Hubbert, L. J., Arabie, P. (1985), Comparing partitions, Journal of Classification, 2:63-76.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....distribution, less attention was paid to the selection of the clustering algorithm and of similarity index. We investigate the impact of various partitioning and hierarchical algorithms when used in conjunction with well known similarity indices like Fowlkes Mallows, Jaccard, Rand [6] and Rand [7]. The definition for the partition distance is introduced in [8] for any two partitions of an object set C.D. Giurc aneanu and I. T abus were supported by Academy of Finland. is the minimum number of elements that must be deleted from , so that restricted to ....

L. Hubert and P. Arabie, "Comparing partitions," J. Classification, vol. 2, pp. 193--218, 1985.

.... index used in [2] A special role in investigating the properties of s( is played by optimal assignment defined for the contingency matrix of two partitions of the same set [7, 9] In this paper, we employ four similarity indices: s( Fowlkes Mallows [12] Jaccard [12] and RandsA [11]. Note that the complete description for all agglomerative hierarchical algorithms used in the sequel, can be found in [12] When applying the estimation method to the glioma dataset, if we choose Pl = 24 we can guarantee that, at each trial, the clustered N x Pl dataset contains at least one ....

L. Hubert and P. Arable. Comparing partitions. J. Classification, 2:193-218, 1985.

....the prediction of the optimal cluster partitioning for those data sets. Normalisation and weighed voting techniques are proposed to improve the prediction of the number of clusters based on multiple indices. Other validation techniques, such as Goodman Kruskal index [24] and Hubert s # statistic [25], as well as the comparison and combination of results obtained from different clustering algorithms, will be part of future work. Comparisons indicate that the normalisation of indices may improve the prediction process. Normalisation allows smoothing the effect of the highest values on the ....

L.J. Hubert, P. Arabie, "Comparing partitions", J. Classification, Vol. 2, 1985, pp. 193-218

....as a sequence of 20 characters, each of which represents an amino acid. The length of each sequence is different from 408 to 442, which makes it difficult to convert a sequence into a vector of fixed dimensionality. In order to evaluate the partitions we use the Adjusted Rand Index (ARI) [4, 18]. Let U 1 ; U c be the obtained clusters and T 1 ; T s be the ground truth clusters. Let n ij be the number of samples which belongs to both U i and T j . Also let n i: and n :j be the number of samples in U i and T j , respectively. ARI is defined as i;j n ij ....

....of HMM States Proposed K Means Figure 4: Adjusted Rand indices of K Means and the proposed method in a sequence classification experiment. the number of clusters is different. When the two partitions are exactly the same, ARI is 1, and the expected value of ARI over random partitions is 0 (see [4] for details) In order to derive the Fisher score, we trained complete connection HMMs via the BaumWelch algorithm, where the number of states s is changed from 2 to 5, and each state emits one of t = 20 characters. This HMM has s initial state probabilities, s terminal state probabilities, s ....

L. Hubert and P. Arabie. Comparing partitions. J. Classif., pages 193--218, 1985.

....gene expression sets with external criteria described in Section 3. 5.1 Measure of agreement A clustering result can be considered as a partition of objects into groups. Thus, comparing two clustering results is equivalent to assessing the agreement of two partitions. The adjusted Rand index [Hubert and Arabie, 1985] assesses the degree of agreement between two partitions. Milligan and Cooper, 1986] recommended the adjusted Rand index as the measure of agreement even when comparing partitions with different number of clusters. Given a set of n objects S = fO 1 ; O n g, suppose U = fu 1 ; uR ....

....a d a b c d . The Rand index lies between 0 and 1. When the two partitions agree perfectly, the Rand index is 1. The problem with the Rand index is that the expected value of the Rand index of two random partitions does not take a constant value (say zero) The adjusted Rand index proposed by [Hubert and Arabie, 1985] 12 6 RESULTS AND DISCUSSION assumes the generalized hypergeometric distribution as the model of randomness, i.e. the U and V partitions are picked at random such that the number of objects in the classes and clusters are fixed. Let n ij be the number of objects that are in both class u i and ....

[Article contains additional citation context not shown here]

Hubert, L. and Arabie, P. (1985) Comparing partitions. Journal of Classification, 193--218.

....should be chosen We think the question is justified, but hard to solve. It certainly is dependent on the context and the intentions of the researcher. There are some examples in the literature, such as the well established RAND index, originally used for the evaluation of cluster analysis results [5,11]. This measure acts on the same domain as # 2 , and can be used to evaluate the equivalence of two partitions. A different look at the normalisation factor resulted in dramatic changes of the evaluation of approximation quality. Assuming statistical independence of the decision attribute from the ....

L. Hubert, P. Arabie, Comparing partitions, J. Classification 2 (1985) 193--218.

....the best solutions, in terms of mean squared error, were used for further analysis. Factor 2, Number of clusters was set to 4 and 9. Factor 3, Number of dimensions was set to 4; 6; or8. Dependent variable 1: mean squared error was computed using Equ. 1. Dependent variable 2, Rand index (see [12]) is a measure of agreement between the true, known partition structure and the obtained clusters. Both the numerator and the denominator of the index reflect frequency counts. The numerator is the number of times a pair of data is either in the same or in different clusters in both known and ....

Hubert L.J., Arabie P.: Comparing partitions, J. of Classification, 2, 63-76, 1985.

....against their baseline distribution, i.e. pure randomness. Then a clustering can be asserted to be valid if it has unusually high values of corrected (normalized) external indices. Let n ij be the value in cell (i, j) in Table 8. Then n i. is the ith row sum and n .j is the jth column sum. Hubert and Arabie (1985) suggested a baseline distribution based on these row and column sums in Table 8 being fixed but the partitions (i.e. K and R) being chosen at random. In that case, an index S is corrected according to the following formula: S# # S # E#S# #Max#S# # E#S## To compute the corrected Rand index, ....

Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193--218.

....gene expression sets with external criteria described in Section 3. 5.1 Measure of Agreement A clustering result can be considered as a partition of objects into groups. Thus, comparing two clustering results is equivalent to assessing the agreement of two partitions. The adjusted Rand index (Hubert and Arabie 1985) assesses the degree of agreement between two partitions. Milligan and Cooper (1986) recommended the adjusted Rand index as the measure of agreement even when comparing partitions with different number of clusters. Given a set of n objects S = fO 1 ; O n g, suppose U = fu 1 ; uR g ....

....a d a b c d . The Rand index lies between 0 and 1. When the two partitions agree perfectly, the Rand index is 1. The problem with the Rand index is that the expected value of the Rand index of two random partitions does not take a constant value (say zero) The adjusted Rand index proposed by Hubert and Arabie (1985) assumes the generalized hypergeometric distribution as the model of randomness, i.e. the U and V partitions are picked at random such that the number of objects in the classes and clusters are fixed. Let n ij be the number of objects that are in both class u i and cluster v j . Let n i: and n ....

[Article contains additional citation context not shown here]

Hubert, L. and P. Arabie (1985). Comparing partitions. Journal of Classification (2), 193--218.

....real gene expression sets with external criteria described in Section 3. 5.1 Measure of Agreement A clustering result can be considered as a partition of objects into groups. Thus, comparing two clustering results is equivalent to assessing the agreement of two partitions. The adjusted Rand index (Hubert and Arabie 1985) assesses the degree of agreement between two partitions. Milligan and Cooper (1986) recommended the adjusted Rand index as the measure of agreement even when comparing partitions with different number of clusters. Given a set of objects 24430 # H , suppose 380 ....

.... . The Rand index lies between 0 and 1. When the two partitions agree perfectly, the Rand index is 1. The problem with the Rand index is that the expected value of the Rand index of two random partitions does not take a constant value (say zero) The adjusted Rand index proposed by Hubert and Arabie (1985) assumes the generalized hypergeometric distribution as the model of randomness, i.e. the and partitions are picked at random such that the number of objects in the classes and clusters are fixed. Let be the number of objects that are in both class and cluster . Let ....

[Article contains additional citation context not shown here]

Hubert, L. and P. Arabie (1985). Comparing partitions. Journal of Classification (2), 193--218.

....gene expression sets with external criteria described in Section 3. 5.1 Measure of agreement A clustering result can be considered as a partition of objects into groups. Thus, comparing two clustering results is equivalent to assessing the agreement of two partitions. The adjusted Rand index [Hubert and Arabie, 1985] assesses the degree of agreement between two partitions. Milligan and Cooper, 1986] recommended the adjusted Rand index as the measure of agreement even when comparing partitions with different number of clusters. Given a set of objects 26210 # H , suppose ....

.... . The Rand index lies between 0 and 1. When the two partitions agree perfectly, the Rand index is 1. The problem with the Rand index is that the expected value of the Rand index of two random partitions does not take a constant value (say zero) The adjusted Rand index proposed by [Hubert and Arabie, 1985] 12 6 RESULTS AND DISCUSSION assumes the generalized hypergeometric distribution as the model of randomness, i.e. the and partitions are picked at random such that the number of objects in the classes and clusters are fixed. Let be the number of objects that are in both class and ....

[Article contains additional citation context not shown here]

Hubert, L. and Arabie, P. (1985) Comparing partitions. Journal of Classification, 193--218.

....sets with external criteria describedinSection3. Measure of agreement: A clustering result can be considered as a partition of objects into groups. Thus, comparing a clustering result to the external criterion is equivalent to assessing the agreement of two partitions. The adjusted Rand index (Hubert and Arabie, 1985) assesses the degree of agreement between two partitions. Based on an extensive empirical study, Milligan and Cooper, 1986) recommended the adjusted Rand index as the measure of agreement even when comparing partitions with different numbers of clusters. In this paper, we used the adjusted Rand ....

....number of pairs of objects that are either in the same groups in both partitions or in different groups in both partitions, divided by the total number of pairs of objects. The Rand index lies between 0 and 1. When the two partitions agree perfectly, the Rand index is 1. The adjusted Rand index (Hubert and Arabie, 1985) adjusts the score so that its expected value in the case of random partitions is 0. A high adjusted Rand index indicates a high level of agreement between the two partitions. Please refer to (Yeung et al. 2001a) for a detailed description of the adjusted Rand index. 5 Results and Discussion In ....

Hubert, L. and Arabie, P. (1985) Comparing partitions. Journal of Classification, 193--218.

....seems advisable to resort to an external criterion which uses the available information concerning the true cluster structure. Following Milligan (1981) I adopted both an external criterion and the Pearson correlation between the external criterion and the internal one. The corrected Rand index (Hubert and Arabie, 1985) was chosen as the external criterion. Its validity was established through several tests of clustering procedures, and high correlation with other indexes, that may, possibly, serve as external criteria as well, was generally found. The corrected Rand index (cR) actually gives a measure of how ....

Hubert L., Arabie P. (1985) Comparing partitions, Journal of Classification, 2, 193-218.

....) is the fraction of unfamiliar class (i.e. not encountered during the training phase) test patterns not either flagged as unfamiliar nor assigned to a new class defined during testing. An additional figure of merit for an LUC classifier is a purity measure, such as the Rand clustering score (Hubert and Arabie, 1985), which rewards the classifier for learning the right number of unfamiliar classes, and correctly assigning them to unfamiliar patterns. The algorithm for fuzzy ARTMAP was modified as follows to incorporate LUC. First, in 18 order to focus on the effects of LUC (as opposed to learning with ....

Hubert, L., & Arabie, P. (1985). Comparing Partitions. Journal of Classification, 2, 193-218.

....of the clustering procedure are equally important. In this paper, clustering quality refers to the degree of similarity between the partitions (clusters) produced by a SONN, and a reference partition based on known category labels. This similarity is assessed by applying the Rand Adjusted [11] and the Jaccard [12] measures to partitions obtained by computer simulation. Convergence time is defined as the number of successive presentations of a finite input data set needed for a SONN s weight set to stabilize. This time is easily determined from computer simulation. Computational ....

....between two clusterings A and B [12] 15] These measures are known in pattern recognition literature as external criterion indices, and are used for evaluating the capacity to recover true cluster structure. Based on a previous comparison of these similarity measures [37] the Rand Adjusted [11], defined by: SRA (A; B) 2(c 11 c 22 Gamma c 12 c 21 ) 2c 11 c 22 (c 11 c 22 ) c 12 c 21 ) c 2 12 c 2 21 (1) and Jaccard statistic [12] defined by: S J (A; B) c 11 c 11 c 12 c 21 (2) have been selected to assess clustering quality for this study. It is worth noting that ....

L. Hubert and P. Arabie, "Comparing Partitions", Journal of Classification, Vol. 2, pp. 193-218, 1985.

....best solutions, in terms of mean squared error, were used for further analysis. Factor 2, Number of clusters was set to 4 and 9. Factor 3, Number of dimensions was set to 4; 6; or8. Dependent variable 1: mean squared error was computed using formula (1) Dependent variable 2, Rand index (see [Hubert Arabie 85] is a measure of agreement between the true, known partition structure and the obtained clusters. Both the numerator and the denominator of the index reflect frequency counts. For the numerator, all possible pairs of data are taken and it is determined, whether the data are treated in the same ....

Hubert L.J., Arabie P.: Comparing partitions, J. of Classification, 2, 63-76, 1985.

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Hubbert, L. J., Arabie, P. (1985), Comparing partitions, Journal of Classification, 2:63-76.

No context found.

L. Hubert, L. and P. Arabie, "Comparing partitions," Journal of Classification, vol. 2, pp. 193-218, 1985.

No context found.

L. Hubert and P. Arabie, "Comparing Partitions," J. Classification, vol. 2, pp. 193-218, 1985.

No context found.

L. Hubert and P. Arabie. Comparing partitions. J. Classif., pages 193--218, 1985.

No context found.

Hubert, L. J. and Arabie, P. (1985). Comparing partitions, Journal of Classification 2: 193--218.

No context found.

Hubert, L, and Arabie, P. (1985) 'Comparing Partitions, ' Journal of Classification, 2, 193-218.

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