Abstract
In real-world applications of multiview clustering, some views may be incomplete due to noise, sensor failure, etc. Most existing studies in the field of incomplete multiview clustering have focused on early fusion strategies, for example, learning subspace from multiple views. However, these studies overlook the fact that clustering results with the visible instances in each view could be reliable under the random missing assumption; accordingly, it seems that learning a final clustering decision via late fusion of the clustering results from incomplete views would be more natural. To this end, we propose a late fusion method for incomplete multiview clustering. More specifically, the proposed method performs kernel k-means clustering on the visible instances in each view and then performs a late fusion of the clustering results from different views. In the late fusion step of the proposed method, we encode each view's clustering result as a zero-one matrix, of which each row serves as a compressed representation of the corresponding instance. We then design an alternate updating algorithm to learn a unified clustering decision that can best group the visible compressed representations in each view according to the k-means clustering objective. We compare the proposed method with several commonly used imputation methods and a representative early fusion method on six benchmark datasets. The superior clustering performance observed validates the effectiveness of the proposed method.
Highlights
In addition to simple filling methods, a few early fusion methods have been proposed for incomplete multiview clustering
We conclude this section by highlighting the main contributions of this work, as follows: (1) We propose a late fusion method for incomplete multiview clustering, while most previous studies have concentrated on early fusion methods
In a departure from conventional subspace methods, we develop a late fusion method for incomplete multiview clustering. is method performs kernel k-means clustering in each incomplete view and nds a consensus cluster according to each view’s clustering result. e rst step of the late fusion method, which is easy to understand, will be introduced only brie y
Summary
We introduce some preliminary knowledge to facilitate better understanding of our proposed method. Suppose the incomplete multiview data have N samples and P views. Suppose the instances in view j are row vectors with length dj, which means the instances in view j have dj features. Us, the instances in view j form a N × dj matrix, which is denoted as Xj. we use Xij to denote the instance for sample i in view j. An N × P zero-one matrix S stores the view missing information, where Sij 1 indicates that view j for sample i is available; otherwise, the view is missing. If the instance of sample i is missing in view j, the ith row of Zj is all zero; otherwise, if sample i belongs to cluster c in view j, we have Zjic 1 and Zjik 0, k ≠ c. We use a zero-one N × K matrix Y to store the clustering decision. Sum-of-squares loss is minimized taondacZhie∈v{e0t,h1i}sNg×oKali.sAtshseumunekthnaotwnxicNil u1st∈erXinisdtichaetsoarmmpaletrsiext, where Zic 1 means that sample i belongs to cluster c. μc is the centroid of cluster c. e objective function of k-means is
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