High-dimensional Big Data processing with dictionary learning and diffusion maps
Published inJyväskylä studies in computing
Algorithms for modern Big Data analysis deal with both massive amount of sam- ples and a large number of features (high-dimension). One way to cope with these challenges is to assume and discover the existence of localization in the data by uncovering its intrinsic geometry. This approach suggests that different data segments can be analyzed separately and then uniﬁed in order to gain an understanding of the whole phenomenon. Methods that utilize efﬁciently local- ized data are attractive for high-dimensional big data analysis, because they can be parallelized, and thus the computational resources, which are needed for their utilization, are realistic and affordable. These methods can explore local proper- ties such as intrinsic dimension that vary among different pieces of data. This thesis presents two different methods to locally analyze large datasets for classiﬁcation, clustering and anomaly detection. The ﬁrst method localizes dictionary learning based on matrix factorization techniques. We utilize random- ized LU decomposition and QR-decomposition algorithms to build dictionaries that describe different types of data. Then, these dictionaries are used to assign new samples to their respective class. One application in cyber security deals with learning of computer ﬁles and detecting executable code hidden in PDF ﬁles. In a different application, a dictionary learned from a normally behaving computer network data is used to detect anomalies in test data which may imply a cyber threat. The second method is localized diffusion process (LDP), which constitutes a coarse-graining of the classic Diffusion Maps algorithm. In LDP, a Markov walk is calculated on small data point clouds instead of the original data points. This work establishes a theoretical foundation for the Localized Diffusion Folders for hierarchical data analysis. ...
PublisherUniversity of Jyväskylä
- Article I: Guy Wolf, Aviv Rotbart, Gil David, Amir Averbuch. Coarse-grained localized diffusion. Applied and Computational Harmonic Analysis(3):388-400, 2012. DOI: 10.1016/j.acha.2012.02.004
- Article II: Guy Wolf, Aviv Rotbart, Gil David, Amir Averbuch. Hierarchical data organization, clustering and denoising via Coarse-grained localized diffusion. CJR conference, Yale, 2012.
- Article III: Aviv Rotbart, Gil Shabat, Yaniv Shmueli, Amir Averbuch. Randomized LU decomposition: An algorithm for dictionaries construction. Submitted to IEEE transaction on Information Forensics and Security, 2014. arxiv.org
- Article IV: Amit Bermanis, Aviv Rotbart, Moshe Salhov, Amir Averbuch. Incomplete Pivoted QR-based Dimensionality Reduction. Submitted, 2015. Please see.
MetadataShow full item record
- Väitöskirjat