Imputing Missing Entries of a Data Matrix: A Review

Abstract

The problem of imputing missing entries of a data matrix is easy to state: Some entries of the matrix are unknown and we want to assign "appropriate values" to these entries. The need for solving such problems arises in several applications, ranging from traditional ields to modern ones. Typical examples of traditional ields are statistical analysis of incomplete survey data, business reports, operations management, psychometrika, meteorology and hydrology. Modern applications arise in machine learning, data mining, DNA microarrays data, chemometrics, computer vision, recommender systems and collaborative iltering. The problem is highly interesting and challenging. Many ingenious algorithms have been proposed, and there is vast literature on imputing techniques. Yet, most of the papers consider the imputing problem within the context of a speci ic application or a speci ic approach. The current survey provides a broad view of the problem, one that exposes the large variety of imputing methods. Old and new methods are examined with focus on the ideas behind the methods. It is illustrated how simple ideas evolve into highly sophisticated algorithms. The review enables us to identify a number of basic concepts and tools which are shared by several imputing methods. Equivalence theorems that we prove reveal surprising relations between apparently different methods.

Estimating Urban Road GPS Environment Friendliness with Bus Trajectories: A City-Scale Approach

“…To complete a matrix, compressive sensing is widely applied [39]. Given a sparse matrix for which most of its items are missing, compressive-based matrix completion will estimate those missing items according to the specific cost function and optimization algorithm.…”

“…Note that the matrix Var was to be completed and could be very sparse. The basic objective function of matrix completion was set as [39]:…”

“…The general objective function of matrix completion can be solved iteratively, where each iteration consists of two steps [39]. First, for a given fixed L, update R element-wisely in the gradient descent direction of the objective function.…”

Identifying Phenogroups in Patients with Subclinical Diastolic Dysfunction Using Unsupervised Statistical Learning

“…Chronic kidney disease stage 1-5 and degree of diastolic dysfunction: mild, moderate or severe) then these were treated as dichotomous data (yes or no) and then converted into numerical data using one-hot encoding. Missing data points were estimated and imputed using a singular value decomposition (SVD) technique for data analysis (16). The squared Euclidean distances between each pair of patients were calculated and put into a distance matrix, which served as the input into the hierarchical clustering algorithm.…”

Identifying Phenogroups in Patients with Subclinical Diastolic Dysfunction Using Unsupervised Statistical Learning

“…Chronic kidney disease stage 1-5 and degree of diastolic dysfunction: mild, moderate or severe) then these were treated as dichotomous data (yes or no) and then converted into numerical data using one-hot encoding. Missing data points were estimated and imputed using a singular value decomposition (SVD) technique for data analysis (14). The squared Euclidean distances between each pair of patients were calculated and put into a distance matrix, which served as the input into the hierarchical clustering algorithm.…”