In this problem set, you will implement multidimensional scaling (MDS) from scratch. You may use standard matrix/vector libraries (e. g. numpy) but you must implement two dimensional MDS itself on your own and not use an existing software package. MDS attempts to find an arrangement of points such that the distances between points match human-judged similarities. To do this, we will minimize the stress, which is the squared difference between psychological and MDS distances: