We decompose a standard embedding space into interpretable orthogonal subspaces and a “remainder” subspace. We consider four interpretable subspaces in this paper: polarity, concreteness, frequency and part-of-speech (POS) subspaces. We introduce a new calculus for subspaces that supports operations like “−1 × hate = love” and “give me a neutral word for greasy” (i.e., oleaginous). This calculu...

High-dimensional data pose challenges to traditional clustering algorithms due to their inherent sparsity and data tend to cluster in different and possibly overlapping subspaces of the entire feature space. Finding such subspaces is called subspace mining. We present SCHISM, a new algorithm for mining interesting subspaces, using the notions of support and Chernoff-Hoeffding bounds. We use a v...

In this paper, using the theory of Hilbert modules we study invariant subspaces of the Bergman spaces on bounded symmetric domains and quasi-invariant sub-spaces of the Segal–Bargmann spaces. We completely characterize small Hankel operators with finite rank on these spaces.

In this paper we show some very interesting properties of weak Chebyshev subspaces and use them to simplify Pinkus's characterization of Asubspaces of C[a, b]. As a consequence we obtain that if the metric projection PG from C[a, b] onto a finite-dimensional subspace G has a continuous selection and elements of G have no common zeros on (a, b), then G is an /4-subspace.

Orthogonal subspaces are effective models to represent object image sets (generally any high-dimensional vector sets). Canonical correlation analysis of the orthogonal subspaces provides a good solution to discriminate objects with sets of images. In such a recognition task involving image sets, an efficient learning over a large volume of image sets, which may be increasing over time, is impor...

In applications ranging from communications to genetics, signals can be modeled as lying in a union of subspaces. Under this model, signal coe cients that lie in certain subspaces are active or inactive together. The potential subspaces are known in advance, but the particular set of subspaces that are active (i.e., in the signal support) must be learned from measurements. We show that exploiti...

One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the definition of a frame of subspaces. We introduce this new notion and prove that it provides us with the link we need. It will also turn out that frames of s...

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has been extensively studied in the literature to partition such highdimensional data into clusters corresponding to their underlying low-dimensional subspaces....

Detecting outliers from high-dimensional data is a challenge task since outliers mainly reside in various lowdimensional subspaces of the data. To tackle this challenge, subspace analysis based outlier detection approach has been proposed recently. Detecting outlying subspaces in which a given data point is an outlier facilitates a better characterization process for detecting outliers for high...

Given a set of vectors (the data) in a Hilbert space H, we prove the existence of an optimal collection of subspaces minimizing the sum of the square of the distances between each vector and its closest subspace in the collection. This collection of subspaces gives the best sparse representation for the given data, in a sense defined in the paper, and provides an optimal model for sampling in u...