# Introduction The Johnson-Lindenstrauss lemma is a mathematical theorem that states that any high dimensional dataset can be randomly projected into a lower dimensional Euclidean space while controlling the distortion in the pairwise distances. In this lab, we will explore the theoretical bounds of the Johnson-Lindenstrauss lemma for embedding with random projections and validate it empirically using Python scikit-learn. ## VM Tips After the VM startup is done, click the top left corner to switch to the **Notebook** tab to access Jupyter Notebook for practice. Sometimes, you may need to wait a few seconds for Jupyter Notebook to finish loading. The validation of operations cannot be automated because of limitations in Jupyter Notebook. If you face issues during learning, feel free to ask Labby. Provide feedback after the session, and we will promptly resolve the problem for you.
Click the virtual machine below to start practicing