Robust Principal Component Analysis Via Instance Factorings For Multimedia Data Analysis

Advancement in technology has led to a wealth of very large and complex multimedia data rich in content,context and users.It has,therefore,become a valuable source of information and insights.Thus,algorithms are used to analyze this multimedia data to discover hidden patterns and knowledge.But the ever-increasing complexities and volumes of multimedia data make it very difficult for most existing algorithms to efficiently and effectively extract the most representative,robust and discriminative features for machine learning tasks.This dissertation,therefore,addresses these challenges by presenting three novel techniques for multimedia data analysis.These techniques are incomplete-data oriented dimension reduction via instance factoring PCA framework,robust deflated principal component analysis via multiple instance factorings for dimension reduction and deflated manifold embedding PCA framework via multiple instance factorings.The first approach extends the PCA idea of minimizing least squares reconstruction error by introducing a scaling-factor.This technique's advantage over the traditional PCA is that a penalty is imposed on the instance space via a scaling-factor to suppress the effect of outliers in pursuing projections.Two scaling-factor strategies,cosine similarity and total distance metrics,are used geometrically to learn the relationship between each instance and the principal projection in the feature space.Through this,better low-rank projections are obtained by scaling the data iteratively to suppress noise in the training set.Extensive experiments on multimedia data prove the superiority of the proposed framework over state-of-the-art dimensionality reduction methods.Additionally,a second approach,improving the first approach,applies a deflation technique for enhanced discrimination between authentic and corrupt instances.Unlike the first approach,which learns the relationship between instances and only the principal projection,this approach uses a deflation procedure to learn multiple relationships between instances and all projections.By applying deflation and using cosine similarity and total distance metrics,we iteratively learn the relationships between each instance and every pursued projection.Multiple scaling-factors are then obtained to discriminate between corrupt and authentic instances thoroughly.Experimental evaluations of the proposed approach show performance improvements over the first approach and other comparative methods.The final approach extends the second approach by unifying PCA with manifold embedding to preserve both global and local geometric structures of linear and nonlinear data in sub-manifolds.Contrary to the second approach,a single structurepreserving method,this approach is a hybrid structure-preserving algorithm.To preserve noise-free hybrid data structures effectively,we recursively distinguish between instances by learning their relationships with projections using cosine similarity and total distance strategies.Further,to avoid repeated relationship learning,we use deflation to iteratively remove each projection after learning its relationship with each instance.Thus,the deflation technique removes redundant information of previous projections while establishing a multi-relationship between each instance and every projection for sufficient discrimination.Experimental results show great improvements in the performance of the proposed methods over state-of-the-art techniques.