ABSTRACT
While Principal Component Analysis (PCA) is a powerful linear dimensionality reduction technique, it fails in the case of non-linear data. However, PCA can be adapted to handle non-linear data by using the kernel trick. That is, PCA can be generalized to a non-linear case by replacing a kernel function for the inner product in the feature space. But the choice of the kernel is very important. Maximum Variance Unfolding (MVU) is a dimensionality reduction technique that learns a kernel matrix from a convex optimization problem to yield low dimensional representation of the data using semidefinite programming. This technique is also called Semidefinite Embedding (SDE). This chapter starts with a detailed explanation of this technique and how MVU finds the optimal kernel to matrix to map the data from high dimensional to low dimensional. Further, the advantages and shortcomings of this algorithm are also discussed along with some practical use cases.
