Data Analysis of Ant Social Structures
Ants, as social insects, exhibit complex behaviors and organizational structures within their colonies. This project focuses on analyzing and extracting relevant information from ant colonies using the framework of convex sets topology. By studying a dataset collected from an entomology study that measured attributes of 300 ants, including size, mass, and protein density, we aim to understand the roles and tasks of individual ants within the colony. These attributes, standardized for ease of data processing, are believed to determine the ants’ roles within the nest.
Through data analysis, we seek to uncover patterns and relationships within the ant colony, shedding light on the intricate social dynamics and division of labor among ant castes. This research not only provides insights into ant behavior but also showcases the application of data science techniques, such as convex set topology, in studying complex biological systems.
Central Trend Analysis
In general, the mean and median have close values, while there is a significant difference with the mode, which is much lower. This suggests the presence of some outliers or extremely large values in the dataset. The discrepancy between the mode and the mean/median suggests that there is complexity in the distribution of your data. This could be due to asymmetry in the distribution, the presence of outliers.
The closeness between the mean and median suggests a symmetric or relatively symmetric distribution of the data. However, the significant difference with the mode, which is much lower, indicates that there are outliers or extremely large values present in the dataset.
Attribute A: There is a slightly higher peak towards the left. This suggests that most of the values are concentrated on the left side of the distribution, indicating a possible left skew or negative bias. This could mean that there is a concentration of lower values compared to higher values. It would be useful to investigate why this is occurring and if there are specific factors that are contributing to this distribution.
Attribute B: The presence of two peaks in the distribution indicates that there are two distinct groups or subsets of data present in your data. This phenomenon is known as a bimodal distribution. There could be different factors or conditions contributing to the formation of these two groups. Further investigation should be conducted to understand the nature of these groups and provide useful insights into the data.
Attribute C: The presence of three peaks suggests that your data have three distinct groups or subsets with different concentrations of values. This distribution is called trimodal. As with the bimodal distribution, understanding the nature and characteristics of these three groups may be essential to comprehend the underlying dynamics of your data.
Machine Learning Algorithms
Is used K-means unsupervised Machine Learning Algorithm to try to identify clusters.
As Elbow and Silhouette criterion depict, the optimal number of clusters is 3.
Let’s try now with a dendogram.
We have that at the first level there are 3 clusters, but 2 are branches of the same branch, so these are more related to each other than to the first cluster, which indicates that we have 3 clusters but 2 of them are closer according to some distance metric.
Now let’s use gaussian mixture model.
Again 3 seems to be the optimal number of clusters.
Data Topology
Here is display a metric analysis of the data.It was made by taking the distance of the most distance point of each clusters as a radius for each sphere.
Finally, we decided to experiment by making clusters using the convex hull of each cluster to explore the geometry of each data group.
Conclusions
The main observation that could be made from the provided data is that there are three groups of ants, each group with several common attributes. This pattern is reflected through numerical analysis, such as Machine Learning criteria, and visually, with topological analysis.
We can notice that the two types of analysis used gave similar results, three clearly defined categories. In a way, we can say that the Machine Learning algorithms we used (K-means, Hierarchical Clustering, GMM) also have topological foundations, as they measure the distance between observations.
Note on Data Availability
It is important to mention that the data used in this study is not public due to privacy restrictions and confidentiality agreements. Therefore, I cannot share the original dataset or the exact details of the observations.
However, I can show the results and the conclusions we have reached through the analysis. These results reflect the trends and patterns that we have identified without compromising the confidentiality or integrity of the data. I appreciate your understanding and hope that the findings presented will be of interest and use to the community, providing valuable insights despite the limitations on data availability.