824 research outputs found
Hashing-Based-Estimators for Kernel Density in High Dimensions
Given a set of points and a kernel , the Kernel
Density Estimate at a point is defined as
. We study the problem
of designing a data structure that given a data set and a kernel function,
returns *approximations to the kernel density* of a query point in *sublinear
time*. We introduce a class of unbiased estimators for kernel density
implemented through locality-sensitive hashing, and give general theorems
bounding the variance of such estimators. These estimators give rise to
efficient data structures for estimating the kernel density in high dimensions
for a variety of commonly used kernels. Our work is the first to provide
data-structures with theoretical guarantees that improve upon simple random
sampling in high dimensions.Comment: A preliminary version of this paper appeared in FOCS 201
Knowledge Extraction in Video Through the Interaction Analysis of Activities
Video is a massive amount of data that contains complex interactions between moving objects. The extraction of knowledge from this type of information creates a demand for video analytics systems that uncover statistical relationships between activities and learn the correspondence between content and labels. However, those are open research problems that have high complexity when multiple actors simultaneously perform activities, videos contain noise, and streaming scenarios are considered. The techniques introduced in this dissertation provide a basis for analyzing video. The primary contributions of this research consist of providing new algorithms for the efficient search of activities in video, scene understanding based on interactions between activities, and the predicting of labels for new scenes
A Memory-Efficient Sketch Method for Estimating High Similarities in Streaming Sets
Estimating set similarity and detecting highly similar sets are fundamental
problems in areas such as databases, machine learning, and information
retrieval. MinHash is a well-known technique for approximating Jaccard
similarity of sets and has been successfully used for many applications such as
similarity search and large scale learning. Its two compressed versions, b-bit
MinHash and Odd Sketch, can significantly reduce the memory usage of the
original MinHash method, especially for estimating high similarities (i.e.,
similarities around 1). Although MinHash can be applied to static sets as well
as streaming sets, of which elements are given in a streaming fashion and
cardinality is unknown or even infinite, unfortunately, b-bit MinHash and Odd
Sketch fail to deal with streaming data. To solve this problem, we design a
memory efficient sketch method, MaxLogHash, to accurately estimate Jaccard
similarities in streaming sets. Compared to MinHash, our method uses smaller
sized registers (each register consists of less than 7 bits) to build a compact
sketch for each set. We also provide a simple yet accurate estimator for
inferring Jaccard similarity from MaxLogHash sketches. In addition, we derive
formulas for bounding the estimation error and determine the smallest necessary
memory usage (i.e., the number of registers used for a MaxLogHash sketch) for
the desired accuracy. We conduct experiments on a variety of datasets, and
experimental results show that our method MaxLogHash is about 5 times more
memory efficient than MinHash with the same accuracy and computational cost for
estimating high similarities
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