Dimensionality Reduction In Machine Learning

dimensionality reduction in machine learning represents a topic that has garnered significant attention and interest. What's the meaning of dimensionality and what is it for this data?. Dimensionality is the number of columns of data which is basically the attributes of data like name, age, sex and so on. While classification or clustering the data, we need to decide what all dimensionalities/columns we want to use to get meaning information. From another angle, dimensionality reduction - Relationship between SVD and PCA.

Furthermore, however, it can also be performed via singular value decomposition (SVD) of the data matrix $\mathbf X$. What is the connection between these two approaches? Additionally, what is the relationship between SVD and PCA?

Or in other words, how to use SVD of the data matrix to perform dimensionality reduction? Why is dimensionality reduction always done before clustering?. I learned that it's common to do dimensionality reduction before clustering.

But, is there any situation that it is better to do clustering first, and then do dimensionality reduction? Does SVM suffer from curse of high dimensionality? Moreover, while I know that some of the classification techniques such as k-nearest neighbour classifier suffer from the curse of high dimensionality, I wonder does the same apply to the support vector machi... What should you do if you have too many features in your dataset .... Whereas dimensionality reduction removes unnecessary/useless data that generates noise.

Similarly, my main question is, if excessive features in a dataset could cause overfitting and regularization can help to reduce the complexity of the model, why is regularization not a valid solution? Intuitive explanation of how UMAP works, compared to t-SNE. I have a PhD in molecular biology. My studies recently started to involve high dimensional data analysis. I got the idea of how t-SNE works (thanks to a StatQuest video on YouTube) but can't seem t...

Building on this, dimensionality reduction - How to reverse PCA and reconstruct original .... Principal component analysis (PCA) can be used for dimensionality reduction. After such dimensionality reduction is performed, how can one approximately reconstruct the original variables/features ...

Generally the dimensionality of the problem is, as you suspected, equal to the number of inputs ( also known as, features, measurement variables ). This perspective suggests that, so in the NN model, that would be the number of nodes in the input layer. There may be unmeasured features from the problem, but normally dimensionality only refers to the measurements you have. Why is Euclidean distance not a good metric in high dimensions?. I read that 'Euclidean distance is not a good distance in high dimensions'.

Moreover, i guess this statement has something to do with the curse of dimensionality, but what exactly? Besides, what is 'high