### Table 5: Convergence of the EM Algorithms for the Two Models.

"... In PAGE 10: ... This validation data consisted of many small sites scattered over an area much larger than that for which soils information was available, and hence could only be used for validating the accuracy of the spectral component of the models. The classi cation error rates are summarised in Table5 , where, for simplicity, only the values of p(l0jl) representing the diagonal entries of the classi cation confusion matrix are given. The validation data used to obtain Table 5 were not of su cient quantity in the study area to evaluate the relative performance of the di erent models tested.... In PAGE 10: ... The classi cation error rates are summarised in Table 5, where, for simplicity, only the values of p(l0jl) representing the diagonal entries of the classi cation confusion matrix are given. The validation data used to obtain Table5 were not of su cient quantity in the study area to evaluate the relative performance of the di erent models tested. More detailed information on salinity was available from the farming group in the form of a salinity risk map.... In PAGE 12: ...Typically, EM algorithms require many iterations to converge, but for some models near optimal results may be obtained after a few iterations. Table5 summarises the conver- gence properties for the rst 10 iterations of the algorithm, from which it is observed that little (relative) change occurs in the parameter estimates after about the fth or sixth iteration. The estimates obtained are given in Table 3.... ..."

### Table 5: Convergence of the EM Algorithms for the Two Models.

"... In PAGE 10: ... This validation data consisted of many small sites scattered over an area much larger than that for which soils information was available, and hence could only be used for validating the accuracy of the spectral component of the models. The classi cation error rates are summarised in Table5 , where, for simplicity, only the values of p(l0jl) representing the diagonal entries of the classi cation confusion matrix are given. The validation data used to obtain Table 5 were not of su cient quantity in the study area to evaluate the relative performance of the di erent models tested.... In PAGE 10: ... The classi cation error rates are summarised in Table 5, where, for simplicity, only the values of p(l0jl) representing the diagonal entries of the classi cation confusion matrix are given. The validation data used to obtain Table5 were not of su cient quantity in the study area to evaluate the relative performance of the di erent models tested. More detailed information on salinity was available from the farming group in the form of a salinity risk map.... In PAGE 12: ...Typically, EM algorithms require many iterations to converge, but for some models near optimal results may be obtained after a few iterations. Table5 summarises the conver- gence properties for the rst 10 iterations of the algorithm, from which it is observed that little (relative) change occurs in the parameter estimates after about the fth or sixth iteration. The estimates obtained are given in Table 3.... ..."

### Table 1: Speaker identification errors for the Gaussian mixture model (GMM), the probabilistic latent semantic analysis model (PLSA) and the regularized probabilis- tic latent semantic analysis model (RPLSA). Test Data

2005

"... In PAGE 8: ... To compare the algorithms in a wide range we tried various lengths of test data. The results are shown in Table1 . Clearly, both PLSA and RPLSA are more effective than the GMM in all cases.... ..."

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### Table 2: Incremental EM algorithm for audio classification.

"... In PAGE 4: ... The unlabeled data points that receive labels are then added to the labeled set, and this new, augmented labeled set is then used to re-estimate model parameters; this process is repeated until all unlabeled points have been labeled. Table2 outlines the algorithm. 4 Experimental Setup We conducted experiments with the above algorithms on two different audio classification tasks: gender identification and speaker identification.... ..."

### Table 2: EM algorithm for the hit-miss mixture model.

2005

"... In PAGE 65: ...3 indicate that case based precision estimates may allow for more robust decision rules when the loss function is asymmetrical. Table2 shows that overarather large domain in the UCI mushrooms data set (five classifiers trained on different portionsofthedatabaseandeachappliedto100cases)theBayesianbootstrapbaseddecision rule has better specificity, and lower average loss for variable misclassification costs. A plausible explanation for this is the tendency of the naive Bayes classifier to probability overshoot , i.... ..."

### Table 1: Experimental results. EM is the conventional EM with random initialization, and EMCS is the proposed EM with component splitting.

2003

"... In PAGE 7: ...1). Table1 -(a) shows the results over 30 trials with different random numbers. We use the on-line EM algorithm ([7]), presenting data one-by-one in a random order.... In PAGE 7: ... We use the mixture of PCA with 10 com- ponents of rank 4, and obtain a compressed image by ^ X = Fh(FT h Fh) 1FT h X, where X is a 64 dimensional block and h indicates the component of the shortest Euclidean distance kX hk. Table1 -(b) shows the residual square error (RSE), P400 j=1 kXj ^ Xjk2, which shows the quality of the compression. In both experi- ments, we can see the better optimization performance... ..."

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### Table 3: The performance of indclus and em-indclus on the human data sets. indclus em-indclus

2001

"... In PAGE 4: ... The first set is a collection of 6 typical data sets from psychological experiments that have been used in previous additive clustering work (orig- inally by Shepard and Arabie (1979), except for animals-s, Mechelen and Storms (1995), and animals, Chaturvedi and Carroll (1994)). The number of objects (n) and the number of features used (k) are listed for each instance as part of Table3 . The second set of problems contains noiseless synthetic data derived from ADCLUS models with 8, 16, 32, 64, and 128 objects.... In PAGE 5: ...data sets are shown in Table 2. (em-indclus took much longer than the other algorithms and its performance is shown separately in Table3 .) The mean VAF for each algorithm is listed, along with the inter-quartile range (IQR) and the mean number of runs that were necessary to achieve time parity with the slowest algorithm on that data set (r).... In PAGE 5: ... This strategy is reminiscent of a proposal by Clouse and Cottrell (1996), although here we are using the ADCLUS model of similarity. In the second algorithm, indclus-pbil, the PBIL algorithm of Baluja (1997) is used 2 Table3 shows one anomaly: no em-indclus run on animals resulted in a VAF 0. This also occurred on all synthetic problems with 32 or more objects (although very good solutions were found on the smaller problems).... ..."

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### Table 1. U-updating algorithm and EM algorithm U-updating algorithm EM algorithm

"... In PAGE 7: ... This iterative procedure is referred to as the U-updating algorithm and gives an alternative to the EM algorithm. The Table1 summarizes the U-updating algorithm in comparison with the EM algorithm. In order to estimate ML parameter (t+1) in M-Step, the EM al- gorithm requires distributions P(xijyi; (t)) in E-Step built on the ML parameter (t) which may be overfltted to the data set at the previous iteration.... ..."

### Table 2: Classi cation performances of four systems on the data from the prediction set. The rst two systems are the HME model trained with the Gibbs sampler algorithm and with the EM algorithm respectively; the last two systems are two versions of CART. Total in Gibbs EM CART I CART II

1995

"... In PAGE 17: ... This candidate value was compared to the current point in the Gibbs sampler chain using a Metropolis test based on the observed posterior. The data in Table2 and Figures 4-6 are based on the nal 500 iterations of each chain. The Metropolis algorithm used to sample from the full conditional distributions was run for 40 iterations, with the variance on the normal distribution equal to 1.... In PAGE 18: ...1, meaning that there was no suggested evidence of lack of convergence for the present dataset and model. Table2 shows the classi cation performances of four systems on the data from the predic- tion set. The rst two systems are the HME model trained with the Gibbs sampler algorithm and with the EM algorithm respectively.... ..."

### Table 1: Speaker identification errors for the Gaussian mixture model (GMM), the probabilistic latent semantic analysis model (PLSA) and the regularized probabilistic latent semantic analysis model (RPLSA). Test Data

2005

"... In PAGE 8: ... Specifically, three pieces of test speech from each speaker that have the lengths of 2, 3 or 5 seconds were used in each experiment. The results are shown in Table1 . Clearly, both PLSA and RPLSA are more effective than the GMM in all cases.... ..."

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