Bhattacharyya Kernel Research Articles

MLBKFD: Probabilistic Model Methods to Infer Pseudo Trajectories from Single-cell Data

Cell trajectory inference is very important to understand the details of tissue cell development, state differentiation and gene dynamic regulation. However, due to the high noise and heterogeneity of the single-cell data, it is challenging to infer cell trajectory in complex biological processes. Here, we proposed a new trajectory inference method, called Metric Learning Bhattacharyya Kernel Feature Decomposition (MLBKFD). In MLBKFD, a statistical model was used to infer cell trajectory by calculating the Markov transition matrix and Bhattacharyya kernel matrix between cells. Before that, to expedite the matrix calculation in the statistical model, a deep feedforward neural network was used to perform dimensionality reduction on single-cell data. The MLBKFD was evaluated on four typical datasets as well as seven recent human fetal lung datasets. Comparisons with the two outstanding methods (i.e., DTFLOW and MARGARET) demonstrate that the MLBKFD is capable of accurately inferring cell development and differentiation trajectories from single-cell data with different sizes and sources. Notably, MLBKFD exhibits nearly twice the speed of DTFLOW while maintaining high precision, particularly when dealing with large datasets. MLBKFD provides accurate and efficient trajectory inference, empowering researchers to gain deeper insights into the complex dynamics of cell development and differentiation.

DTFLOW: Inference and Visualization of Single-cell Pseudotime Trajectory Using Diffusion Propagation

One of the major challenges in single-cell data analysis is the determination of cellular developmental trajectories using single-cell data. Although substantial studies have been conducted in recent years, more effective methods are still strongly needed to infer the developmental processes accurately. This work devises a new method, named DTFLOW, for determining the pseudo-temporal trajectories with multiple branches. DTFLOW consists of two major steps: a new method called Bhattacharyya kernel feature decomposition (BKFD) to reduce the data dimensions, and a novel approach named Reverse Searching on k-nearest neighbor graph (RSKG) to identify the multi-branching processes of cellular differentiation. In BKFD, we first establish a stationary distribution for each cell to represent the transition of cellular developmental states based on the random walk with restart algorithm, and then propose a new distance metric for calculating pseudotime of single cells by introducing the Bhattacharyya kernel matrix. The effectiveness of DTFLOW is rigorously examined by using four single-cell datasets. We compare the efficiency of DTFLOW with the published state-of-the-art methods. Simulation results suggest that DTFLOW has superior accuracy and strong robustness properties for constructing pseudotime trajectories. The Python source code of DTFLOW can be freely accessed at https://github.com/statway/DTFLOW.

Graph kernel based link prediction for signed social networks

By revealing potential relationships between users, link prediction has long been considered as a fundamental research issue in singed social networks. The key of link prediction is to measure the similarity between users. Existing works use connections between target users or their common neighbors to measure user similarity. Rich information available for link prediction is missing since use similarity is widely influenced by many users via social connections. We therefore propose a novel graph kernel based link prediction method, which predicts links by comparing user similarity via signed social network’s structural information: we first generate a set of subgraphs with different strength of social relations for each user, then calculate the graph kernel similarities between subgraphs, in which Bhattacharyya kernel is used to measure the similarity of the k-dimensional Gaussian distributions related to each k-order Krylov subspace generated for each subgraph, and finally train SVM classifier with user similarity information to predict links. Experiments held on real application datasets show that our proposed method has good link prediction performances on both positive and negative link prediction. Our method has significantly higher link prediction accuracy and F1-score than existing works.

Fast and robust object tracking via Accept–Reject color histogram-based method

We present a new framework for real-time tracking method of complex non-rigid objects. This new method successfully coped with camera motion, partial occlusions, and target scale variations. The shape of the object tracker is approximated by an ellipse and its appearance by histogram based features derived from local image properties. We use an efficient search scheme (Accept–Reject color histogram-based method (AR), using Bhattacharyya kernel as a similarity measure) to find the image region with a histogram most similar to the target of object tracker. In this paper, we address the problem of scale/shape adaptation and orientation changes of the target. The proposed approach is compared with recent state-of-the-art algorithms. Extensive experiments are performed to testify the proposed method and validate its robustness and effectiveness to track the scale and orientation changes of the target in real-time.

Generative Topographic Mapping (GTM): Universal Tool for Data Visualization, Structure-Activity Modeling and Dataset Comparison.

Here, the utility of Generative Topographic Maps (GTM) for data visualization, structure-activity modeling and database comparison is evaluated, on hand of subsets of the Database of Useful Decoys (DUD). Unlike other popular dimensionality reduction approaches like Principal Component Analysis, Sammon Mapping or Self-Organizing Maps, the great advantage of GTMs is providing data probability distribution functions (PDF), both in the high-dimensional space defined by molecular descriptors and in 2D latent space. PDFs for the molecules of different activity classes were successfully used to build classification models in the framework of the Bayesian approach. Because PDFs are represented by a mixture of Gaussian functions, the Bhattacharyya kernel has been proposed as a measure of the overlap of datasets, which leads to an elegant method of global comparison of chemical libraries.

Using geometric properties of topographic manifold to detect and track eyes for human-computer interaction

Automatic eye detection and tracking is an important component for advanced human-computer interface design. Accurate eye localization can help develop a successful system for face recognition and emotion identification. In this article, we propose a novel approach to detect and track eyes using geometric surface features on topographic manifold of eye images. First, in the joint spatial-intensity domain, a facial image is treated as a 3D terrain surface or image topographic manifold. In particular, eye regions exhibit certain intrinsic geometric traits on this topographic manifold, namely, the pit -labeled center and hillside -like surround regions. Applying a terrain classification procedure on the topographic manifold of facial images, each location of the manifold can be labeled to generate a terrain map. We use the distribution of terrain labels to represent the eye terrain pattern. The Bhattacharyya affinity is employed to measure the distribution similarity between two topographic manifolds. Based on the Bhattacharyya kernel, a support vector machine is applied for selecting proper eye pairs from the pit-labeled candidates. Second, given detected eyes on the first frame of a video sequence, a mutual-information-based fitting function is defined to describe the similarity between two terrain surfaces of neighboring frames. By optimizing the fitting function, eye locations are updated for subsequent frames. The distinction of the proposed approach lies in that both eye detection and eye tracking are performed on the derived topographic manifold, rather than on an original-intensity image domain. The robustness of the approach is demonstrated under various imaging conditions and with different facial appearances, using both static images and video sequences without background constraints.