlerinde başarılı olduğunu göstermektedir. Başka bir deyişle; her metrik, kendi varsayımıyla örtüşen veri kümelerinin lehinedir. Ayrıca öğrenme algoritmalarında olduğu gibi metrikler için de sınıflandırma görevlerinde eksiklikler mevcuttur.

Keywords

Makine öğrenmesi, Metrik öğrenme, Bilgi kazancı, No free lunch teoremleri, K-en yakın komşular

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