Abstract
The advent of high-throughput technologies and the concurrent advances in information sciences have led to an explosion in size and complexity of the data sets collected in biological sciences. The biggest challenge today is to assimilate this wealth of information into a conceptual framework that will help us decipher biological functions. A large and complex collection of data, usually called a data cloud, naturally embeds multi-scale characteristics and features, generically termed geometry. Understanding this geometry is the foundation for extracting knowledge from data. We have developed a new methodology, called data cloud geometry-tree (DCG-tree), to resolve this challenge. This new procedure has two main features that are keys to its success. Firstly, it derives from the empirical similarity measurements a hierarchy of clustering configurations that captures the geometric structure of the data. This hierarchy is then transformed into an ultrametric space, which is then represented via an ultrametric tree or a Parisi matrix. Secondly, it has a built-in mechanism for self-correcting clustering membership across different tree levels. We have compared the trees generated with this new algorithm to equivalent trees derived with the standard Hierarchical Clustering method on simulated as well as real data clouds from fMRI brain connectivity studies, cancer genomics, giraffe social networks, and Lewis Carroll's Doublets network. In each of these cases, we have shown that the DCG trees are more robust and less sensitive to measurement errors, and that they provide a better quantification of the multi-scale geometric structures of the data. As such, DCG-tree is an effective tool for analyzing complex biological data sets.
Highlights
Advances in Information Technology have led to an exponential increase in the amount of data that scientists collect, to the extent that they are in dire need of new methodologies to summarize and visualize the corresponding large datasets efficiently and rapidly
The complete procedure, which we refer to as DCG-tree, includes four main steps, namely: 1) Generate the potential landscape that represents the graph on the data points weighted with the empirical similarity measure, 2) Explore the potential landscape at different temperatures using a Dynamic Monte Carlo procedure to derive its geometry, 3) Build the ultrametric space from the information collected from these multiple Markovian walks, 4) Visualize this ultrametric space using a hierarchical tree or a Parisi matrix
S1A and S1B a comparison between this DCG-tree and the hierarchical clustering (HC)-trees generated from the same fMRI data
Summary
Advances in Information Technology have led to an exponential increase in the amount of data that scientists collect, to the extent that they are in dire need of new methodologies to summarize and visualize the corresponding large datasets efficiently and rapidly. The main reasons for the popularity of HC methods are that they are seemingly easy to set up, their computing requirements are usually small, and they provide visual information on data at low costs As it has become common practice a HC tree is constructed on the basis of a choice of a empirical relational measure, either similarity or distance, among object nodes constituting a data cloud of interest, and an ad hoc choice of module, such as complete, single linkage or many others, for prescribing ‘‘distances’’ among sets of nodes [5]. It is not unusual for some scientists to report achieving the ideal ultimate goal of partitioning object nodes into optimally homogeneous clusters in a multi-scale fashion with the HC technique
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