Adjusted Concordance Index: an Extensionl of the Adjusted Rand Index to Fuzzy Partitions

This study proposes the concept of families of triangular norm (t-norm)-based kernel functions, and discusses their positive-definite property and the conditions for applicable t-norms. A clustering experiment with kernel k-means is performed in order to analyze the characteristics of the proposed concept, as well as the effects of the t-norm and parameter selections. It is evaluated that the clusters obtained in terms of the adjusted rand index and the experimental results suggested the following : (1) the adjusted rand index values obtained by the proposed method were almost the same or higher than those produced using the linear kernel for all of the data sets; (2) the proposed method slightly improved the adjusted rand index values for some data sets compared with the radial basis function (RBF) kernel; (3) the proposed method tended to map data to a higher dimensional feature space than the linear kernel but the dimension was lower than that using the RBF kernel.

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A Way to Obtain the Quality of a Partition by Adjusted Rand Index

2013 2nd Workshop-School on Theoretical Computer Science ◽

10.1109/weit.2013.33 ◽

2013 ◽

Cited By ~ 4

Author(s):

Rogerio R. de Vargas ◽

Benjamin R.C. Bedregal

Keyword(s):

Rand Index ◽

Adjusted Rand Index

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Detecting genomic regions associated with a disease using variability functions and Adjusted Rand Index

BMC Bioinformatics ◽

10.1186/1471-2105-12-s9-s9 ◽

2011 ◽

Vol 12 (Suppl 9) ◽

pp. S9 ◽

Cited By ~ 3

Author(s):

Dunarel Badescu ◽

Alix Boc ◽

Abdoulaye Diallo ◽

Vladimir Makarenkov

Keyword(s):

Rand Index ◽

Adjusted Rand Index ◽

Genomic Regions

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Clustering for Probability Density Functions by New k-Medoids Method

Scientific Programming ◽

10.1155/2018/2764016 ◽

2018 ◽

Vol 2018 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

D. Ho-Kieu ◽

T. Vo-Van ◽

T. Nguyen-Trang

Keyword(s):

Probability Density ◽

Clustering Algorithm ◽

Real Life ◽

Probability Density Functions ◽

Rand Index ◽

Computational Time ◽

Adjusted Rand Index ◽

Density Functions ◽

Potential Applications ◽

Iteration Number

This paper proposes a novel and efficient clustering algorithm for probability density functions based on k-medoids. Further, a scheme used for selecting the powerful initial medoids is suggested, which speeds up the computational time significantly. Also, a general proof for convergence of the proposed algorithm is presented. The effectiveness and feasibility of the proposed algorithm are verified and compared with various existing algorithms through both artificial and real datasets in terms of adjusted Rand index, computational time, and iteration number. The numerical results reveal an outstanding performance of the proposed algorithm as well as its potential applications in real life.

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CLUSTERING QUALITY MEASURES BASED ON COMPARING THE PROXIMITY MATRICES FOR THE MEMBERSHIP VECTORS AND THE OBJECTS

International Journal of Pattern Recognition and Artificial Intelligence ◽

10.1142/s0218001408006922 ◽

2008 ◽

Vol 22 (08) ◽

pp. 1513-1538 ◽

Cited By ~ 1

Author(s):

ROELOF K. BROUWER

Keyword(s):

Quality Measures ◽

Rand Index ◽

Adjusted Rand Index ◽

Wide Range ◽

Proximity Matrix ◽

Clustering Quality ◽

Feature Values ◽

Membership Matrix ◽

Cluster Quality ◽

Membership Vector

There are several commonly accepted clustering quality measures (clustering quality as opposed to cluster quality) such as the rand index, the adjusted rand index and the jacquard index. Each of these however is based on comparing the partition produced by the clustering process to a correct partition. They can therefore only be used to determine the quality of a clustering process when the correct partition is known. This paper therefore proposes another clustering quality measure that does not require the comparison to a correct partition. The proposed metric is based on the assumption that the proximities between the membership vectors should correlate positively with the proximities between the objects which may be the proximities between their feature vectors. The values of the components of the membership vector, corresponding to a pattern, are the membership degrees of the pattern in the various clusters. The membership vector is just another object data vector or type of feature vector with the feature values for an object being the membership values of the object in the various clusters. Based on this premise, this paper describes some new cluster quality metrics derived from standard correlation measures and other proposed correlation metrics. Simulations on data with a wide range of clusterability or separability show that the approach of comparing the proximity matrix based on the membership matrix to the object proximity matrix is quite effective.

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Regression Mixture Model Clustering of Multimodel Ensemble Forecasts of Hurricane Sandy: Partition Characteristics

Monthly Weather Review ◽

10.1175/mwr-d-16-0099.1 ◽

2016 ◽

Vol 144 (10) ◽

pp. 3825-3846 ◽

Cited By ~ 7

Author(s):

Alex M. Kowaleski ◽

Jenni L. Evans

Keyword(s):

Mixture Model ◽

Forecast Error ◽

Potential Temperature ◽

Lower Troposphere ◽

Hurricane Sandy ◽

Rand Index ◽

Ensemble Prediction ◽

Adjusted Rand Index ◽

Cluster Assignment ◽

Regression Mixture

Track and cyclone phase space (CPS) forecasts of Hurricane Sandy from four global ensemble prediction systems are clustered using regression mixture models. Bayesian information criterion, cluster assignment strength, and mean-squared forecast error are used to select optimal model specifications. Fourth-order (third order) polynomials for 168-h forecasts (60-h forecast segments) and 5 (6) clusters for track (CPS) forecasts are selected. Mean cluster paths from eight initialization times show that track and CPS clustering meaningfully partition potential tracks and structural evolutions, distilling a large number of ensemble members into several representative and distinct solutions. Rand index and adjusted Rand index calculations demonstrate a relationship between track and CPS cluster membership for both 168-h forecasts and 60-h forecast segments, indicating that certain tracks are preferentially associated with certain structural evolutions. These relationships are explained in greater detail using forecasts initialized at 0000 UTC 25 October. Storm-centered cluster composite maps of 500-hPa geopotential height and 850-hPa equivalent potential temperature for the 120-h forecast valid at 0000 UTC 30 October (initialized at 0000 UTC 25 October) indicate that both track and CPS clustering successfully capture variations in the Sandy–trough interaction and the strength of the lower-troposphere warm core of Sandy at the time of observed landfall. Together, these results illustrate the relationship between the track and structural evolution of Sandy and suggest the potential of multiensemble mixture-model path clustering for tropical cyclone forecasting.

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