Related papers: Non-Empty Bins with Simple Tabulation Hashing
Empirical evidence suggests that hashing is an effective strategy for dimensionality reduction and practical nonparametric estimation. In this paper we provide exponential tail bounds for feature hashing and show that the interaction…
Bin covering is a dual version of classic bin packing. Thus, the goal is to cover as many bins as possible, where covering a bin means packing items of total size at least one in the bin. For online bin covering, competitive analysis fails…
We present here new mechanisms for hashing data via binary embeddings. Contrary to most of the techniques presented before, the embedding matrix of our mechanism is highly structured. That enables us to perform hashing more efficiently and…
A new method for binning a set of $n$ data values into a set of m bins for the case where the bins are of different sizes is proposed. The method skips binning using a binary search across the bins all the time. It is proven the method…
The analysis of large datasets is often complicated by the presence of missing entries, mainly because most of the current machine learning algorithms are designed to work with full data. The main focus of this work is to introduce a…
Various forms of sorting problems have been studied over the years. Recently, two kinds of sorting puzzle apps are popularized. In these puzzles, we are given a set of bins filled with colored units, balls or water, and some empty bins.…
Randomized algorithms and data structures are often analyzed under the assumption of access to a perfect source of randomness. The most fundamental metric used to measure how "random" a hash function or a random number generator is, is its…
We consider the unsupervised learning problem of assigning labels to unlabeled data. A naive approach is to use clustering methods, but this works well only when data is properly clustered and each cluster corresponds to an underlying…
Bloom filters are data structures used to determine set membership of elements, with applications from string matching to networking and security problems. These structures are favored because of their reduced memory consumption and fast…
Imagine handling collisions in a hash table by storing, in each cell, the bit-wise exclusive-or of the set of keys hashing there. This appears to be a terrible idea: For $\alpha n$ keys and $n$ buckets, where $\alpha$ is constant, we expect…
A typical image retrieval pipeline starts with the comparison of global descriptors from a large database to find a short list of candidate matches. A good image descriptor is key to the retrieval pipeline and should reconcile two…
The Bloom filter---or, more generally, an approximate membership query data structure (AMQ)---maintains a compact, probabilistic representation of a set S of keys from a universe U. An AMQ supports lookups, inserts, and (for some AMQs)…
Unsupervised clustering of feature matrix data is an indispensible technique for exploratory data analysis and quality control of experimental data. However, clusters are difficult to assess for statistical significance in an objective way.…
In this paper, we use techniques of enumerative combinatorics to study the following problem: we count the number of ways to split $n$ balls into nonempty, ordered bins so that the most crowded bin has exactly $k$ balls. We find closed…
Double hashing has recently found more common usage in schemes that use multiple hash functions. In double hashing, for an item $x$, one generates two hash values $f(x)$ and $g(x)$, and then uses combinations $(f(x) +k g(x)) \bmod n$ for…
Probability density functions (PDF) of statistical distributions of cluster sizes N, where N is the number of particles in the cluster, often seem to have less freedom than expected from considering the number of degrees of freedom at the…
Finding meaningful groups, i.e., clusters, in high-dimensional data such as images or texts without labeled data at hand is an important challenge in data mining. In recent years, deep clustering methods have achieved remarkable results in…
Minimal perfect hash functions provide space-efficient and collision-free hashing on static sets. Existing algorithms and implementations that build such functions have practical limitations on the number of input elements they can process,…
In dynamic load balancing, we wish to distribute balls into bins in an environment where both balls and bins can be added and removed. We want to minimize the maximum load of any bin but we also want to minimize the number of balls and bins…
Recent advances in random linear systems on finite fields have paved the way for the construction of constant-time data structures representing static functions and minimal perfect hash functions using less space with respect to existing…