See all by looking at a few: Sparse modeling for finding representative objects

Abstract

We consider the problem of finding a few representatives for a dataset, i.e., a subset of data points that efficiently describes the entire dataset. We assume that each data point can be expressed as a linear combination of the representatives and formulate the problem of finding the representatives as a sparse multiple measurement vector problem. In our formulation, both the dictionary and the measurements are given by the data matrix, and the unknown sparse codes select the representatives via convex optimization. In general, we do not assume that the data are lowrank or distributed around cluster centers. When the data do come from a collection of low-rank models, we show that our method automatically selects a few representatives from each low-rank model. We also analyze the geometry of the representatives and discuss their relationship to the vertices of the convex hull of the data. We show that our framework can be extended to detect and reject outliers in datasets, and to efficiently deal with new observations and large datasets. The proposed framework and theoretical foundations are illustrated with examples in video summarization and image classification using representatives.

Scalable gastroscopic video summarization via similar-inhibition dictionary selection

“…Liu et al [24] model the summarization procedure as a maximum a posterior problem by integrating both shot boundary detection and key frame selection. In [2], the key frames are selected via a novel dictionary selection model, and similar ideas are also applied in [25][26][27][28].…”

Learning Exemplar-Represented Manifolds in Latent Space for Classification

“…Specifically, for example, the negative sign of some atoms are hard to interpret, and the unit Euclidean length of the atoms means they just act as bases for reconstruction of data points but not for representing them. This intrinsic problem in dictionary learning has also been recognized in [7]. Therefore, the learned dictionary atoms cannot be considered as good representatives for the collection of data points when meeting various tasks such as classification.…”

“…On the other hand, since datasets usually contain a large number of data, dimensionality reduction in the object space is a desirable solution [7]. This can be achieved either by learning an adaptive dictionary [8,9] or finding exemplars [7].…”

“…Therefore, the learned dictionary atoms cannot be considered as good representatives for the collection of data points when meeting various tasks such as classification. In contrast, one can find a small subset of the data to appropriately represent the whole data collection owing to the self-expressiveness property, which has been studied for subspace clustering using sparse representation [13,7] and low-rank representation [14]. The selected exemplars can naturally represent the manifold structure of the dataset, and thus reduce the dimensionality in the object space.…”

“…This can be achieved either by learning an adaptive dictionary [8,9] or finding exemplars [7]. Learning a compact dictionary to represent data (see [10] and therein) and the problem of learning a supervised dictionary for classification have been well studied in literature [9,11].…”