# Ellipsoidal K-Means: An Automatic Clustering Approach for Non-Uniform Data Distributions
## 4 Experimental Study
### Datasets  
The 14 datasets considered are summarized in Table 1, and most of them are also represented graphically in Figures 6 and 7. The details of the datasets are described below.  
1. **Data_5_2:** This dataset, used in [23], includes 250 two-dimensional data points distributed over five spherical clusters. The clusters in this dataset are highly overlapping; each of the 50 objects in each of five classes has 2 variables. This dataset is shown in Figure 6a.
2. **Data_10_2:** As described in [44], this dataset includes 500 data points in two dimensions, divided into 10 clusters, with some clusters overlapping. Each cluster has 50 data points. A visual representation is shown in Figure 6b.
3. **Mixed_3_2:** This dataset contains 600 two-dimensional points arranged into three clusters, with shapes that are either ellipsoidal or hyperspherical. Figure 6c illustrates this dataset.
4. **Sym_3_2:** Introduced in [28], this dataset contains 350 points in two dimensions, with clusters that are ring-shaped, spherically compact, or linear. It is depicted in Figure 6d.
5. **Ellip_2_2:** Cited in [45], this dataset consists of 400 two-dimensional points forming two intersecting ellipsoidal shells. See Figure 7a for a visual representation.
6. **Square1:** Used in [21], this dataset includes 1000 points distributed across four square-shaped clusters, as shown in Figure 7b.
7. **Square4:** Similar to Square1 and also from [21], this dataset has 1000 points spread over four square clusters. Figure 7c illustrates the dataset.
8. **Sizes5:** Referenced in [21], this dataset contains 1000 points divided into four clusters of varying sizes. It is represented in Figure 7d.
9. **Iris** The Iris dataset features 150 flower samples from three species (Setosa, Versicolor, Virginia). Each class contains 50 samples, with four features: sepal length, sepal width, petal length, and petal width.
10. **Cancer:** The cancer dataset is based on breast cancer in Wisconsin. It is a diagnosis of breast cancer, with 2 classes (classify a tumor as benign or malignant). The cancer dataset contains 683 objects and 9 variables.
11. **Newthyroid:** Thyroid involves the diagnosis of thyroid, whether it is hyper or hypofunction. Five attributes are used to classify 3 classes of thyroid functions as over-function, normal-function, or under-function. The dataset is based on new thyroid data and contains 215 patterns.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Datasets** & **Objects** & **Attributes** & **Class** \\ \hline Data\_5\_2 & 250 & 2 & 5 \\ Data\_10\_2 & 500 & 2 & 10 \\ Mixed\_3\_2 & 600 & 2 & 3 \\ Sym\_3\_2 & 350 & 2 & 3 \\ Ellip\_2\_2 & 400 & 2 & 2 \\ Squarel & 1000 & 2 & 4 \\ Sizes5 & 1000 & 2 & 4 \\ Iris & 150 & 3 & 3 \\ Cancer & 683 & 9 & 2 \\ Newthyroid & 215 & 5 & 3 \\ Lungcancer & 32 & 56 & 3 \\ Wine & 178 & 13 & 3 \\ LiverDisorder & 345 & 6 & 2 \\ \hline \end{tabular}
\end{table}
Table 1: Description of the datasets.  
12. **Lungcancer:** The Lung Cancer dataset from the UCI repository contains data on lung cancer patients. It includes information on various attributes like age, smoking habits, and cancer type, among others, to help in the classification and prediction of lung cancer incidences.
* 13. **Wine:** Wine data, obtained through chemical analysis, originate from three different cultivators. Consequently, the analysis categorizes the wines into three types. The dataset comprises 178 samples of wine, each characterized by 13 inputs.
* 14. **LiverDisorder:** The liver disorder dataset consists of 345 instances and 6 conditional attributes. It contains records of individuals with liver disorders, intended for binary classification tasks to predict liver disease. The attributes include various liver function tests and a selector field used to split the data into training and validation sets.