A restaurant process with cocktail bar and relations to the three-parameter mittag–leffler distribution

In addition to the features of the two-parameter Chinese restaurant process (CRP), the restaurant under consideration has a cocktail bar and hence allows for a wider range of (bar and table) occupancy mechanisms. The model depends on three real parameters, $\alpha$ , $\theta_1$ , and $\theta_2$ , fulfilling certain conditions. Results known for the two-parameter CRP are carried over to this model. We study the number of customers at the cocktail bar, the number of customers at each table, and the number of occupied tables after n customers have entered the restaurant. For $\alpha>0$ the number of occupied tables, properly scaled, is asymptotically three-parameter Mittag–Leffler distributed as n tends to infinity. We provide representations for the two- and three-parameter Mittag–Leffler distribution leading to efficient random number generators for these distributions. The proofs draw heavily from methods known for exchangeable random partitions, martingale methods known for generalized Pólya urns, and results known for the two-parameter CRP.

Fragmented Spatial Maps: State Abstraction and Efficient Planning from Surprisal

When animals explore spatial environments, their representations often fragment into multiple maps. What determines these map fragmentations, and can we predict where they will occur with simple principles? We pose the problem of fragmentation of an environment as one of (online) spatial clustering. Taking inspiration from the notion of a "contiguous region" in robotics, we develop a theory in which fragmentation decisions are driven by surprisal. When this criterion is implemented with boundary, grid, and place cells in various environments, it produces map fragmentations from the first exploration of each space. Augmented with a long-term spatial memory and a rule similar to the distance-dependent Chinese Restaurant Process for selecting among relevant memories, the theory predicts the reuse of map fragments in environments with repeating substructures. Our model provides a simple rule for generating spatial state abstractions and predicts map fragmentations observed in electrophysiological recordings. It further predicts that there should be "fragmentation decision" or "fracture" cells, which in multicompartment environments could be called "doorway" cells. Finally, we show that the resulting abstractions can lead to large (orders of magnitude) improvements in the ability to plan and navigate through complex environments.

A Nested Chinese Restaurant Topic Model for Short Texts with Document Embeddings

In recent years, short texts have become a kind of prevalent text on the internet. Due to the short length of each text, conventional topic models for short texts suffer from the sparsity of word co-occurrence information. Researchers have proposed different kinds of customized topic models for short texts by providing additional word co-occurrence information. However, these models cannot incorporate sufficient semantic word co-occurrence information and may bring additional noisy information. To address these issues, we propose a self-aggregated topic model incorporating document embeddings. Aggregating short texts into long documents according to document embeddings can provide sufficient word co-occurrence information and avoid incorporating non-semantic word co-occurrence information. However, document embeddings of short texts contain a lot of noisy information resulting from the sparsity of word co-occurrence information. So we discard noisy information by changing the document embeddings into global and local semantic information. The global semantic information is the similarity probability distribution on the entire dataset and the local semantic information is the distances of similar short texts. Then we adopt a nested Chinese restaurant process to incorporate these two kinds of information. Finally, we compare our model to several state-of-the-art models on four real-world short texts corpus. The experiment results show that our model achieves better performances in terms of topic coherence and classification accuracy.

Clustering and the efficient use of cognitive resources

A central component of human intelligence is the ability to make abstractions, to gloss over some details in favor of drawing out higher-order structure. Clustering stimuli together is a classic example of this. However, the crucial question remains of how one should make these abstractions -- what details to retain and what to throw away? How many clusters to form? We provide an analysis of how a rational agent with limited cognitive resources should approach this problem, considering not only how well a clustering fits the data but also by how 'complex' it is, i.e. how cognitively expensive it is to represent. We show that the solution to this problem provides a way to reinterpret a wide range of psychological models that are based on principles from non-parametric Bayesian statistics. In particular, we show that the Chinese Restaurant Process prior, ubiquitous in models of human and animal clustering behavior, can be interpreted as minimizing an intuitive formulation of representational complexity.

Robust Cell Image Segmentation via Improved Markov Random Field Based on a Chinese Restaurant Process Model

In this paper, a segmentation method for cell images using Markov random field (MRF) based on a Chinese restaurant process model (CRPM) is proposed. Firstly, we carry out the preprocessing on the cell images, and then we focus on cell image segmentation using MRF based on a CRPM under a maximum a posteriori (MAP) criterion. The CRPM can be used to estimate the number of clusters in advance, adjusting the number of clusters automatically according to the size of the data. Finally, the conditional iteration mode (CIM) method is used to implement the MRF based cell image segmentation process. To validate our proposed method, segmentation experiments are performed on oral mucosal cell images. The segmentation results were compared with other methods, using precision, Dice, and mean square error (MSE) as the objective evaluation criteria. The experimental results show that our method produces accurate cell image segmentation results, and our method can effectively improve segmentation for the nucleus, binuclear cell, and micronucleus cell. This work will play an important role in cell image recognition and analysis.

Novel trajectory clustering method based on distance dependent Chinese restaurant process

Trajectory clustering and path modelling are two core tasks in intelligent transport systems with a wide range of applications, from modeling drivers’ behavior to traffic monitoring of road intersections. Traditional trajectory analysis considers them as separate tasks, where the system first clusters the trajectories into a known number of clusters and then the path taken in each cluster is modelled. However, such a hierarchy does not allow the knowledge of the path model to be used to improve the performance of trajectory clustering. Based on the distance dependent Chinese restaurant process (DDCRP), a trajectory analysis system that simultaneously performs trajectory clustering and path modelling was proposed. Unlike most traditional approaches where the number of clusters should be known, the proposed method decides the number of clusters automatically. The proposed algorithm was tested on two publicly available trajectory datasets, and the experimental results recorded better performance and considerable improvement in both datasets for the task of trajectory clustering compared to traditional approaches. The study proved that the proposed method is an appropriate candidate to be used for trajectory clustering and path modelling.