12953441
A Simultaneous Search Problem
Abstract. We introduce a new search problem motivated by computational metrology. The problem is as follows: we would like to locate two unknown numbers x,y ∈ [0,1] with as little uncertainty as possible, using some given number k of probes. Each probe is specified by a real number r∈ [0,1] . After a probe at r , we are told whether x≤ r or x \geq r , and whether y≤ r or y\geq r . We derive the optimal strategy and prove that the asymptotic behavior of the total uncertainty after k probes is 13/7 2-(k+1)/2 for odd k and 13/10 2-k/2 for even k .
9658544
Effect of Malicious Synchronization
We study the impact of malicious synchronization on computer systems that serve customers periodically. Systems supporting automatic periodic updates are common in web servers providing regular news update, sports scores or stock quotes. Our study focuses on the possibility of launching an effective low rate attack on the server to degrade performance measured in terms of longer processing time and request drops due to timeouts. The attackers are assumed to behave like normal users and send one request per update cycle. The only parameter utilized in the attack is the timing of the requests sent. By exploiting the periodic nature of the updates, a small number of attackers can herd users' update requests to a cluster and arrive in a short period of time. Herding can be used to discourage new users from joining the system and to modify the user arrival distribution, so that the subsequent burst attack will be effective. While the herding based attacks can be launched with a small amount of resource, they can be easily prevented by adding a small random component to the length of the update interval.
3144439
Fast rendering of foveated volumes in wavelet-based representation
A foveated volume can be viewed as a blending of multiple regions, each with a different level of resolution. It can be efficiently represented in the wavelet domain by retaining a small number of wavelet coefficients. We exploit the arrangement of those wavelet coefficients to achieve fast volume rendering. The running time is O(n2+m), where n is the width of the rendered image, and m is the number of wavelet coefficients retained for the foveated volume. Our algorithm consists of two phases. The first phase is a fast reconstruction of the super-voxels from the wavelet coefficients, and the second phase renders the super-voxels by carefully tracking rays with different thickness in the super-voxels. No expensive preprocessing on the wavelet coefficients is required. Hence, it is possible to interactively modify different viewing parameters like the transfer functions. A potential application of our algorithm is in remote visualization of large volume data-sets.
2005681
Hiding Secret Points Amidst Chaff
Motivated by the representation of biometric and multimedia objects, we consider the problem of hiding noisy point-sets using a secure sketch. A point-set X consists of s points from a d-dimensional discrete domain [0,N – 1]d. Under permissible noises, for every point $\left \langle x_1,..,x_d\right \rangle \in X$, each xi may be perturbed by a value of at most δ. In addition, at most t points in X may be replaced by other points in [0,N – 1]d. Given an original X, we want to compute a secure sketch P. A known method constructs the sketch by adding a set of random points R, and the description of (X∪R) serves as part of the sketch. However, the dependencies among the random points are difficult to analyze, and there is no known non-trivial bound on the entropy loss. In this paper, we first give a general method to generate R and show that the entropy loss of (X∪R) is at most s(dlogΔ+ d + 0.443), where Δ= 2δ+1. We next give improved schemes for d = 1, and special cases for d = 2. Such improvements are achieved by pre-rounding, and careful partition of the domains into cells. It is possible to make our sketch short, and avoid using randomness during construction. We also give a method in d = 1 to demonstrate that, using the size of R as the security measure would be misleading.
42674644
Shortest Path amidst Disc Obstacles Is Computable
An open question in Exact Geometric Computation is whether there are transcendental computations that can be made "geometrically exact". Perhaps the simplest such problem in computational geometry is that of computing the shortest obstacle-avoiding path between two points p,q in the plane, where the obstacles are a collection of n discs. This problem can be solved in O(n2log n) time in the Real RAM model, but nothing was known about its computability in the standard (Turing) model of computation. We first give a direct proof of the Turing-computability of this problem, provided the radii of the discs are rationally related. We make the usual assumption that the numerical input data are real algebraic numbers. By appealing to effective bounds from transcendental number theory, we further show a single-exponential time upper bound when the input numbers are rational. Our result appears to be the first example of a non-algebraic combinatorial problem which is shown computable. It is also a rare example of transcendental number theory yielding positive computational results.
1227971
Rotation of foveated image in the wavelet domain
An advantage of wavelet transform is its efficiency in representing natural images, that is, a natural image can be accurately represented by only a small number of retained wavelet coefficients. It is interesting to know whether some common image operations, e.g., rotation, can be performed very fast in wavelet domain. Preferably, the running time should depend only on the number of retained coefficients, not the size of the original image. However, it is not clear how this can be achieved. In this paper, we consider rotation and images with a special structure: foveated images. Wavelet coefficients of a foveated image vanish outside an arrangement of circles. We exploit this structure to derive algorithms that accurately approximate rotation. The running time is /spl Theta/(m) where m is the number of retained coefficients. Experiments show the accuracy of the approximation.
18331143
Kronecker Factorization for Speeding up Kernel Machines
In kernel machines, such as kernel principal component analysis (KPCA), Gaussian Processes (GPs), and Support Vector Machines (SVMs), the computational complexity of finding a solution is O(n), where n is the number of training instances. To reduce this expensive computational complexity, we propose using Kronecker factorization, which approximates a positive definite kernel matrix by the Kronecker product of two smaller positive definite matrices. This approximation can speed up the calculation of the kernel-matrix inverse or eigendecomposition involved in kernel machines. When the two factorized matrices have about the same dimensions, the computational complexity is improved from O(n) to O(n). We propose two methods to carry out Kronecker factorization and apply them to speed up KPCA. In Experiments show that our methods can drastically reduce the computation time of kernel machines without any significant degradation in their effectiveness.
7236137
Efficient top-k hyperplane query processing for multimedia information retrieval
A query can be answered by a binary classifier, which separates the instances that are relevant to the query from the ones that are not. When kernel methods are employed to train such a classifier, the class boundary is represented as a hyperplane in a projected space. Data instances that are farthest from the hyperplane are deemed to be most relevant to the query, and that are nearest to the hyperplane to be most uncertain to the query. In this paper, we address the twin problems of efficient retrieval of the approximate set of instances (a) farthest from and (b) nearest to a query hyperplane. Retrieval of instances for this hyperplane-based query scenario is mapped to the range-query problem allowing for the reuse of existing index structures. Empirical evaluation on large image datasets confirms the effectiveness of our approach.
6693066
Nnew: nearest neighbor expansion by weighting in image database retrieval
Various systems have been developed for supporting content-based image retrieval. Most systems make very strong assumptions in modeling users’ query concepts. However, since the information need of users can be very diverse, these assumptions may not always hold and hence can lead to poor search results. For instance, if a system assumes that the query-concept is convex but a user issues a disjunctive query, and vice versa, the search result cannot be satisfactory. In this study, we propose a method that can approximate more complex (non-convex and disjunctive) query concepts. Our method uses intelligent modeling and learning to increase query speed and accuracy. Empirical results show that our method converges consistently faster than some traditional approaches on different datasets.
6942556
Multi-camera spatio-temporal fusion and biased sequence-data learning for security surveillance
We present a framework for multi-camera video surveillance. The framework consists of three phases: detection, representation, and recognition. The detection phase handles multi-source spatio-temporal data fusion for efficiently and reliably extracting motion trajectories from video. The representation phase summarizes raw trajectory data to construct hierarchical, invariant, and content-rich descriptions of the motion events. Finally, the recognition phase deals with event classification and identification on the data descriptors. Because of space limits, we describe only briefly how we detect and represent events, but we provide in-depth treatment on the third phase: event recognition. For effective recognition, we devise a sequence-alignment kernel function to perform sequence data learning for identifying suspicious events. We show that when the positive training instances (i.e., suspicious events) are significantly outnumbered by the negative training instances (benign events), then SVMs (or any other learning methods) can suffer a high incidence of errors. To remedy this problem, we propose the kernel boundary alignment (KBA) algorithm to work with the sequence-alignment kernel. Through empirical study in a parking-lot surveillance setting, we show that our spatio-temporal fusion scheme and biased sequence-data learning method are highly effective in identifying suspicious events.
35270580
Mining image features for efficient query processing
The number of features required to depict an image can be very large. Using all features simultaneously to measure image similarity and to learn image query-concepts can suffer from the problem of dimensionality curse, which degrades both search accuracy and search speed. Regarding search accuracy, the presence of irrelevant features with respect to a query can contaminate similarity measurement, and hence decrease both the recall and precision of that query. To remedy this problem, we present a mining method that learns online users' query concepts and identifies important features quickly. Regarding search speed, the presence of a large number of features can slow down query-concept learning and indexing performance. We propose a divide-and-conquer method that divides the concept-learning task into G subtasks to achieve speedup. We notice that a task must be divided carefully, or search accuracy may suffer. We thus propose a genetic-based mining algorithm to discover good feature groupings. Through analysis and mining results, we observe that organizing image features in a multi-resolution manner and minimizing intra-group feature correlation, can speed up query-concept learning substantially while maintaining high search accuracy.