Coresets-Methods and History: A Theoreticians Design Pattern for Approximation and Streaming Algorithms

We present a technical survey on the state of the art approaches in data reduction and the coreset framework. These include geometric decompositions, gradient methods, random sampling, sketching and random projections. We further outline their importance for the design of streaming algorithms and give a brief overview on lower bounding techniques

Sketching for Large-Scale Learning of Mixture Models

Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch is a collection of generalized moments of the underlying probability distribution of the data. It can be computed in a single pass on the training set, and is easily computable on streams or distributed datasets. The proposed framework shares similarities with compressive sensing, which aims at drastically reducing the dimension of high-dimensional signals while preserving the ability to reconstruct them. To perform the estimation task, we derive an iterative algorithm analogous to sparse reconstruction algorithms in the context of linear inverse problems. We exemplify our framework with the compressive estimation of a Gaussian Mixture Model (GMM), providing heuristics on the choice of the sketching procedure and theoretical guarantees of reconstruction. We experimentally show on synthetic data that the proposed algorithm yields results comparable to the classical Expectation-Maximization (EM) technique while requiring significantly less memory and fewer computations when the number of database elements is large. We further demonstrate the potential of the approach on real large-scale data (over 10 8 training samples) for the task of model-based speaker verification. Finally, we draw some connections between the proposed framework and approximate Hilbert space embedding of probability distributions using random features. We show that the proposed sketching operator can be seen as an innovative method to design translation-invariant kernels adapted to the analysis of GMMs. We also use this theoretical framework to derive information preservation guarantees, in the spirit of infinite-dimensional compressive sensing

SPIDA: Abstracting and generalizing layout design cases

Abstraction and generalization of layout design cases generate new knowledge that is more widely applicable to use than specific design cases. The abstraction and generalization of design cases into hierarchical levels of abstractions provide the designer with the flexibility to apply any level of abstract and generalized knowledge for a new layout design problem. Existing case-based layout learning (CBLL) systems abstract and generalize cases into single levels of abstractions, but not into a hierarchy. In this paper, we propose a new approach, termed customized viewpoint - spatial (CV-S), which supports the generalization and abstraction of spatial layouts into hierarchies along with a supporting system, SPIDA (SPatial Intelligent Design Assistant)

Human motion retrieval based on freehand sketch

In this paper, we present an integrated framework of human motion retrieval based on freehand sketch. With some simple rules, the user can acquire a desired motion by sketching several key postures. To retrieve efficiently and accurately by sketch, the 3D postures are projected onto several 2D planes. The limb direction feature is proposed to represent the input sketch and the projected-postures. Furthermore, a novel index structure based on k-d tree is constructed to index the motions in the database, which speeds up the retrieval process. With our posture-by-posture retrieval algorithm, a continuous motion can be got directly or generated by using a pre-computed graph structure. What's more, our system provides an intuitive user interface. The experimental results demonstrate the effectiveness of our method. © 2014 John Wiley & Sons, Ltd