A study on some dimensionality reduction algorithms in machine learning

In recent decades, there has been an explosion in the amount of data in most fields of life and science, especially in the practical sciences like physics, chemistry, biology, and astronomy. The data coming from experiments and laboratory devices are becoming increasingly complicated, and reports hundreds or thousands of measurements for a single experiment, and that makes statistical approaches facing difficulty in dealing with such high-dimensional data. This not only does make processing extremely slow, but it can also make it much harder to find a good solution. However, much of the data is redundant, and it is possible to reduce the number of variables to a manageable level without losing too much information. Dimensionality reduction techniques are mathematical procedures that enable this reduction; they have been widely developed in fields such as statistics and machine learning, and are now a hot research topic. In this thesis, we discussed dimensionality reduction, the common approaches used for dimensionality reduction, and then went through four of the most popular dimensionality reduction techniques: PCA, Multidimensional scaling, LLE, and Isomap. We applied these algorithms to real and artificial data sets and discussed the results for a better understanding of these algorithms.