Clustering is an important analytical technique that has proven to affect human life positively through its application in cancer research, market segmentation, city planning etc. In this time of growing technological systems, mixed data has seen another face of longitudinal, directional and functional attributes which is worth paying attention to and analyzing. Previous research works on clustering relied largely on the inverse weight technique and B-spline in smoothing data and assessing the performance of various clustering algorithms. In 1971, Gower proposed a method of clustering for mixed variable types which has been extended to include functional and directional variables by Hendrickson (2014). In this study, we will do a comparative analysis of the performance of the hierarchical clustering mechanism using a simulated Functional data with mixed structure. We will adopt the Fourier basis smoothing procedure and use the Rand index (Rand 1971) and adjusted Rand index for the comparison of the various clustering algorithms.

Sorting out data into partitions is increasing becoming complex as the constituents of data is growing outward everyday. Mixed data comprises continuous, categorical, directional functional and other types of variables. Clustering mixed data is based on special dissimilarities of the variables. Some data types may influence the clustering solution. Assigning appropriate weight to the functional data may improve the performance of the clustering algorithm. In this paper we use the extension of the Gower coefficient with judciously chosen weight for the L2 to cluster mixed data.The benefits of weighting are demonstrated both in in applications to the Buoy data set as well simulation studies. Our studies show that clustering algorithms with application of proper weight give superior recovery level when a set of data with mixed continuous, categorical directional and functional attributes is clustered. We discuss open problems for future research in clustering mixed data.

Clustering is a widely used technique in data mining applications to source, manage, analyze and extract vital information from large amounts of data. Most clustering procedures are limited in their performance when it comes to data with mixed attributes. In recent times, mixed data have evolved to include directional and functional data. In this study, we will give an introduction to clustering with an eye towards the application of the extended Gower coefficient by Hendrickson (2014). We will conduct a simulation study to assess the performance of this coefficient on mixed data whose functional component has strictly-decreasing signal curves and also those whose functional component has a mixture of strictly-decreasing signal curves and periodic tendencies. We will assess how four different hierarchical clustering algorithms perform on mixed data simulated under varying conditions with and without weights. The comparison of the various clustering solutions will be done using the Rand Index.