Counting people by clustering person detector outputs

In machine learning and data mining tasks, Clustering is considered to be one of the most important techniques. The same sorts of documents are grouped by performing clustering techniques. Similarity measuring is used to determine transaction relationships. Hierarchical clustering model generates tree structured results. Partitioned based clustering produces the result in grid format. Text documents are unstructured data values with high dimensional attributes. Document clustering group transforms unlabeled text documents into meaningful clusters. In the event of document grouping process, traditional clustering methods require cluster count (K). Clustering accuracy degrades drastically with reference to the unsuitable cluster count. It is observed that document features are automatically partitioned into two groups namely — discriminative words and non-discriminative words. In particular, discriminative words are only useful for grouping documents. The involvement of non-discriminative words confuses the clustering process and leads to poor clustering solution in return. A variation inference algorithm is used to infer the document collection structure and partition of document words simultaneously. Dirichlet Process Mixture (DPM) model is used to partition documents in a way utilizing both the data likelihood and the clustering property of the Dirichlet Process (DP). Dirichlet Process Mixture Model for Feature Extraction (DPMFE) is used to discover the latent cluster structure based on the DPM model and it is performed without involving the number of clusters as input.

The aim of this study was to implement a Dirichlet process mixture (DPM) model for automatic tumor edge identification on (18)F-fluorodeoxyglucose positron emission tomography ((18)F-FDG PET) images by optimizing the parameters on which the algorithm depends, to validate it experimentally, and to test its robustness. The DPM model belongs to the class of the Bayesian nonparametric models and uses the Dirichlet process prior for flexible nonparametric mixture modeling, without any preliminary choice of the number of mixture components. The DPM algorithm implemented in the statistical software package R was used in this work. The contouring accuracy was evaluated on several image data sets: on an IEC phantom (spherical inserts with diameter in the range 10-37 mm) acquired by a Philips Gemini Big Bore PET-CT scanner, using 9 different target-to-background ratios (TBRs) from 2.5 to 70; on a digital phantom simulating spherical/uniform lesions and tumors, irregular in shape and activity; and on 20 clinical cases (10 lung and 10 esophageal cancer patients). The influence of the DPM parameters on contour generation was studied in two steps. In the first one, only the IEC spheres having diameters of 22 and 37 mm and a sphere of the digital phantom (41.6 mm diameter) were studied by varying the main parameters until the diameter of the spheres was obtained within 0.2% of the true value. In the second step, the results obtained for this training set were applied to the entire data set to determine DPM based volumes of all available lesions. These volumes were compared to those obtained by applying already known algorithms (Gaussian mixture model and gradient-based) and to true values, when available. Only one parameter was found able to significantly influence segmentation accuracy (ANOVA test). This parameter was linearly connected to the uptake variance of the tested region of interest (ROI). In the first step of the study, a calibration curve was determined to automatically generate the optimal parameter from the variance of the ROI. This "calibration curve" was then applied to contour the whole data set. The accuracy (mean discrepancy between DPM model-based contours and reference contours) of volume estimation was below (1 ± 7)% on the whole data set (1 SD). The overlap between true and automatically segmented contours, measured by the Dice similarity coefficient, was 0.93 with a SD of 0.03. The proposed DPM model was able to accurately reproduce known volumes of FDG concentration, with high overlap between segmented and true volumes. For all the analyzed inserts of the IEC phantom, the algorithm proved to be robust to variations in radius and in TBR. The main advantage of this algorithm was that no setting of DPM parameters was required in advance, since the proper setting of the only parameter that could significantly influence the segmentation results was automatically related to the uptake variance of the chosen ROI. Furthermore, the algorithm did not need any preliminary choice of the optimum number of classes to describe the ROIs within PET images and no assumption about the shape of the lesion and the uptake heterogeneity of the tracer was required.

Hidden Markov random field (HMRF) models are widely used for image segmentation, as they appear naturally in problems where a spatially constrained clustering scheme is asked for. A major limitation of HMRF models concerns the automatic selection of the proper number of their states, i.e., the number of region clusters derived by the image segmentation procedure. Existing methods, including likelihood- or entropy-based criteria, and reversible Markov chain Monte Carlo methods, usually tend to yield noisy model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (DP, infinite) mixture models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori; infinite mixture models based on the original DP or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results. Under this motivation, to resolve the aforementioned issues of HMRF models, in this paper, we introduce a nonparametric Bayesian formulation for the HMRF model, the infinite HMRF model, formulated on the basis of a joint Dirichlet process mixture (DPM) and Markov random field (MRF) construction. We derive an efficient variational Bayesian inference algorithm for the proposed model, and we experimentally demonstrate its advantages over competing methodologies.

This paper presents an empirical study of endogenous treatment effects in the presence of heterogeneous responses. We estimate the incentive and selection effects of having prescription drug coverage on total drug expenditures using a sample from the Medicare Current Beneficiary Survey (MCBS). A Dirichlet process mixture (DPM) model is used to model the heterogeneity in treatment effects. Rather than estimating a finite mixture model with a fixed number of components, we specify a DP prior on the parameters, thus allowing the data and prior knowledge to determine the number of components. Endogeneity is modeled by the covariance of the error terms of the selection and the outcome equations in a two-equation selection model. We find that there are strong incentive and advantageous selection effects, with the average treatment effect and the average treatment effect for the treated estimated at $1132 and $858, respectively. Substantial heterogeneity is found to exist in the selection effects, particularly for those having lower drug expenditures. Copyright © 2014 John Wiley & Sons, Ltd.

Dirichlet process mixture models (or mixture of Dirichlet process [MDP]) are Bayesian non‐parametric mixture models that can solve the problem of determining the number of components in mixture models by assuming infinitely many components. We propose a new approach for MDP by using a matrix‐generalized half‐ distribution as a non‐informative prior for the covariance in the base distribution. This new approach aims to improve the performance of MDP in cases where conjugacy constraints cause underperformance of current priors, such as Wishart distribution or inverse‐Wishart. The effectiveness of this approach is demonstrated through simulations and by comparing its performance on the Old Faithful geyser dataset with existing MDP specifications.

We present an object tracking framework that employs Dirichlet Process Mixture Models (DPMMs) in a multiple hypothesis tracker. DPMMs enable joint detection and tracking of an unknown and variable number of objects in a fully automatic fashion without any initial labeling. At each frame, we extract foreground superpixels and cluster them into objects by propagating clusters across consecutive frames. Since no constraint on the number of clusters is required, we can track multiple cluster hypotheses at the same time. By incorporating superpixels and an efficient pruning scheme, we keep the total number of hypotheses low and tractable. We refine object boundaries with Markov random fields and connectivity analysis of the tracked clusters. Finally, we group tracked hypotheses to combine possible parts of an object as one.

Multistate models, that is, models with more than two distributions, are preferred over single-state probability models in modeling the distribution of travel time. Literature review indicated that the finite multistate modeling of travel time using lognormal distribution is superior to other probability functions. In this study, we extend the finite multistate lognormal model of estimating the travel time distribution to unbounded lognormal distribution. In particular, a nonparametric Dirichlet Process Mixture Model (DPMM) with stick-breaking process representation was used. The strength of the DPMM is that it can choose the number of components dynamically as part of the algorithm during parameter estimation. To reduce computational complexity, the modeling process was limited to a maximum of six components. Then, the Markov Chain Monte Carlo (MCMC) sampling technique was employed to estimate the parameters’ posterior distribution. Speed data from nine links of a freeway corridor, aggregated on a 5-minute basis, were used to calculate the corridor travel time. The results demonstrated that this model offers significant flexibility in modeling to account for complex mixture distributions of the travel time without specifying the number of components. The DPMM modeling further revealed that freeway travel time is characterized by multistate or single-state models depending on the inclusion of onset and offset of congestion periods.

The accurate modeling of uncertain variables, such as wind power and load uncertainty, is an essential foundation for the planning operation and scheduling decisions in power systems. Currently, Gaussian mixture model (GMM) and Dirichlet process mixture model (DPMM) are the primary techniques used to characterize uncertainties in power systems, which are commonly solved by expectation-maximization (EM) algorithm. However, for the massive data of uncertain variables, the algorithm encounters challenges in accurately obtaining GMM and DPMM with a lower time consumption. To address this issue, we propose a method for GMM uncertainty modeling in power systems considering the mutual assistance of latent variables. Specifically, the GMM of uncertain variables is first constructed, and the conditional probability is employed to characterize the mutual assistance of latent variables. Then, an improved EM algorithm is developed to obtain the optimal GMM parameters, in which the expectation step (E-step) and maximization step (M-step) of the algorithm are revised using the conditional probability. Importantly, the closed-form solutions for GMM parameters are rederived in the revised E-step and M-step. Finally, the proposed uncertainty modeling method is compared with the traditional GMM and DPMM on actual wind power and load data from Australia. The proposed method performs the efficiency and accuracy in characterizing uncertainty.

Unsupervised outlier detection using random subspace and subsampling ensembles of Dirichlet process mixtures

The increasing use of electronic health records (EHRs) in medical research and AI-driven healthcare necessitates high-fidelity synthetic data that balances patient privacy with statistical and clinical utility. Traditional generative models, such as generative adversarial networks (GANs) and variational autoencoders (VAEs), struggle with mode collapse, limited sample diversity, and difficulties in modelling complex dependencies in high-dimensional tabular data. This study introduces a diffusion model-based approach for generating synthetic EHR data and evaluates its utility in clustering multimorbidity patterns using Dirichlet process mixture models (DPMMs). Denoising diffusion probabilistic models (DDPMs) iteratively refine noise through a structured denoising process, producing diverse, high-fidelity synthetic records. The DPMM framework, a Bayesian nonparametric clustering method, dynamically determines the number of clusters, effectively handling heterogeneous, imbalanced datasets. Model evaluation incorporates statistical similarity measures, feature correlation analysis, privacy risk assessments, and predictive performance metrics. Results demonstrate that DDPM-generated data surpasses GANs and VAEs in fidelity (Jensen–Shannon divergence (JSD) = 0.020, Pearson pairwise correlation (PPC) = 0.94), and privacy preservation (membership inference attack (MIA) Risk = 0.25). DPMM clustering reveals clinically meaningful disease patterns, outperforming traditional clustering models. These findings highlight the potential of diffusion models for privacy-preserving synthetic EHR generation and robust multimorbidity clustering in healthcare analytics.

Hidden Markov Random Field (HMRF) models are important statistical tools for image segmentation. However, such models cannot automatically determine the number of clusters. In many practical applications, to determine the number of clusters in advance is impossible. The Dirichlet process mixture (DPM) models are nonparametric Bayesian models which can automatically determine the number of clusters for the clustering problem. A new HMRF model which combines the DPM model with Student's t-distribution is proposed in this paper. Compared to the Gaussian distribution, the Student's t-distribution with heavier-tailed can have more applications. This model can automatically determine the appropriate clustering number from the observed data. In addition, an efficient variational Bayesian inference algorithm is derived to the proposed model. Experimental results show that the proposed model outperforms other DPM-based models in image segmentation.

Trajectory analysis is the basis for many applications, such as indexing of motion events in videos, activity recognition, and surveillance. In this paper, the Dirichlet process mixture model (DPMM) is applied to trajectory clustering, modeling, and retrieval. We propose an incremental version of a DPMM-based clustering algorithm and apply it to cluster trajectories. An appropriate number of trajectory clusters is determined automatically. When trajectories belonging to new clusters arrive, the new clusters can be identified online and added to the model without any retraining using the previous data. A time-sensitive Dirichlet process mixture model (tDPMM) is applied to each trajectory cluster for learning the trajectory pattern which represents the time-series characteristics of the trajectories in the cluster. Then, a parameterized index is constructed for each cluster. A novel likelihood estimation algorithm for the tDPMM is proposed, and a trajectory-based video retrieval model is developed. The tDPMM-based probabilistic matching method and the DPMM-based model growing method are combined to make the retrieval model scalable and adaptable. Experimental comparisons with state-of-the-art algorithms demonstrate the effectiveness of our algorithm.

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