287 research outputs found

    Manifold Elastic Net: A Unified Framework for Sparse Dimension Reduction

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    It is difficult to find the optimal sparse solution of a manifold learning based dimensionality reduction algorithm. The lasso or the elastic net penalized manifold learning based dimensionality reduction is not directly a lasso penalized least square problem and thus the least angle regression (LARS) (Efron et al. \cite{LARS}), one of the most popular algorithms in sparse learning, cannot be applied. Therefore, most current approaches take indirect ways or have strict settings, which can be inconvenient for applications. In this paper, we proposed the manifold elastic net or MEN for short. MEN incorporates the merits of both the manifold learning based dimensionality reduction and the sparse learning based dimensionality reduction. By using a series of equivalent transformations, we show MEN is equivalent to the lasso penalized least square problem and thus LARS is adopted to obtain the optimal sparse solution of MEN. In particular, MEN has the following advantages for subsequent classification: 1) the local geometry of samples is well preserved for low dimensional data representation, 2) both the margin maximization and the classification error minimization are considered for sparse projection calculation, 3) the projection matrix of MEN improves the parsimony in computation, 4) the elastic net penalty reduces the over-fitting problem, and 5) the projection matrix of MEN can be interpreted psychologically and physiologically. Experimental evidence on face recognition over various popular datasets suggests that MEN is superior to top level dimensionality reduction algorithms.Comment: 33 pages, 12 figure

    Non-negative Matrix Factorization: A Survey

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    Learning Ideological Latent space in Twitter

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    People are shifting from traditional news sources to online news at an incredibly fast rate. However, the technology behind online news consumption forces users to be confined to content that confirms with their own point of view. This has led to social phenomena like polarization of point-of-view and intolerance towards opposing views. In this thesis we study information filter bubbles from a mathematical standpoint. We use data mining techniques to learn a liberal-conservative ideology space in Twitter and presents a case study on how such a latent space can be used to tackle the filter bubble problem on social networks. We model the problem of learning liberal-conservative ideology as a constrained optimization problem. Using matrix factorization we uncover an ideological latent space for content consumption and social interaction habits of users in Twitter. We validate our model on real world Twitter dataset on three controversial topics - "Obamacare", "gun control" and "abortion". Using the proposed technique we are able to separate users by their ideology with 95% purity. Our analysis shows that there is a very high correlation (0.8 - 0.9) between the estimated ideology using machine learning and true ideology collected from various sources. Finally, we re-examine the learnt latent space, and present a case study showcasing how this ideological latent space can be used to develop exploratory and interactive interfaces that can help in diffusing the information filter bubble. Our matrix factorization based model for learning ideology latent space, along with the case studies provide a theoretically solid as well as a practical and interesting point-of-view to online polarization. Further, it provides a strong foundation and suggests several avenues for future work in multiple emerging interdisciplinary research areas, for instance, humanly interpretable and explanatory machine learning, transparent recommendations and a new field that we coin as Next Generation Social Networks

    Ranking Preserving Nonnegative Matrix Factorization

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    Nonnegative matrix factorization (NMF), a wellknown technique to find parts-based representations of nonnegative data, has been widely studied. In reality, ordinal relations often exist among data, such as data i is more related to j than to q. Such relative order is naturally available, and more importantly, it truly reflects the latent data structure. Preserving the ordinal relations enables us to find structured representations of data that are faithful to the relative order, so that the learned representations become more discriminative. However, this cannot be achieved by current NMFs. In this paper, we make the first attempt towards incorporating the ordinal relations and propose a novel ranking preserving nonnegative matrix factorization (RPNMF) approach, which enforces the learned representations to be ranked according to the relations. We derive iterative updating rules to solve RPNMF’s objective function with convergence guaranteed. Experimental results with several datasets for clustering and classification have demonstrated that RPNMF achieves greater performance against the state-of-the-arts, not only in terms of accuracy, but also interpretation of orderly data structure
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