# Efficient High-Dimensional Kernel k-Means++ with Random Projection
## 4 Experiments  
### Datasets  
We used six datasets to evaluate the improvement of our method. The first two are computer vision datasets, namely MNIST [29] and ImageNet [30]. Another two datasets are from bioinformatics datasets, called SMK-187 [31] and GLI-85 [32] (the SMK-187 and GLI-85 datasets could be downloaded from [[https://jundongl.github.io/scikit-feature/OLD/datasets_old.html](https://jundongl.github.io/scikit-feature/OLD/datasets_old.html)]([https://jundongl.github.io/scikit-feature/OLD/datasets_old.html](https://jundongl.github.io/scikit-feature/OLD/datasets_old.html)) accessed date 27 July 2021). The last two datasets are for text mining, called 20 newsgroups [33] and Reuters-21578 [34]. MNIST is a ten-class database for handwritten digit recognition. There are 60,000 samples and 10,000 samples in the training set and the testing set, respectively. In the testing set, there are 1000 samples per class label. Every sample consists of 28 by 28 pixels (i.e., 784 features) with which the value is inside the interval [0,255], and represents the greyscale of that pixel. We evaluate clustering performance by comparing how well different methods optimize clustering with the WCSS measure. In our experiments, we only sample a subset of 5000 data points from the training set. Thus, the dataset to be examined consists of 5000 data points with dimensionality 784 (i.e., \(n=5000\), \(D=784\)). The ImageNet [30] database consists of over 14.2 million images that are organized according to the WordNet hierarchy. Each node in this hierarchy represents a concept (known as the \"synset\"), and all the images are indexed by over 21-thousand synsets. In our analysis, we chose 14,112 images from ten cat-like synsets (namely, an Egyptian cat, a fourant, a lynx, a Madagascar cat, a mountain lion, a Persian cat, a Siamese cat, a skunk, a tabby cat, and a tiger cat). They are all from the leaf nodes in the hierarchy. We called this dataset the ImageNet-Cat dataset. Figure 1 shows an example from each synset used to form this dataset. We used the bag-of-visual-words features of these images from image-net.org. It consists of 1000 visual-words features per photo. In our experiments, we only sampled 2000 images from the ImageNet-Cat dataset for evaluation with \(n~{}=~{}2000\) and \(D~{}=~{}1000\). SMK-187 is a dataset with gene expression data from smokers with lung cancer and also samples from smokers without lung cancer. There are 19,993 features in each sample in SMK-187. This is a two-class dataset with \(n=187\) and \(D=19,993\). GLI-85 is a dataset with transcriptional profiling of gliomas. The dataset is collected from 74 patients where transcriptional profiling has been applied to 85 gliomas. The 74 patients studied were analyzed if their initial tumor was diagnosed as a Grade III or IV glioma of any histologic type on initial surgical treatment. There are 22,283 features in each sample in GLI-85 with \(n=85\) and \(D=22,283\). The 20-Newsgroups dataset contains a collection of newsgroup articles from 20 different newsgroups. It consists of approximately 1000 documents from each of these newsgroups. In our experiment, we only clustered data from 5 of these newsgroups, including alt.atheism, os.ms-windows, sport.baseball, sci.space and religion.misc. With the corpus, we applied a number of data pre-processing steps that include converting characters to lower cases, removing punctuations, removing white spaces, and removing stop words  
Figure 1: Ten different types of cats from ImageNet. in English. Stop words are 174 predefined English common words that are believed to contain very little information for text mining (such as \"we\", \"your\", \"the\", \"any\", and \"only\"). Terms in the corpus are columns, while documents are the rows. Columns with a sparsity of 98% or above were removed, and only 2000 data points were sampled before each iteration of the evaluation. This resulted in a subsampled set with 2000 data points and 929 dimensions, i.e., \(n=2000\), \(D=929\).