Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models.

However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points.

These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets. Giacomo Zanella. Brenda Betancourt. Hanna Wallach. Jeffrey Miller. Abbas Zaidi. Rebecca C.

Most generative models for clustering implicitly assume that the number Traditional Bayesian random partition models assume that the size of eac The goal of data clustering is to partition data points into groups to m In this paper, we have derived a set of sufficient conditions for reliab In model-based clustering using finite mixture models, it is a significa In database management, record linkage aims to identify multiple records Mixture models combine multiple components into a single probability denThe paper presents an alternative prior for Bayesian non-parametric clustering.

The prior is a better fit for applications where the size of data in each cluster doesn't grow linearly with the number of data points i. The authors explicitly modeled the distribution of cluster sizes in the new process and provided two incarnations of the process using different forms of distributions over cluster sizes.

They gave a Gibbs-sampling algorithm as well as a split-merge algorithm in the appendix. The authors addressed an important problem in BNP clustering and gave an interesting prior. However, the paper have the following weaknesses: 1- As the authors mentioned in line 64, [13] had a take on the same problem by defining a uniform prior rather than the rich gets richer prior implicit in DP and PYP.

They showed that their prior produces larger number of clusters than DP. Unfortunately, the authors didn't compare with [13] nor discussed in any details, beyond a passing mention in line 64, how their work relates and differs from [13] in terms of the properties of the resulting prior.

Are any of the improvements statistically significant? I don't see a radical dominating performance across all measures of the new processes over exciting ones. Lots of symbols! Could use some work and simplifications. The paper proposes a distribution over partitions of integers that supports micro-clustering. Specifically, the paper shows that that for existing infinitely exchangeable clustering models, such as Dirichlet Process DP and Pitman-Yor Process PYP mixture models, the cluster sizes grow linearly with the number of data points N.

For applications such as entity resolution, the paper defines the micro-clustering property, where the ratio of the cluster size and number of data points N goes to 0 as N goes to infinity.

The paper proposes a general distribution framework over partitions of integers that satisfies this micro-clustering property. This is done by first sampling the number of clusters from a distribution with positive integers as support, and then explicitly sampling each of the cluster sizes from a distribution over cluster sizes again with positive integers as support.

This model achieves the micro-clustering property by sacrificing consistency of marginals, while preserving exchangeability.

The paper then proposes two specific instances of this framework. The first uses the negative binomial for both distributions. The second uses a Dirichlet with an infinite dimensional base distribution for the distribution over cluster sizes to provide more flexibility for large datasets. Reseating algorithms similar to the Chinese Restaurant Process and the Pitman-Yor Process are provided for both models.

Making use of the exchangeability property, sampling based algorithms are used for inference in both models.

Experiments over 4 semi-synthetic datasets are used to illustrate that the proposed models outperform models without the micro-clustering property DP and PYP for the entity resolution task. The following are the main strengths of the paper. There could be many applications, including and not limited to entity resolution, that require this property to be satisfied.

It then proposes two specific and interesting instances of this class using specific distributions for the number of clusters and cluster sizes and derives reseating algorithms for these instances.

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Experiments in the supplement show that draws from the proposed model satisfy the micro-clustering property. This should be moved to the main paper.Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitmanâ€”Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models.

However, for some applications, this assumption is inappropriate.

### Flexible Models for Microclustering with Application to Entity Resolution

For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points. These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set.

We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.

Share this page:. Download BibTex. Research Areas Artificial intelligence.Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points. Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models.

However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points.

These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets. Comment: 15 pages, 3 figures, 1 table, to appear NIPS Location of Repository.

OAI identifier: oai:arXiv. Provided by: arXiv. Suggested articles.Most generative models for clustering implicitly assume that the number of data points in each cluster grows linearly with the total number of data points.

Finite mixture models, Dirichlet process mixture models, and Pitman--Yor process mixture models make this assumption, as do all other infinitely exchangeable clustering models. However, for some applications, this assumption is inappropriate. For example, when performing entity resolution, the size of each cluster should be unrelated to the size of the data set, and each cluster should contain a negligible fraction of the total number of data points.

These applications require models that yield clusters whose sizes grow sublinearly with the size of the data set. We address this requirement by defining the microclustering property and introducing a new class of models that can exhibit this property. We compare models within this class to two commonly used clustering models using four entity-resolution data sets.

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The advantage Seattle has in this matchup is the fact the Seahawks offense practices against this scheme every day. Now, they have to travel all the way across the country, and Jacksonville is ready for a slugfest. This is a supreme test for both teams.

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Who draws first blood: Jared Goff or Carson Wentz. When the Los Angeles Rams took Jared Goff No. And when they face off Sunday at the Los Angeles Memorial Coliseum, it will be just the fifth time in that era that those two quarterbacks will face each other. Try Week 15 of the 1983 season, when defending Super Bowl champion Washington (34.

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Up next as contenders for the Legion of Boom mantle. Here come the Jaguars, trying to become the first team in the Super Bowl era to lead the NFL in points allowed, yards allowed, takeaways and sacks. The key for the Jags on Sunday, though, will be to keep the ball out of Russell Wilson's hands late.

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The Jags are the FPI favorite at 56. And with 82 catches with four games to go, Fitzgerald has a chance to join Jerry Rice (1994-96) as the only players with three consecutive 100-catch seasons over the age of 30. Since returning to the NFL in 1999, the Browns have run through eight general managers and nine coaches while having only two winning seasons and one playoff appearance in that time frame, a wild-card loss to the Steelers in 2002.

It will be tied for the fifth-most meetings between quarterbacks, including the playoffs, in the Super Bowl era, along with Tony Romo vs. Eli Manning (Romo won 10 times) and Tom Brady vs. Peyton Manning (Brady won 11).

Roethlisberger leads the rivalry 10-6. Jim Kelly and Dan Marino met 21 times in their respective careers, with Kelly going 14-7.

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