We investigate the averaging problem in cosmology as the problem of introducing a distance between spaces. We first introduce the spectral distance, which is a measure of closeness between spaces defined in terms of the spectra of the Laplacian. Then we define SN , a space of all spaces equipped with the spectral distance. We argue that SN can be regarded as a metric space and that it also poss...

Adaptive sketchy shape recognition is a critical problem in sketch-based user interface. In this paper, an SVM-based incremental learning algorithm is made to solve this problem. Our algorithm utilizes only the support vectors instead of all the historical samples, and selects some important samples from all newly added samples as training data. The importance of a sample is measured according ...

Simple and fast methods for transforming color photographs into non-photorealistic images such as stained-glass and color-sketch images. We propose two types of methods decomposing images into homogeneous color regions. One type is an edge-based method and the other is a region-based approach. In the edge-based methods, an input image is tessellated into Apollonius cells by using the distance t...

Abstract Conditional Random Sampling (CRS) was originally proposed for efficiently computing pairwise (l2, l1) distances, in static, large-scale, and sparse data. This study modifies the original CRS and extends CRS to handle dynamic or streaming data, which much better reflect the real-world situation than assuming static data. Compared with many other sketching algorithms for dimension reduct...

Given a massive collection of sequences, it is infeasible to perform pairwise alignment for basic tasks like sequence clustering and search. To address this problem, we demonstrate that the MinHash technique, first applied to clustering web pages, can be applied to biological sequences with similar effect, and extend this idea to include biologically relevant distance and significance measures....

We study a natural generalization of the heavy hitters problem in the streaming context. We term this generalization block heavy hitters and define it as follows. We are to stream over a matrix A, and report all rows that are heavy, where a row is heavy if its `1-norm is at least φ fraction of the `1 norm of the entire matrix A. In comparison, in the standard heavy hitters problem, we are requi...

Distance Geometry puts the concept of distance at its center. The basic problem in distance geometry could be described as drawing an edge-weighted undirected graph in R for some given K such that the positions for adjacent vertices have distance which is equal to the corresponding edge weight. As we are unaware of any work in this field using any other norm but `2, we move some first steps usi...

The automatic recognition of facial expression presents a significant challenge to the pattern analysis and man-machine interaction research community. In this paper, a novel system is proposed to recognize human facial expressions based on the expression sketch. Firstly, facial expression sketch is extracted by an GPU-based real-time edge detection and sharpening algorithm from original gray i...

Due to the inaccuracy and noisy, uncertainty is inherent in time series streams, and increases the complexity of streams clustering. For the continuous arriving and massive data size, efficient data storage is a crucial task for clustering uncertain data streams. With hash-compressed structure, an extended uncertain sketch and update strategy are proposed to store uncertain data streams. And ba...

In this paper, we propose a method for creating freeform surfaces from sketch-annotated images. Beginning from an image, the user sketches object boundaries, features, and holes. Sketching is made easier by a magnetic pen that follows strong edges in the image. To create a surface from the sketch, a planar mesh is constructed such that its geometry aligns with the boundary and interior features...