Data Clustering And Visualization Through Matrix Factorization

Clustering is traditionally an unsupervised task which is to find natural groupings or clusters in multidimensional data based on perceived similarities among the patterns. The purpose of clustering is to extract useful information from unlabeled data. In order to present the extracted useful knowledge obtained by clustering in a meaningful way, data visualization becomes a popular and growing area of research field. Visualization can provide a qualitative overview of large and complex data sets, which help us the desired insight in truly understanding the phenomena of interest in data. The contribution of this dissertation is two-fold: Semi-Supervised Non-negative Matrix Factorization (SS-NMF) for data clustering/co-clustering and Exemplar-based data Visualization (EV) through matrix factorization. Compared to traditional data mining models, matrix-based methods are fast, easy to understand and implement, especially suitable to solve large-scale challenging problems in text mining, image grouping, medical diagnosis, and bioinformatics. In this dissertation, we present two effective matrix-based solutions in the new directions of data clustering and visualization. First, in many practical learning domains, there is a large supply of unlabeled data but limited labeled data, and in most cases it might be expensive to generate large amounts of labeled data. Traditional clustering algorithms completely ignore these valuable labeled data and thus are inapplicable to these problems. Consequently, semi-supervised clustering, which can incorporate the domain knowledge to guide a clustering algorithm, has become a topic of significant recent interest. Thus, we develop a Non-negative Matrix Factorization (NMF) based framework to incorporate prior knowledge into data clustering. Moreover, with the fast growth of Internet and computational technologies in the past decade, many data mining applications have advanced swiftly from the simple clustering of one data type to the co-clustering of multiple data types, usually involving high heterogeneity. To this end, we extend SS-NMF to perform heterogeneous data co-clustering. From a theoretical perspective, SS-NMF for data clustering/co-clustering is mathematically rigorous. The convergence and correctness of our algorithms are proved. In addition, we discuss the relationship between SS-NMF with other well-known clustering and co-clustering models. Second, most of current clustering models only provide the centroids (e.g., mathematical means of the clusters) without inferring the representative exemplars from real data, thus they are unable to better summarize or visualize the raw data. A new method, Exemplar-based Visualization (EV), is proposed to cluster and visualize an extremely large-scale data. Capitalizing on recent advances in matrix approximation and factorization, EV provides a means to visualize large scale data with high accuracy (in retaining neighbor relations), high efficiency (in computation), and high flexibility (through the use of exemplars). Empirically, we demonstrate the superior performance of our matrix-based data clustering and visualization models through extensive experiments performed on the publicly available large scale data sets

No Pattern, No Recognition: a Survey about Reproducibility and Distortion Issues of Text Clustering and Topic Modeling

Extracting knowledge from unlabeled texts using machine learning algorithms can be complex. Document categorization and information retrieval are two applications that may benefit from unsupervised learning (e.g., text clustering and topic modeling), including exploratory data analysis. However, the unsupervised learning paradigm poses reproducibility issues. The initialization can lead to variability depending on the machine learning algorithm. Furthermore, the distortions can be misleading when regarding cluster geometry. Amongst the causes, the presence of outliers and anomalies can be a determining factor. Despite the relevance of initialization and outlier issues for text clustering and topic modeling, the authors did not find an in-depth analysis of them. This survey provides a systematic literature review (2011-2022) of these subareas and proposes a common terminology since similar procedures have different terms. The authors describe research opportunities, trends, and open issues. The appendices summarize the theoretical background of the text vectorization, the factorization, and the clustering algorithms that are directly or indirectly related to the reviewed works

Clustering and its Application in Requirements Engineering

Large scale software systems challenge almost every activity in the software development life-cycle, including tasks related to eliciting, analyzing, and specifying requirements. Fortunately many of these complexities can be addressed through clustering the requirements in order to create abstractions that are meaningful to human stakeholders. For example, the requirements elicitation process can be supported through dynamically clustering incoming stakeholders’ requests into themes. Cross-cutting concerns, which have a significant impact on the architectural design, can be identified through the use of fuzzy clustering techniques and metrics designed to detect when a theme cross-cuts the dominant decomposition of the system. Finally, traceability techniques, required in critical software projects by many regulatory bodies, can be automated and enhanced by the use of cluster-based information retrieval methods. Unfortunately, despite a significant body of work describing document clustering techniques, there is almost no prior work which directly addresses the challenges, constraints, and nuances of requirements clustering. As a result, the effectiveness of software engineering tools and processes that depend on requirements clustering is severely limited. This report directly addresses the problem of clustering requirements through surveying standard clustering techniques and discussing their application to the requirements clustering process

Semantic image retrieval using relevance feedback and transaction logs

Due to the recent improvements in digital photography and storage capacity, storing large amounts of images has been made possible, and efficient means to retrieve images matching a user’s query are needed. Content-based Image Retrieval (CBIR) systems automatically extract image contents based on image features, i.e. color, texture, and shape. Relevance feedback methods are applied to CBIR to integrate users’ perceptions and reduce the gap between high-level image semantics and low-level image features. The precision of a CBIR system in retrieving semantically rich (complex) images is improved in this dissertation work by making advancements in three areas of a CBIR system: input, process, and output. The input of the system includes a mechanism that provides the user with required tools to build and modify her query through feedbacks. Users behavioral in CBIR environments are studied, and a new feedback methodology is presented to efficiently capture users’ image perceptions. The process element includes image learning and retrieval algorithms. A Long-term image retrieval algorithm (LTL), which learns image semantics from prior search results available in the system’s transaction history, is developed using Factor Analysis. Another algorithm, a short-term learner (STL) that captures user’s image perceptions based on image features and user’s feedbacks in the on-going transaction, is developed based on Linear Discriminant Analysis. Then, a mechanism is introduced to integrate these two algorithms to one retrieval procedure. Finally, a retrieval strategy that includes learning and searching phases is defined for arranging images in the output of the system. The developed relevance feedback methodology proved to reduce the effect of human subjectivity in providing feedbacks for complex images. Retrieval algorithms were applied to images with different degrees of complexity. LTL is efficient in extracting the semantics of complex images that have a history in the system. STL is suitable for query and images that can be effectively represented by their image features. Therefore, the performance of the system in retrieving images with visual and conceptual complexities was improved when both algorithms were applied simultaneously. Finally, the strategy of retrieval phases demonstrated promising results when the query complexity increases

Advances in independent component analysis with applications to data mining

This thesis considers the problem of finding latent structure in high dimensional data. It is assumed that the observed data are generated by unknown latent variables and their interactions. The task is to find these latent variables and the way they interact, given the observed data only. It is assumed that the latent variables do not depend on each other but act independently. A popular method for solving the above problem is independent component analysis (ICA). It is a statistical method for expressing a set of multidimensional observations as a combination of unknown latent variables that are statistically independent of each other. Starting from ICA, several methods of estimating the latent structure in different problem settings are derived and presented in this thesis. An ICA algorithm for analyzing complex valued signals is given; a way of using ICA in the context of regression is discussed; and an ICA-type algorithm is used for analyzing the topics in dynamically changing text data. In addition to ICA-type methods, two algorithms are given for estimating the latent structure in binary valued data. Experimental results are given on all of the presented methods. Another, partially overlapping problem considered in this thesis is dimensionality reduction. Empirical validation is given on a computationally simple method called random projection: it does not introduce severe distortions in the data. It is also proposed that random projection could be used as a preprocessing method prior to ICA, and experimental results are shown to support this claim. This thesis also contains several literature surveys on various aspects of finding the latent structure in high dimensional data.reviewe

Clustering and Latent Semantic Indexing Aspects of the Nonnegative Matrix Factorization

This paper provides a theoretical support for clustering aspect of the nonnegative matrix factorization (NMF). By utilizing the Karush-Kuhn-Tucker optimality conditions, we show that NMF objective is equivalent to graph clustering objective, so clustering aspect of the NMF has a solid justification. Different from previous approaches which usually discard the nonnegativity constraints, our approach guarantees the stationary point being used in deriving the equivalence is located on the feasible region in the nonnegative orthant. Additionally, since clustering capability of a matrix decomposition technique can sometimes imply its latent semantic indexing (LSI) aspect, we will also evaluate LSI aspect of the NMF by showing its capability in solving the synonymy and polysemy problems in synthetic datasets. And more extensive evaluation will be conducted by comparing LSI performances of the NMF and the singular value decomposition (SVD), the standard LSI method, using some standard datasets.Comment: 28 pages, 5 figure