Missing Entries Research Articles

Matrix completion with column outliers and sparse noise

Matrix completion from very limited information is an important machine learning topic, and has received extensive attention in various scientific applications. Matrix completion aims at finding a low-rank matrix to approximate the incomplete data matrix. However, noise in the data matrix may degrade the performance of the existing matrix completion algorithms, especially if there are different types of noise. In this paper, we proposed a robust matrix completion method with column outliers and sparse noise. The incomplete matrix is iteratively divided into low-rank and sparse parts. The ℓ2,1-norm based objective function makes the recovered matrix keeps a low-rank structure and lets the algorithm robust to column outliers, while the regularization term based on ℓ1-norm can alleviate the influence of sparse noise. Besides, a vector completion algorithm has been proposed to help us estimate the missing entries of the out-of-sample vectors. Moreover, the proposed model can be optimized by an efficient iterative re-weighted method, without introducing any additional parameters, while the adaptive weights obtained in the optimization process can help us detect column outliers. Both theoretical analysis and experiments based on synthetic datasets and real world datasets are implemented to validate the performance of the proposed method.

The Parameterized Complexity of Clustering Incomplete Data

We study fundamental clustering problems for incomplete data. Specifically, given a set of incomplete d-dimensional vectors (representing rows of a matrix), the goal is to complete the missing vector entries in a way that admits a partitioning of the vectors into at most k clusters with radius or diameter at most r. We give tight characterizations of the parameterized complexity of these problems with respect to the parameters k, r, and the minimum number of rows and columns needed to cover all the missing entries. We show that the considered problems are fixed-parameter tractable when parameterized by the three parameters combined, and that dropping any of the three parameters results in parameterized intractability. A byproduct of our results is that, for the complete data setting, all problems under consideration are fixed-parameter tractable parameterized by k+r.

Joint Modeling for Longitudinal Data with Missing Values: A Bayesian Perspective on Human Intelligence

Joint modeling in longitudinal data is an interesting area of research since it predicts the outcome with covariates that are measured repeatedly over the time. However, there is no proper methodology available in literature to incorporate the joint modeling approach for count-count response data. In addition, there are several situations where longitudinal data might not be possible to collect the complete data and the Missingness may occur due to the absence of the subjects at the follow-up. In this paper, joint modelling for longitudinal count data is adopted using Bayesian Generalized Linear Mixed Model framework to understand the association between the variables. Further, an imputation method is used to handle the missing entries in the data and the efficiency of the methodology has been studied using Markov Chain Monte-Carlo (MCMC) technique. An application to the proposed methodology has been discussed and identified the suitable nutritional supplements in Bayesian perspective without eliminating the missing entries in the dataset.

Tensor Data Imputation by PARAFAC with Updated Chaotic Biases by Adam Optimizer

The big data pattern analysis suffers from incorrect responses due to missing data entries in the real world. Data collected for digital movie platforms like Netflix and intelligent transportation systems is Spatio-temporal data. Extracting the latent and explicit features from this data is a challenge. We present the high dimensional data imputation problem as a higher-order tensor decomposition. The regularized and biased PARAFAC decomposition is proposed to generate the missing data entries. The biases are created and updated by a chaotic exponential factor in Adam’s optimization, which reduces the imputation error. This chaotic perturbed exponentially update in the learning rate replaces the fixed learning rate in the bias update by Adam optimization. The idea has experimented with Netflix and traffic datasets from Guangzhou, China.

DOA estimation via shift-invariant matrix completion

This paper presents a method to estimate the direction of arrival (DOA) of multiple sources received by a uniform linear array (ULA) with a reduced number of radio-frequency (RF) chains. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low-rank structure of the signal subspace, but also the shift-invariance property of ULAs, which results in a better estimation of the signal subspace. Further, the effect of MC on DOA estimation is discussed under the perturbation theory framework. The simulation results suggest that the proposed method provides accurate DOA estimates even in the small-sample regime with a significant reduction in the number of RF chains required for a given spatial resolution.

An adaptation for iterative structured matrix completion

<p style='text-indent:20px;'>The task of predicting missing entries of a matrix, from a subset of known entries, is known as <i>matrix completion</i>. In today's data-driven world, data completion is essential whether it is the main goal or a pre-processing step. Structured matrix completion includes any setting in which data is not missing uniformly at random. In recent work, a modification to the standard nuclear norm minimization (NNM) for matrix completion has been developed to take into account <i>sparsity-based</i> structure in the missing entries. This notion of structure is motivated in many settings including recommender systems, where the probability that an entry is observed depends on the value of the entry. We propose adjusting an Iteratively Reweighted Least Squares (IRLS) algorithm for low-rank matrix completion to take into account sparsity-based structure in the missing entries. We also present an iterative gradient-projection-based implementation of the algorithm that can handle large-scale matrices. Finally, we present a robust array of numerical experiments on matrices of varying sizes, ranks, and level of structure. We show that our proposed method is comparable with the adjusted NNM on small-sized matrices, and often outperforms the IRLS algorithm in structured settings on matrices up to size <inline-formula><tex-math id="M1">\begin{document}$ 1000 \times 1000 $\end{document}</tex-math></inline-formula>.</p>

Regularized Sparse Modelling for Microarray Missing Value Estimation

The existence of missing values in microarray data inevitably hinders downstream biological analyses that expect complete data as input, therefore how to effectively explore the underlying structure of data to accurately estimate missing entries remains crucial and meaningful. In this study, we formalize the problem under a regularized sparse framework and accordingly propose local learning-based imputation models to capture the relationships that are hidden in gene expression profiles towards better imputation. Specifically, in view of the simultaneous variable selection and grouping effect of the elastic net penalty, we present an elastic net regularized local least squares-based imputation method to estimate the missing entries of a target gene with its neighbors. Besides, we investigate different similarity filtering metrics to select neighbor genes and develop another four imputation methods under the framework. Furthermore, the proposed methods process the target genes in ascending order of their associated missing rates. Finally, extensive comparative experiments against other eight commonly-used methods are conducted on multiple microarray datasets having varying missing rates. Results indicate the power of sparse regularization techniques and the superiority of elastic net over its competitors in terms of statistical analysis metrics.

Hybrid Matrix Completion Model for Improved Images Recovery and Recommendation Systems

Matrix completion methods have been widely applied in images recovery and recommendation systems. Most of them are only based on the low-rank characteristics of matrices to predict the missing entries. However, these methods lack consideration of local information. To further improve the performance of matrix completion. In this paper, we propose a novel model based on matrix decompositions and matrix local information. Specifically, we update a number of rank-one matrices, which circumvented the rank estimation in matrix decomposition. And a penalty function is designed to punish singular values without introducing additional parameters. The local information component extracts similar information by an adaptive filter via convolution operation which kernel is obtained by the minimum variance. Finally, we integrate matrix decomposition and local information components via different weights. We apply the proposed method to real-world image datasets and recommendation system datasets. The experimental results demonstrate the proposed model has a lower error and better robustness than several competing matrix completion methods.

Bayesian Low Rank Tensor Ring for Image Recovery.

Low rank tensor ring based data recovery can recover missing image entries in signal acquisition and transformation. The recently proposed tensor ring (TR) based completion algorithms generally solve the low rank optimization problem by alternating least squares method with predefined ranks, which may easily lead to overfitting when the unknown ranks are set too large and only a few measurements are available. In this article, we present a Bayesian low rank tensor ring completion method for image recovery by automatically learning the low-rank structure of data. A multiplicative interaction model is developed for low rank tensor ring approximation, where sparsity-inducing hierarchical prior is placed over horizontal and frontal slices of core factors. Compared with most of the existing methods, the proposed one is free of parameter-tuning, and the TR ranks can be obtained by Bayesian inference. Numerical experiments, including synthetic data, real-world color images and YaleFace dataset, show that the proposed method outperforms state-of-the-art ones, especially in terms of recovery accuracy.

Hierarchical Factorization Strategy for High-Order Tensor and Application to Data Completion

Low-rank tensor completion (LRTC) aims to impute the missing entries from partially observed tensor data, among which low-rankness is of vital importance to get satisfactory results. In this letter, we propose a hierarchical low-rank factorization framework for high-order tensors. For the first layer, the low TR rank is exploited, and for the second layer the low-rankness of each TR core is further considered. With the hierarchical model, the low-rankness of the original tensor can be fully utilized and thus achieving better completion performance. Experimental results on synthetic data and on inpainting tasks using various datasets demonstrate the superior performance and efficiency of our proposed method as compared to the state-of-the-art algorithms.

Photovoltaic power generation data filling model based on tensor decomposition

With the development of new energy and the increase in demand, photovoltaic power generation has received more and more attention. However, due to the susceptibility of photovoltaic power generation to the influence of weather factors, especially the influence of solar irradiation, it is intermittent and fluctuating. Understanding the power generation data of a PV plant has a great effect on the subsequent photovoltaic power generation planning and photovoltaic power plant situation assessment. However, these data are often incompletely recorded due to frequent communication problems or equipment failures. Most current studies focus on photovoltaic power generation predictions, it is still a challenge to speculate the missing data around photovoltaic power plants. In this paper, a context-sensitive tensor decomposition model is proposed to intelligently fill the missing power generation entries. The experimental results show that our model can effectively fill missing data and obtain good results.

Structured Alternating Minimization for Union of Nested Low-Rank Subspaces Data Completion

In this article, we consider a particular data structure consisting of a union of several nested low-rank subspaces with missing data entries. Given the rank of each subspace, we treat the data completion problem, i.e., to estimate the missing entries. Starting from the case of two-dimensional data, i.e., matrices, we show that the union of nested subspaces data structure leads to a structured decomposition U = XY where the factor Y has blocks of zeros that are determined by the rank values. Moreover, for high-dimensional data, i.e., tensors, we show that a similar structured CP decomposition also exists, U = Σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l=1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> ⊗ a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> ⊗ ··· ⊗ a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</sup> , where A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> = [a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> ···a <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sup> ] contains blocks of zeros determined by the rank values. Based on such structured decompositions, we develop efficient alternating minimization algorithms for both matrix and tensor completions, by enforcing the above structures in each iteration including the initialization. Compared with naive approaches where either the additional rank constraints are ignored, or data completion is performed part by part, the proposed structured alternating minimization approaches exhibit faster convergence and higher recovery accuracy.

Robust Estimation of Breast Cancer Incidence Risk in Presence of Incomplete or Inaccurate Information.

Purpose:To evaluate the robustness of multiple machine learning classifiers for breast cancer risk estimation in the presence of incomplete or inaccurate information. Data and methods:Open data for this study was obtained from the BCSC Data Resource (http://breastscreening.cancer.gov/). We conducted two ablation-type experiments to compare the robustness of different classifiers where we randomly switched known information to missing with a missing probability of pm in one experiment, and randomly corrupted the existing information with a probability of pc in another experiment. We considered three prominent machine-learning classifiers such as Logistic regression (LR), Random Forests (RF) and a custom Neural Network (NN) architecture and compared their degradation of discrimination performance as a function of increasing probability of missing or inaccurate data. Results:LR, RF and custom NN resulted in an Area Under Curve (AUC) of 0.645, 0.643 and 0.649, respectively, on a test set with 500,000 total observations. When we manipulated the data by varying probabilities pm and pc from 0 to 1, NN resulted in better performance in terms of AUC compared to RF and LR as long as less than half the data was missing/inaccurate (that is, for values of pm < 0.5 and pc < 0.5). However, for missing (pm) or corruption (pc) probabilities above 0.5, LR gave similar performance as the custom NN. RF resulted in overall poorer performance when the data had additional missing or incorrect entries. Conclusion:In cases where the input information is missing or inaccurate, our experiments show that the proposed custom NN provides reliable risk estimates in medical datasets like BCSC. These results are particularly important in health care applications where not every attribute of the individual participant might be available.

Enhanced POCS reconstruction for partial Fourier imaging in multi-echo and time-series acquisitions.

To improve partial Fourier (PF) imaging reconstruction in time-series or multi-echo acquisitions. Many PF methods use a phase estimate to restore Hermitian symmetry before filling missing k-space entries with measured data from the opposite half. This estimate is obtained from the symmetrically sampled, central part of k-space and its low-resolution results in artifacts near high-frequency phase effects (eg, tissue boundaries, vessels), limiting PF undersampling. Enhanced projection onto convex sets (POCS) uses full-resolution phase estimates and relies on alternating the half of k-space that is acquired in time series or multi-echo acquisitions. This enables full-resolution phase estimates to be calculated for each volume/echo, which are fed into the POCS framework. We apply enhanced POCS to high-resolution multi-echo FLASH and 3D-EPI functional MRI time-series data. Reconstruction errors and their bias dramatically reduce compared with existing methods, without leading to temporal blurring in time-series acquisitions. This allows for higher PF acceleration factors at virtually no cost. Enhanced POCS results in superior PF reconstructions. Furthermore, as the resolution of the phase estimate used for symmetry correction no longer depends on the PF factor, enhanced POCS is more robust against larger PF omission.

A dynamic reaction picklist for improving allergy reaction documentation in the electronic health record.

Incomplete and static reaction picklists in the allergy module led to free-text and missing entries that inhibit the clinical decision support intended to prevent adverse drug reactions. We developed a novel, data-driven, "dynamic" reaction picklist to improve allergy documentation in the electronic health record (EHR). We split 3 decades of allergy entries in the EHR of a large Massachusetts healthcare system into development and validation datasets. We consolidated duplicate allergens and those with the same ingredients or allergen groups. We created a reaction value set via expert review of a previously developed value set and then applied natural language processing to reconcile reactions from structured and free-text entries. Three association rule-mining measures were used to develop a comprehensive reaction picklist dynamically ranked by allergen. The dynamic picklist was assessed using recall at top k suggested reactions, comparing performance to the static picklist. The modified reaction value set contained 490 reaction concepts. Among 4234327 allergy entries collected, 7463 unique consolidated allergens and 469 unique reactions were identified. Of the 3 dynamic reaction picklists developed, the 1 with the optimal ranking achieved recalls of 0.632, 0.763, and 0.822 at the top 5, 10, and 15, respectively, significantly outperforming the static reaction picklist ranked by reaction frequency. The dynamic reaction picklist developed using EHR data and a statistical measure was superior to the static picklist and suggested proper reactions for allergy documentation. Further studies might evaluate the usability and impact on allergy documentation in the EHR.

Improving Lives of Indebted Farmers Using Deep Learning: Predicting Agricultural Produce Prices Using Convolutional Neural Networks

Farmer suicides have become an urgent social problem which governments around the world are trying hard to solve. Most farmers are driven to suicide due to an inability to sell their produce at desired profit levels, which is caused by the widespread uncertainty/fluctuation in produce prices resulting from varying market conditions. To prevent farmer suicides, this paper takes the first step towards resolving the issue of produce price uncertainty by presenting PECAD, a deep learning algorithm for accurate prediction of future produce prices based on past pricing and volume patterns. While previous work presents machine learning algorithms for prediction of produce prices, they suffer from two limitations: (i) they do not explicitly consider the spatio-temporal dependence of future prices on past data; and as a result, (ii) they rely on classical ML prediction models which often perform poorly when applied to spatio-temporal datasets. PECAD addresses these limitations via three major contributions: (i) we gather real-world daily price and (produced) volume data of different crops over a period of 11 years from an official Indian government administered website; (ii) we pre-process this raw dataset via state-of-the-art imputation techniques to account for missing data entries; and (iii) PECAD proposes a novel wide and deep neural network architecture which consists of two separate convolutional neural network models (trained for pricing and volume data respectively). Our simulation results show that PECAD outperforms existing state-of-the-art baseline methods by achieving significantly lesser root mean squared error (RMSE) - PECAD achieves ∼25% lesser coefficient of variance than state-of-the-art baselines. Our work is done in collaboration with a non-profit agency that works on preventing farmer suicides in the Indian state of Jharkhand, and PECAD is currently being reviewed by them for potential deployment.

Polynomial Matrix Completion for Missing Data Imputation and Transductive Learning

This paper develops new methods to recover the missing entries of a high-rank or even full-rank matrix when the intrinsic dimension of the data is low compared to the ambient dimension. Specifically, we assume that the columns of a matrix are generated by polynomials acting on a low-dimensional intrinsic variable, and wish to recover the missing entries under this assumption. We show that we can identify the complete matrix of minimum intrinsic dimension by minimizing the rank of the matrix in a high dimensional feature space. We develop a new formulation of the resulting problem using the kernel trick together with a new relaxation of the rank objective, and propose an efficient optimization method. We also show how to use our methods to complete data drawn from multiple nonlinear manifolds. Comparative studies on synthetic data, subspace clustering with missing data, motion capture data recovery, and transductive learning verify the superiority of our methods over the state-of-the-art.

A machine learning-based predictive model for progression of knee osteoarthritis from clinical data

Purpose: Knee Osteoarthritis (KOA) is a multi-factorial disease. It poses challenges to precisely predict the progression of KOA, which is required for personalized medicine to prevent the deterioration of joint destruction. There are three KOA progression definitions: WOMAC progression refers to a persistent increase of at least nine points under a normalised scale from 0-100 of McMaster Universities Osteoarthritis Index (WOMAC); KL progression is any increase in KL grade (KLG), except for the increase from KLG 0 to KLG 1; Joint Space Width progression (JSW) progression, which is the loss in the medial knee joint space width of at least 0.7mm. In this study, the rate of KOA progression is further classified as rapid and chronic progression (aggravation of KOA conditions within 48 months and between 48 and 96 months respectively). This study aims to develop a patient-specific predictive model for the progression of KOA via a machine learning approach using the database of FNIH OA biomarker consortium. Methods: In feature selection, as shown in Figure 1, 36 features were selected from the dataset, which could enhance the prediction result of the supervised machine learning model. In order to maintain an adequate sample size for training the model, the Multivariate Imputation by Chained Equation (MICE) was employed to gave the approximation to the missing entries to complete the dataset. It was found that for all the progression types, the Non-progressor Class outnumbered its counterpart in all the instances, resulting in class imbalance. (see Table 1) We developed the ‘Random Feature Generator’, which generated combinations from the feature pool. The outputs were fed into a Logistic Regression model using the 48 and 96-month datasets, cross-validated with 5-fold, finally calculated the average accuracy. Downsampling was used to lower the computational cost. To investigate the performance trend over time, the data points from the 72-month dataset were recruited and compared with 48 and 96-month datasets using paired T-test for all three KOA progression types. In order to examine feature specificity, we extracted the top 50 best performing feature combinations from 48 and 96-month datasets for further analysis. A chart of occurrence frequency of each feature from the 50 selected combinations was plotted. It was hypothesised that the more frequent the feature appears, the more the importance it holds towards KOA progression. Results: From Table 2a and 2b, it was found that the top-performing combinations were from KL progression in both datasets. Moreover, it was observed that both models with feature selection outperformed those without in terms of accuracy using Logistic Regression. Table 3 showed the performance of the original Logistic Regression model could be boost by Multi-layer Perceptron in all metrics. In Figure 2, all the progression types demonstrated a significant increasing accuracy as time proceeds, with KL progression outperforms other progression types in all instances. It could be inferred that the more frequently a feature appears in the top-performing combinations, the more important it is to the prediction of KOA progression. As from Figure 3, it could be observed that the feature frequency distributions for 48 and 96-month datasets were different. However, the most frequently appeared features all fell into the categories of either generic or radiographic information of the subject. It could also be observed features of metabolic syndrome exerted a greater degree of impact to KOA progression in the short term (48 months) than long term (96 months). In short, the above frequency plot could reflect the extent of influence towards KOA progression from different features. Conclusions: In this study, we achieved a top model prediction accuracy for rapid and chronic KOA progression of 0.7059 and 0.7272 respectively. It was also found that the prediction accuracy increases as time progresses for all progression types. This may because due to the characteristic of KOA is a degenerative disease, such that signs and symptoms manifest over time. Furthermore, the model predictive capability was discovered to be specific to each time point, meaning features poses varying influence in model predictive prowess chronologically. As the top five most important and highly correlated features for rapid KOA progression predication were: joint space width, OARSI joint space narrowing grade in the medial compartment, sex, race, and medial meniscus extrusion. As for the chronic KOA progression prediction, sex, KL-grade, weight, habit of smoking, and OARSI joint space narrowing grade in lateral compartment were of most importance. Notably, the above features were all from either generic or radiographic information of the subject. In conclusion, the findings in this study may give insights to the treatment protocol for short, mid and long term disease management.

Matrix Completion via Sparse Factorization Solved by Accelerated Proximal Alternating Linearized Minimization

Classical matrix completion methods are not effective in recovering missing entries of data drawn from multiple subspaces because the matrices are often of high-rank. Recently a few advanced matrix completion methods were proposed to solve the problem but they are not scalable to large matrices and big data problems. This paper proposes a sparse factorization method for matrix completion on multiple-subspace data. The method factorizes the given incomplete matrix into a dense matrix and a sparse matrix, while the factorization errors of the observed entries are minimized. To solve the optimization problem, an accelerated proximal alternating linearized minimization (APALM) algorithm is proposed. As a non-trivial task owing to the alternation, linearization, nonconvexity, and extrapolation, the convergence of APALM is proved. APALM can solve a large class of optimization problems such as matrix factorization with nonsmooth regularizations. In addition, we show that, to recover an $m\times n$ m × n matrix consisting of data drawn from $k$ k subspaces of dimension $r_0$ r 0 , the number of observed entries required in our matrix completion method is $O(nr_0\,\log k\,\log n)$ O ( n r 0 log k log n ) while that in conventional methods is $O(nr_0k\,\log n)$ O ( n r 0 k log n ) , which theoretically proves the superiority of our method on multiple-subspace data and high-rank matrices. The proposed matrix completion method is compared with state-of-the-art on synthetic data and real collaborative filtering problems. The experimental results corroborate that the proposed method can handle large matrices efficiently and provide high recovery accuracy.

Three-way formal concept clustering technique for matrix completion in recommender system

PurposeIn today’s world, the recommender systems are very valuable systems for the online users, as the World Wide Web is loaded with plenty of available information causing the online users to spend more time and money. The recommender systems suggest some possible and relevant recommendation to the online users by applying the recommendation filtering techniques to the available source of information. The recommendation filtering techniques take the input data denoted as the matrix representation which is generally very sparse and high dimensional data in nature. Hence, the sparse data matrix is completed by filling the unknown or missing entries by using many matrix completion techniques. One of the most popular techniques used is the matrix factorization (MF) which aims to decompose the sparse data matrix into two new and small dimensional data matrix and whose dot product completes the matrix by filling the logical values. However, the MF technique failed to retain the loss of original information when it tried to decompose the matrix, and the error rate is relatively high which clearly shows the loss of such valuable information.Design/methodology/approachTo alleviate the problem of data loss and data sparsity, the new algorithm from formal concept analysis (FCA), a mathematical model, is proposed for matrix completion which aims at filling the unknown or missing entries without loss of valuable information to a greater extent. The proposed matrix completion algorithm uses the clustering technique where the users who have commonly rated the items and have not commonly rated the items are captured into two classes. The matrix completion algorithm fills the mean cluster value of the unknown entries which well completes the matrix without actually decomposing the matrix.FindingsThe experiment was conducted on the available public data set, MovieLens, whose result shows the prediction error rate is minimal, and the comparison with the existing algorithms is also studied. Thus, the application of FCA in recommender systems proves minimum or no data loss and improvement in the prediction accuracy of rating score.Social implicationsThe proposed matrix completion algorithm using FCA performs good recommendation which will be more useful for today’s online users in making decision with regard to the online purchasing of products.Originality/valueThis paper presents the new technique of matrix completion adopting the vital properties from FCA which is applied in the recommender systems. Hence, the proposed algorithm performs well when compared to other existing algorithms in terms of prediction accuracy.