Zhang, Daoqiang


Nystr\"om Subspace Learning for Large-scale SVMs

arXiv.org Machine Learning

As an implementation of the Nystr\"{o}m method, Nystr\"{o}m computational regularization (NCR) imposed on kernel classification and kernel ridge regression has proven capable of achieving optimal bounds in the large-scale statistical learning setting, while enjoying much better time complexity. In this study, we propose a Nystr\"{o}m subspace learning (NSL) framework to reveal that all you need for employing the Nystr\"{o}m method, including NCR, upon any kernel SVM is to use the efficient off-the-shelf linear SVM solvers as a black box. Based on our analysis, the bounds developed for the Nystr\"{o}m method are linked to NSL, and the analytical difference between two distinct implementations of the Nystr\"{o}m method is clearly presented. Besides, NSL also leads to sharper theoretical results for the clustered Nystr\"{o}m method. Finally, both regression and classification tasks are performed to compare two implementations of the Nystr\"{o}m method.


Deep Hyperalignment

Neural Information Processing Systems

This paper proposes Deep Hyperalignment (DHA) as a regularized, deep extension, scalable Hyperalignment (HA) method, which is well-suited for applying functional alignment to fMRI datasets with nonlinearity, high-dimensionality (broad ROI), and a large number of subjects. Unlink previous methods, DHA is not limited by a restricted fixed kernel function. Further, it uses a parametric approach, rank-m Singular Value Decomposition (SVD), and stochastic gradient descent for optimization. Therefore, DHA has a suitable time complexity for large datasets, and DHA does not require the training data when it computes the functional alignment for a new subject. Experimental studies on multi-subject fMRI analysis confirm that the DHA method achieves superior performance to other state-of-the-art HA algorithms.


Supervised Hyperalignment for multi-subject fMRI data alignment

arXiv.org Machine Learning

Hyperalignment has been widely employed in Multivariate Pattern (MVP) analysis to discover the cognitive states in the human brains based on multi-subject functional Magnetic Resonance Imaging (fMRI) datasets. Most of the existing HA methods utilized unsupervised approaches, where they only maximized the correlation between the voxels with the same position in the time series. However, these unsupervised solutions may not be optimum for handling the functional alignment in the supervised MVP problems. This paper proposes a Supervised Hyperalignment (SHA) method to ensure better functional alignment for MVP analysis, where the proposed method provides a supervised shared space that can maximize the correlation among the stimuli belonging to the same category and minimize the correlation between distinct categories of stimuli. Further, SHA employs a generalized optimization solution, which generates the shared space and calculates the mapped features in a single iteration, hence with optimum time and space complexities for large datasets. Experiments on multi-subject datasets demonstrate that SHA method achieves up to 19% better performance for multi-class problems over the state-of-the-art HA algorithms.


A Graph-Based Decoding Model for Incomplete Multi-Subject fMRI Functional Alignment

arXiv.org Machine Learning

Aggregating multi-subject fMRI data is indispensable for generating valid and general inferences from patterns distributed across human brains. The disparities in anatomical structures and functional topographies of human brains call for aligning fMRI data across subjects. However, the existing functional alignment methods cannot tackle various kinds of fMRI datasets today, especially when they are incomplete, i.e., some of the subjects probably lack the responses to some stimuli, or different subjects might follow different sequences of stimuli. In this paper, a cross-subject graph that depicts the (dis)similarities between samples across subjects is taken as prior information for developing a more flexible framework that suits an assortment of fMRI datasets. However, the high dimension of fMRI data and the use of multiple subjects makes the crude framework time-consuming or unpractical. Therefore, we regularize the framework so that a feasible kernel-based optimization, which permits non-linear feature extraction, could be theoretically developed. Specifically, a low-dimension assumption is imposed on each new feature space to avoid overfitting caused by the high-spatial-low-temporal resolution of fMRI data. Empirical studies confirm that the proposed method under both incompleteness and completeness can achieve better performance than other state-of-the-art functional alignment methods under completeness.


Gradient-based Representational Similarity Analysis with Searchlight for Analyzing fMRI Data

arXiv.org Machine Learning

Representational Similarity Analysis (RSA) aims to explore similarities between neural activities of different stimuli. Classical RSA techniques employ the inverse of the covariance matrix to explore a linear model between the neural activities and task events. However, calculating the inverse of a large-scale covariance matrix is time-consuming and can reduce the stability and robustness of the final analysis. Notably, it becomes severe when the number of samples is too large. For facing this shortcoming, this paper proposes a novel RSA method called gradient-based RSA (GRSA). Moreover, the proposed method is not restricted to a linear model. In fact, there is a growing interest in finding more effective ways of using multi-subject and whole-brain fMRI data. Searchlight technique can extend RSA from the localized brain regions to the whole-brain regions with smaller memory footprint in each process. Based on Searchlight, we propose a new method called Spatiotemporal Searchlight GRSA (SSL-GRSA) that generalizes our ROI-based GRSA algorithm to the whole-brain data. Further, our approach can handle some computational challenges while dealing with large-scale, multi-subject fMRI data. Experimental studies on multi-subject datasets confirm that both proposed approaches achieve superior performance to other state-of-the-art RSA algorithms.


Multi-Objective Cognitive Model: a supervised approach for multi-subject fMRI analysis

arXiv.org Machine Learning

In order to decode the human brain, Multivariate Pattern (MVP) classification generates cognitive models by using functional Magnetic Resonance Imaging (fMRI) datasets. As a standard pipeline in the MVP analysis, brain patterns in multi-subject fMRI dataset must be mapped to a shared space and then a classification model is generated by employing the mapped patterns. However, the MVP models may not provide stable performance on a new fMRI dataset because the standard pipeline uses disjoint steps for generating these models. Indeed, each step in the pipeline includes an objective function with independent optimization approach, where the best solution of each step may not be optimum for the next steps. For tackling the mentioned issue, this paper introduces the Multi-Objective Cognitive Model (MOCM) that utilizes an integrated objective function for MVP analysis rather than just using those disjoint steps. For solving the integrated problem, we proposed a customized multi-objective optimization approach, where all possible solutions are firstly generated, and then our method ranks and selects the robust solutions as the final results. Empirical studies confirm that the proposed method can generate superior performance in comparison with other techniques.


Gradient Hyperalignment for multi-subject fMRI data alignment

arXiv.org Machine Learning

Multi-subject fMRI data analysis is an interesting and challenging problem in human brain decoding studies. The inherent anatomical and functional variability across subjects make it necessary to do both anatomical and functional alignment before classification analysis. Besides, when it comes to big data, time complexity becomes a problem that cannot be ignored. This paper proposes Gradient Hyperalignment (Gradient-HA) as a gradient-based functional alignment method that is suitable for multi-subject fMRI datasets with large amounts of samples and voxels. The advantage of Gradient-HA is that it can solve independence and high dimension problems by using Independent Component Analysis (ICA) and Stochastic Gradient Ascent (SGA). Validation using multi-classification tasks on big data demonstrates that Gradient-HA method has less time complexity and better or comparable performance compared with other state-of-the-art functional alignment methods.


Deep Hyperalignment

Neural Information Processing Systems

This paper proposes Deep Hyperalignment (DHA) as a regularized, deep extension, scalable Hyperalignment (HA) method, which is well-suited for applying functional alignment to fMRI datasets with nonlinearity, high-dimensionality (broad ROI), and a large number of subjects. Unlink previous methods, DHA is not limited by a restricted fixed kernel function. Further, it uses a parametric approach, rank-m Singular Value Decomposition (SVD), and stochastic gradient descent for optimization. Therefore, DHA has a suitable time complexity for large datasets, and DHA does not require the training data when it computes the functional alignment for a new subject. Experimental studies on multi-subject fMRI analysis confirm that the DHA method achieves superior performance to other state-of-the-art HA algorithms.


Deep Hyperalignment

arXiv.org Machine Learning

This paper proposes Deep Hyperalignment (DHA) as a regularized, deep extension, scalable Hyperalignment (HA) method, which is well-suited for applying functional alignment to fMRI datasets with nonlinearity, high-dimensionality (broad ROI), and a large number of subjects. Unlink previous methods, DHA is not limited by a restricted fixed kernel function. Further, it uses a parametric approach, rank-$m$ Singular Value Decomposition (SVD), and stochastic gradient descent for optimization. Therefore, DHA has a suitable time complexity for large datasets, and DHA does not require the training data when it computes the functional alignment for a new subject. Experimental studies on multi-subject fMRI analysis confirm that the DHA method achieves superior performance to other state-of-the-art HA algorithms.


Anatomical Pattern Analysis for decoding visual stimuli in human brains

arXiv.org Machine Learning

Background: A universal unanswered question in neuroscience and machine learning is whether computers can decode the patterns of the human brain. Multi-Voxels Pattern Analysis (MVPA) is a critical tool for addressing this question. However, there are two challenges in the previous MVPA methods, which include decreasing sparsity and noise in the extracted features and increasing the performance of prediction. Methods: In overcoming mentioned challenges, this paper proposes Anatomical Pattern Analysis (APA) for decoding visual stimuli in the human brain. This framework develops a novel anatomical feature extraction method and a new imbalance AdaBoost algorithm for binary classification. Further, it utilizes an Error-Correcting Output Codes (ECOC) method for multiclass prediction. APA can automatically detect active regions for each category of the visual stimuli. Moreover, it enables us to combine homogeneous datasets for applying advanced classification. Results and Conclusions: Experimental studies on 4 visual categories (words, consonants, objects and scrambled photos) demonstrate that the proposed approach achieves superior performance to state-of-the-art methods.