Design And Development Of Efficient Algorithms For Subspace Clustering And Allied Applications

Abstract

There has been a tremendous volume of high dimensional data generated from newlinedifferent sources all around the world in recent decades. This high dimensional data newlinehas actually been originated from a wide variety sources such as images or videos newlinefrom millions of cameras, surveillance systems, satellites and other infotainment newlinemedias. However, this huge volume of data originated from the aforementioned newlinesources are mostly unstructured in nature. When the number of dimensions increases, newlineso does the number of features, resulting in massive sparsity associated with the newlinehigh dimensional features. Hence, to extract meaningful information, proper data newlinemanagement strategies are required. Unsupervised techniques can uncover the hidden newlinestructures in a data and group the data without any prior training. Clustering is a well newlineknown unsupervised data analysis technique in which the datapoints are categorized newlineon the basis of their inherent similarity. However, the increase in dimensionality of newlinethe data often affects the performance of the clustering algorithms. It is also realized newlinethat, in a high-dimensional space, the distance measures utilized by traditional newlineclustering methods become less meaningful. Clustering algorithms that employ the newlinedimensionality reduction techniques can effectively handle the higher dimensionality newlineof the data. Those techniques aim at grouping the datapoints into respective clusters newlineusing a reduced number of features without much loss of information. newlineSubspace clustering is a popular dimensionality reduction technique which maps newlinethe datapoints from a large dimensional space into various low dimensional spaces newlineand cluster the datapoints based on their inherent similarity. The underlying idea newlineis the self-expressive representation of datapoints such that each datapoint that newlinebelongs to a subspace can be represented as the linear combination of other data newlinepoints in the same subspace.