## 4 Empirical Evaluation of Proposed Algorithms
### Experiments with Reference Datasets
#### 4.1.1 Experimental Setup  
Basic information about the datasets is shown in Table 1. The parallel implementations of the proposed methods and K-means\(\|\) (omitting K-means++ readily tested in [6]) were applied to the seven largest datasets and serial implementations were used otherwise. For the serial experiments, we used the following eight datasets: Human Activity Recognition Using Smartphones ([[http://archive.ics.uci.edu/ml/index.php](http://archive.ics.uci.edu/ml/index.php)]([http://archive.ics.uci.edu/ml/index.php](http://archive.ics.uci.edu/ml/index.php))) (HAR), ISOLET (ISO), Letter Recognition (LET), Grammatical Facial Expressions (GFE), MNIST ([[http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)]([http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/))) (MNI), Birch3 ([[http://cs.joensuu.fi/sipu/datasets/](http://cs.joensuu.fi/sipu/datasets/)]([http://cs.joensuu.fi/sipu/datasets/](http://cs.joensuu.fi/sipu/datasets/))) (BIR), Buzz in Social Media (BSM), and Covertype (COV). For the parallel experiments, the following seven large high-dimensional datasets were used: KDD Cup 1999 Data (KDD), US Census Data 1990 (USC), Oxford Buildings ([[http://www.robots.ox.ac.uk/~vgg/data/](http://www.robots.ox.ac.uk/~vgg/data/)]([http://www.robots.ox.ac.uk/~vgg/data/](http://www.robots.ox.ac.uk/~vgg/data/))oxbuildings/) (OXB), Tiny Images ([[http://horatio.cs.nyu.edu/mit/tiny/data/](http://horatio.cs.nyu.edu/mit/tiny/data/)]([http://horatio.cs.nyu.edu/mit/tiny/data/](http://horatio.cs.nyu.edu/mit/tiny/data/))) (TIN), MNIST8M (M8M), RCV1v2 collection of documents ([[https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets](https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets)]([https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets](https://www.csie.ntu.edu.tw/~cjlin/libsvmtools/datasets))) (RCV) and Street View House Numbers ([[http://ufldl.stanford.edu/housenumbers/](http://ufldl.stanford.edu/housenumbers/)]([http://ufldl.stanford.edu/housenumbers/](http://ufldl.stanford.edu/housenumbers/))) (SVH). The BIR dataset [44] was selected to test SK-means\(\|\) for low-dimensional data. With the OXB dataset, we used the transformed dataset with 128-dimensional SIFT descriptors extracted from the original dataset. For the TIN dataset, we sampled a 20% subset from the Gist binary file (tinygist80 million.bin), where 79,302,017 images are characterized with 384-dimensional Gist descriptors. The highest-dimensional dataset was SVH, where we combined the training, testing, and validation subsets into a single dataset. We excluded the attack type feature (class label) from the KDD dataset, used the Twitter data for the BSM dataset, and restricted to the training dataset of the HAR dataset. For the RCV dataset, we used the full industries test set (350 categories) and selected 1000 out 47,236 features with the same procedure as in [45]. For the M8M and the RCV datasets, we used the scaled datasets given in [[http://cs.joensuu.fi/sipu/datasets/](http://cs.joensuu.fi/sipu/datasets/)]([http://cs.joensuu.fi/sipu/datasets/](http://cs.joensuu.fi/sipu/datasets/)), all other datasets were min-max scaled into \([-1,1]\). In Section 3.1, we discussed the selection of parameter \(S\). Because the results in [30; 35] and that the computing nodes' have typically the number of cores in powers of two, we fixed \(S=8\) in the experiments. This means that each dataset was randomly divided into 8 subsets, which were roughly of equal size. Matlab 2018a environment was used in the serial experiments with the K-means\(++\), K-means\(\|\), SK-means\(\|\) and SRPK-means\(\|\) methods. In Matlab 2018a version, we were not able to modify gop-function and gplus-function (see Section 3.3). In Matlab R2014a environment, these modifications were possible for the proposed methods. To follow the good practices of running time evaluation [46], all the parallel experiments with the K-means\(\|\), SK-means\(\|\) and SRPK-means\(\|\) methods were run Matlab R2014a environment.