### Table 1: Average error rates for simulated data. LAC PROCLUS K-means DOC

"... In PAGE 4: ... Results on Simulated Data. The performance results reported in Table1 clearly demonstrate the large gain in performance obtained by the LAC algorithm with respect to PROCLUS and K-means with high dimensional data. The good performance of LAC on Examples 4 and 5 shows that our algorithm is able to detect clusters folded in subspaces not necessarily aligned with the input axes.... In PAGE 4: ... PROCLUS requires the average number of dimensions per cluster as parameter in input; its value has to be at least two. We have cross-validated this parameter and report the best error rates obtained in Table1 . PROCLUS is able to select highly relevant features for low dimensional data, but fails to do so in higher dimensions, as the large error rates for Examples 2 and 3 show.... ..."

### Table 2: A sample data set illustrates clusters embedded in subspaces of a high dimensional space.

2003

"... In PAGE 2: ... Hence, a good subspace clustering algorithm should be able to find clusters and the maximum associated set of dimensions. Consider, for example, a data set with 5 data points of 6 dimensional(given in Table2 ). In this data set, it is obvious that C = {x1, x2, x3} is a cluster and the maximum set of dimensions should be P = {1, 2, 3, 4}.... In PAGE 3: ...here sj is a vector defined as sj = (Aj1, Aj2, ..., Ajnj)T. Since there are possibly multiple states(or values) for a vari- able, a symbol table of a data set is usually not unique. For example, for the data set in Table2 , Table 3 is one of its symbol tables. BC BS A A A A B B B B C C C C D D D D BD BT Table 3: One of the symbol tables of the data set in Table 2.... In PAGE 3: ... For a given symbol table of the data set, the frequency table of each cluster is unique according to that symbol table. For example, for the data set in Table2 , let (C, P) be a subspace cluster, where C = {x1, x2, x3} and P = {1, 2, 3, 4}, if we use the symbol table presented in Table 3, then the corre- sponding frequency table for the subspace cluster (C, P) is given in Table 4. From the definition of frequency fjr in Equation (6), we have the following equalities: nj CG r=1 fjr(C) = |C|, j = 1, 2, .... ..."

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### Table 6. The cluster assignments of the privacy-preserving k-means algorithm compared to the regular k-means clustering.

"... In PAGE 64: ... Although the descriptive information might provide interesting insights about the data, the actual use of the clustering method for predictions will be the cluster assignments The cluster assignments tell us which segment each customer belongs to and, in case of a new customer, the potential segment. Table6 shows the assignments of the models, how the assignments of the protocols differ. The assignments of the normal k-means are taken as the baseline to which the assignments of our privacy-preserving k-means are being compared.... In PAGE 64: ... The assignments of the normal k-means are taken as the baseline to which the assignments of our privacy-preserving k-means are being compared. The results in Table6 show that misassignments grow as the number ... ..."

### Table 3 K-means Clustering Analysis

"... In PAGE 71: ... A preliminary analysis using K-means clustering algorithm[84] and three clusters have resulted in groups having the means as shown in Figure 23. Plot of Means for Each matsim Group Cluster Cluster 1 Cluster 2 Cluster 3 WClock -100 0 100 200 300 400 500 600 700 800 Execution Time [s] Figure 23 Plot of Means for Each matsim Group Cluster Further details of the clustering analysis are given in Table3 . Cluster separation distances are given as distances below diagonal or squared distances above ... ..."

### Table 6 the cluster assignments of the privacy preserving k means algorithm compared to the regular k means clustering.

"... In PAGE 61: ... Although the descriptive information might provide interesting insights about the data, the actual use of clustering method on predictions will be the cluster assignments The cluster assignments tell us which segment each customer belongs to and in case of a new customer, the potential segment. The Table6 shows the assignments of the models, how the assignments of the protocols differ. The assignments of the normal k means are taken as baseline to which the assignments of our privacy preserving k means are being compared at.... In PAGE 61: ... The assignments of the normal k means are taken as baseline to which the assignments of our privacy preserving k means are being compared at. The results in the Table6 shows that the miss assignments grow as the number of... ..."

### Table 3 summarizes the experiments performed. Spher- ical K-means is used for the last two datasets because they are so high-dimensional and non-Gaussian that regular K- means performs miserably on them [18]. Ensemble-A indi- cates the original ranges of a2 chosen. We found that, given

2002

"... In PAGE 10: ... Algo. Similarity Natural-a243 Ensemble-A Ensemble-B 8D5K K-Means Euclidean 5 a243a245a244a247a246 a248a66a249a150a248a98a249a92a250a19a251a13a252 a243a126a244a242a246 a253a126a249a92a250a254a249a32a255a57a252 PENDIG K-Means Euclidean 10 a243a245a244a247a246 a248a66a249a65a253a126a249a1a0a65a251a13a252 a243a126a244a247a246 a255a98a249a92a250a254a249a92a250a64a248a64a252 NEWS20 Spherical K-Means Cosine 20 a243a245a244a3a2a5a4a7a6a9a8a165a246a169a250a19a251a98a249a92a250a9a251a98a249a1a10a65a251a13a252 a243a126a244a242a246a169a250a18a253a245a249a32a248a98a249a150a248a11a10a57a252 YAHOO Spherical K-Means Cosine 20 a243a245a244a3a2a5a4a7a6a9a8a165a246a169a250a19a251a98a249a92a250a9a251a98a249a1a10a65a251a13a252 a243a126a244a242a246a169a250a18a253a245a249a32a248a98a249a150a248a11a10a57a252 Table3 . Details of the datasets and cluster ensembles with varying a243 .... ..."

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### Table 19. Test error (in % ), high-dimensional data sets.

2006

"... In PAGE 95: ... Table19 Cont. NMC KNNC LDC QDC natural textures Original 54.... ..."

### Table 3. Comparison of generalisation performance between the SAKM and a PNN using the k-means clustering algorithm.

2004

"... In PAGE 5: ... of the link weights which establish connections between the kernels with the same class labels, though the results are not shown in this paper). Table3 summarises the performance comparison between the SAKM constructed (i.e.... ..."

### Table 5: Confusion Matrix for IRIS dataset. (a) K-Means; (b) Parallel GA.

1995

"... In PAGE 6: ... The cluster labels for the 30 patterns of IRIS data are shown in Figure 5. For the full IRIS data (150 pat- terns) the confusion matrices of assigned labels are shown in Table5 (a) and Table 5(b) using K-Means and parallel genetic algorithm respectively. Out of 150 patterns, 15 patterns were misclassi ed by the paral- lel genetic algorithm in contrast to 16 patterns being misclassi ed by the K-Means algorithm.... ..."

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### Table 1. Performance results of the K-means and MSF clustering algorithms

"... In PAGE 5: ... The F-measure was used as the quality measure. The results are listed in Table1 . The results indicate that the flocking algorithm achieves better result compared to the K-means for document clustering although the K-means algorithm has prior knowledge of the exact cluster number.... ..."