Isomap is a classic and representative manifold learning algorithm for nonlinear dimensionality reduction, which aims to circumvent the problem of “the curse of dimensionality” and attempts to recover the intrinsic structure hidden in high-dimensional data based on the assumption that data lie in or near a single manifold. However, Isomap fails to work when data set consists of multi-clusters o...

Topic-focused multi-document summarization aims to produce a summary biased to a given topic or user profile. This paper presents a novel extractive approach based on manifold-ranking of sentences to this summarization task. The manifold-ranking process can naturally make full use of both the relationships among all the sentences in the documents and the relationships between the given topic an...

Many real-world applications are characterized by multiple conflicting objectives. In such problems optimality is replaced by Pareto optimality and the goal is to find the Pareto frontier, a set of solutions representing different compromises among the objectives. Despite recent advances in multi-objective optimization, achieving an accurate representation of the Pareto frontier is still an imp...

We propose a generative model for high dimensional data consisting of intrinsically low dimensional clusters that are noisily sampled. The proposed model is a mixture of probabilistic principal surfaces (MiPPS) optimized using expectation maximization. We use a Bayesian prior on the model parameters to maximize the corresponding marginal likelihood. We also show empirically that this optimizati...

Manifold learning [2, 5, 28, 32, 36, 12] has become a popular topic in machine learning and computer vision in the last few years, as many objects of interests (like natural images, or sequences representing walking persons), in spite of their apparent high dimensionality, live in a non-linear space of usually limited dimension. Many unsupervised algorithms (e.g. locally linear embedding [27]) ...

Many observable data sets such as images, videos and speech can be modeled by a mixture of manifolds which are the result of multiple factors (latent variables). In this paper, we propose a novel algorithm to learn multiple linear manifolds for face recognition, called Group Sparse Non-negative Matrix Factorization (GSNMF). Via the group sparsity constraint imposed on the column vectors of the ...

The binary bracket of a Courant algebroid structure on (E,〈⋅,⋅〉) can be extended to n-ary Γ(E), yielding multi-Courant algebroid. These brackets form Poisson algebra and were defined, in an algebraic setting, by Keller Waldmann. We construct higher geometric version Keller-Waldmann define algebroids. As structures seen as degree 3 functions graded symplectic manifold 2, n≥3 that manifold.

Multi-scale gist (MS-gist) feature manifold for building recognition is presented in the paper. It is described as a two-stage model. In the first stage, we extract the multi-scale gist features that represent the structural information of the building images. Since the MS-gist features are extrinsically high dimensional and intrinsically low dimensional, in the second stage, an enhanced fuzzy ...