Data Nuggets: A Method for Reducing Big Data While Preserving Data Structure

Big data, with <i>N</i> × <i>P</i> dimension where <i>N</i> is extremely large, has created new challenges for data analysis, particularly in the realm of creating meaningful clusters of data. Clustering techniques, such as K-means or hierarchical clustering are popular methods for performing exploratory analysis on large datasets. Unfortunately, these methods are not always possible to apply to big data due to memory or time constraints generated by calculations of order P*N(N−1)2. To circumvent this problem, typically the clustering technique is applied to a random sample drawn from the dataset; however, a weakness is that the structure of the dataset, particularly at the edges, is not necessarily maintained. We propose a new solution through the concept of “data nuggets”, which reduces a large dataset into a small collection of nuggets of data, each containing a center, weight, and scale parameter. The data nuggets are then input into algorithms that compute methods such as principal components analysis and clustering in a more computationally efficient manner. We show the consistency of the data nuggets based covariance estimator and apply the methodology of data nuggets to perform exploratory analysis of a flow cytometry dataset containing over one million observations using PCA and K-means clustering for weighted observations. Supplementary materials for this article are available online.