Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier

Rodrigues, Érick Oliveira

doi:10.1016/j.patrec.2018.03.021

Cited by 67 publications

(27 citation statements)

References 7 publications

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“…When w 1 is bigger than w 2 , this distance is similar to Minkowski distance, and vice versa. The Minkowski-Chebyshev distance is defined as [23]:…”

Section: E Mikowski-chebyshev Distancementioning

confidence: 99%

Distance Functions Study in Fuzzy C-Means Core and Reduct Clustering

Eliyanto

Surono

2021

Jurnal Ilmiah Teknik Elektro Komputer Dan Informatika

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Fuzzy clustering aims to produce clusters that take into account the possible membership of each dataset point in a particular cluster. Fuzzy C-Means Clustering Core and Reduct is a fuzzy clustering method is a Fuzzy C-Means Clustering method that has been optimized using the reduction of Core and Reduct dimensions. The method studied is highly dependent on the distance function used. As a further in-depth study, this study was compiled to see the performance of the Fuzzy C-Means Clustering Core and Reduct using various distance functions. We aim to see how consistent the results of this method are across various distance functions and find the best distance function. The seven distance functions are applied to the same dataset. The seven distances are the Euclidean, Manhattan, Minkowski, Chebyshev, Minkowski-Chebyshev, Canberra, and Averages distances. We use UCI Machine Learning datasets for this research. The quality of the clustering results is compared through several measures. Accuracy, Silhouette score, and Davies Bouldin Index are used as internal measurements. The results of Fuzzy C-Means Core and Reduct clustering on all distance functions have significantly decreased computational load. Accuracy and purity values can be maintained with values above 80%. There was an increase in the value of the Silhouette Coefficient Score and a decrease in the Davies Bouldin Index after the application of dimension reduction. This means the quality of the clustering results can be maintained. The distance with the best evaluation result is the Euclidean distance. This method runs consistently across all tested distance functions.

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“…When w 1 is bigger than w 2 , this distance is similar to Minkowski distance, and vice versa. The Minkowski-Chebyshev distance is defined as [23]:…”

Section: E Mikowski-chebyshev Distancementioning

confidence: 99%

Distance Functions Study in Fuzzy C-Means Core and Reduct Clustering

Eliyanto

Surono

2021

Jurnal Ilmiah Teknik Elektro Komputer Dan Informatika

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“…Moreover, in [16], a method to reduce the number of points for line approximation was proposed. One of the latest articles in this area by Rodrigues [17] offers a method for calculating distances based on the combination of the Minkowski and Chebyshev distances. Nowadays, this method is widely used in computer vision applications [18,19].…”

Section: Related Workmentioning

confidence: 99%

An algorithm for line matching in an image by mapping into an n-dimensional vector space

Sultanov¹,

Atakan²,

İsmailova³

2019

Turk J Elec Eng & Comp Sci

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This paper proposes a minimal length difference algorithm for construction of a line in an image by solving the problem of optimal contour approximation. In this algorithm, a method for finding interest points is proposed, and the object matching (classification) is done by mapping interest points onto a vector space. In cases where the lines in the representation of the images are not smooth, the algorithm converges rapidly. The results of the experiments showed that for convergence of the contour simplification, there were 5-6 iterations for n = 13. To check how close the curve approximation calculated by the algorithm above, the researchers have calculated the length of the curve simplification manually. This length was then compared to the length of the original curve. The results showed that the length of the simplified curve grew rapidly to 92%-95% of the original curve length. The further increase in the number of points does not affect this indicator. According to the obtained results, the relative difference and the relative difference distance are good metrics to match objects.

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“…The first parameter is the proximity measure that defines the closest instances. The second one is the k variable representing an upper limit for the number of instances that will be handled [13]. Distance metrics are generally used as proximity measure.…”

Section: Introductionmentioning

confidence: 99%

“…They also stated that there is no optimal distance measure appropriate for all datasets and each dataset supported a certain distance measure. Rodrigues [13] proposed a new distance that combines Minkowski and Chebychev distances. To evaluate the efficiency of the proposed distance using kNN an experiment was performed using 33 datasets from the UCI.…”

Section: Introductionmentioning

confidence: 99%

A Weighted Similarity Measure for k-Nearest Neighbors Algorithm

Karabulut

Arslan

Ünver

2019

Celal Bayar Üniversitesi Fen Bilimleri Dergisi

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One of the most important problems in machine learning, which has gained importance in recent years, is classification. The k-nearest neighbors (kNN) algorithm is widely used in classification problem because it is a simple and effective method. However, there are several factors affecting the performance of kNN algorithm. One of them is determining an appropriate proximity (distance or similarity) measure. Although the Euclidean distance is often used as a proximity measure in the application of the kNN, studies show that the use of different proximity measures can improve the performance of the kNN. In this study, we propose the Weighted Similarity k-Nearest Neighbors algorithm (WS-kNN) which use a weighted similarity as proximity measure in the kNN algorithm. Firstly, it calculates the weight of each attribute and similarity between the instances in the dataset. And then, it weights similarities by attribute weights and creates a weighted similarity matrix to use as proximity measure. The proposed algorithm is compared with the classical kNN method based on the Euclidean distance. To verify the performance of our algorithm, experiments are made on 10 different real-life datasets from the UCI (UC Irvine Machine Learning Repository) by classification accuracy. Experimental results show that the proposed WS-kNN algorithm can achieve comparative classification accuracy. For some datasets, this new algorithm gives highly good results.

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Combining Minkowski and Chebyshev: New distance proposal and survey of distance metrics using k-nearest neighbours classifier

Cited by 67 publications

References 7 publications

Distance Functions Study in Fuzzy C-Means Core and Reduct Clustering

Distance Functions Study in Fuzzy C-Means Core and Reduct Clustering

An algorithm for line matching in an image by mapping into an n-dimensional vector space

A Weighted Similarity Measure for k-Nearest Neighbors Algorithm

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