# UFODMV: Unsupervised Feature Selection for Online Dynamic Multi-Views
## 1 Introduction  
Data that arrive from heterogeneous views (i.e., multiple heterogeneous sources of data) are more likely to provide complementary information for machine learning (ML) models than does a single view [1]. Each instance in multi-view data has different groups of features, meaning that different views have different representations of the same set of instances, and each view comprises a group of features. For example, in medical applications, it is better to look at patients' healthcare conditions (i.e., instances) from different groups (i.e., views) of laboratory tests (i.e., features) for a more precise medical diagnosis. However, as not all features in different views are representative, this exacerbates the problem of high dimensionality. Indeed, the non-representative features not only increase the time complexity of the ML algorithms; they also decrease the accuracy of the classification [2]. Additionally, these non-representative features also waste storage space [3]. _Feature selection_ (FS) is an efficient method that can reduce the dimensionality ofthe original feature set. This is achieved through the selection of a reduced set of features from the original feature space that can represent the entire feature set.  
Traditional unsupervised feature selection methods [4; 5; 6; 7] assume that data are independent and identically distributed (iid). However, this assumption does not apply when there are heterogeneous families/views of features, as multi-view data has a dependency/correlation between the views due to the representation of the same instance. Additionally, these traditional methods are unable to exploit the correlation between views that are concatenated, as data could lose their meaning if concatenated. For these two reasons, they are inappropriate for multi-view learning [8]. There are three main approaches for the feature clustering of multi-view data: _concatenation_, _distribution_, and _centralisation_[9]. With the concatenation method suggested in [4; 5; 6; 7; 10; 11], all the data views are combined into a single matrix, ignoring the heterogeneous nature of the multi-view data. However, data lose their actual meaning if combined, resulting in poor feature selection. With the distribution method, features are selected from each view independently [12; 13]. However, this method focuses on local feature selection at each view and it does not correlate the features of all the views, thereby possibly resulting in redundant features. Finally, the centralisation method [14] simultaneously considers the correlation of the features of all the views, which produces a better selection of representative features.  
Few unsupervised feature selection methods are available for multi-view learning [8; 15; 16; 17; 18]. However, all the existing methods assume that the number of the views is static, meaning that they are complete and pre-existing and no new additional views can be added. However, this assumption is not appropriate for real applications where new views and features can be added at any given time. Additionally, the number of instances can increase. To the best of our knowledge, this is still an open problem that has not been properly addressed, which motivated us to investigate this problem further and contribute to the development of innovative methods. This paper proposes a method that overcomes the limitations of existing unsupervised feature selection methods for multi-view applications for dynamic multi-view applications in an online environment so that the number of both instances and views can increase overtime and be incrementally clustered.