While Big Data offers the great potential for revolutionizing all aspects of our society, harvesting of valuable knowledge from Big Data is an extremely challenging task. The large scale and rapidly growing information hidden in the unprecedented volumes of non-traditional data requires the development of decision-making algorithms. Recent successes in machine learning, particularly deep learning, has led to breakthroughs in real-world applications such as autonomous driving, healthcare, cybersecurity, speech and image recognition, personalized news feeds, and financial markets.

While these models may provide the state-of-the-art and impressive prediction accuracies, they usually offer little insight into the inner workings of the model and how a decision is made. The decision-makers cannot obtain human-intelligible explanations for the decisions of models, which impede the applications in mission-critical areas. This situation is even severely worse in complex data analytics. It is, therefore, imperative to develop explainable computation intelligent learning models with excellent predictive accuracy to provide safe, reliable, and scientific basis for determination.

Numerous recent works have presented various endeavors on this issue but left many important questions unresolved. The first challenging problem is how to construct self-explanatory models or how to improve the explicit understanding and explainability of a model without the loss of accuracy. In addition, high-dimensional or ultra-high-dimensional data are common in large and complex data analytics. In these cases, the construction of interpretable model becomes quite difficult and complex. Further, how to evaluate and quantify the explainability of a model is a lack of consistent and clear description. Moreover, auditable, repeatable and reliable process of the computational models is crucial to decision-makers. For example, decision-makers need explicit explanation and analysis of the intermediate features produced in a model; thus, the interpretation of intermediate processes is requisite. Subsequently, the problem of efficient optimization exists in explainable computational intelligent models. These raise many essential issues on how to develop explainable data analytics in computational intelligence.

This Topical Collection aims to bring together original research articles and review articles that will present the latest theoretical and technical advancements of machine and deep learning models. We hope that this Topical Collection will: 1) improve the understanding and explainability of machine learning and deep neural networks; 2) enhance the mathematical foundation of deep neural networks; and 3) increase the computational efficiency and stability of the machine and deep learning training process with new algorithms that will scale.

Le et al. propose the SPINet, a novel Selfsupervised Point Cloud Frame Interpolation Network. Given two consecutive point cloud frames, by using the proposed method, low frame rate point cloud streams can be upsampled to high frame rate ones even though the ground-truth point cloud of the intermediate frame is not accessible. To achieve that, a coarse intermediate frame generation module is utilized to generate coarse intermediate point cloud frame adaptive to any desired motion. Then, a novel local spatial fusion module is presented to efficiently retain local geometric consistency. Eventually, self-supervised strategy is applied to relieve the model from the ground-truth data and guide the training process. Extensive experiments on KITTI odometry dataset and nuScenes dataset demonstrate the performance and effectiveness of the proposed SPINet.

Qin et al. design a neural network to investigate this kind of optimization problem. The global existence and boundedness of state solutions are demonstrated. In addition, it is proved that the state solution of the proposed approach converges to the optimal solution set of the problem. Compared with the existing optimization approaches, the proposed neural network has a simple structure with few numbers of state variables. Moreover, strict convexity and strong convexity are not required. Finally, a simulation and a real application are given to certificate the characteristic of obtained conclusions.

Gu et al. apply the graph pointer network model (GPN) trained by hierarchical reinforcement learning (HRL) and the multi-head attention-based pointer network model trained by Advantage Actor-Critic (A2C) to solve the constrained 0–1 quadratic programming problem (CBQP) with linear constraints. In addition, the bidirectional mask mechanism is introduced into the network to increase the constraint satisfaction rate of the solution. The experiment shows that no matter the objective function of the CBQP problem is linear or nonlinear, different data set distribution, or the scale, the pointer network trained by reinforcement learning has better results than traditional optimization algorithms in solving time, accuracy, stability and constraint satisfaction rate, and with the increase in the size of the problem, this advantage becomes more obvious.

Che et al. introduced l0 norm to enhance the sparsity of factorized matrices, which can improve the robustness of GNMF. As the discontinuity of l0 norm and minimizing it is a NP-hard problem, five functions approximating l0 norm are used to transform the problem of the sparse graph nonnegative matrix factorization (SGNMF) to a global optimization problem. Finally, the multiplicative updating rules (MUR) are designed to solve the problem, and the convergence of algorithm is proven. In the experiment, the accuracy and normalized mutual information of clustering results show the superior performance of SGNMF on five public datasets.

Hoedt et al. investigate the performance of different explanation methods on detecting non-obvious causes for a prediction by using adversarial perturbations as a ground truth. In addition, these explainers are compared to a new non-random baseline in both audio (singing voice detector) and images (different ImageNet classifiers) domains. To treat perturbation- and gradient-based explainers fairly, a pixel-wise attribution aggregation is proposed, where different granularities are overcome by mapping all attributions to interpretable segments. The results suggest that the investigated explainers often fail to identify the input regions most relevant for a prediction; hence, it remains questionable whether explanations are useful or potentially misleading.

Njah et al. propose an interpretable approach for dimension reduction under the curse of dimensionality. The framework explicitly employs the unification strategy in order to tackle the complexity-related challenges of high-dimensional data. It allows clustering the features into highly dependent groups through the density-based hierarchical partitioning algorithm, and it ensures abstracting the information among each group into a representative latent variable, through the hierarchical expectation maximization algorithm. The results prove that the proposed dimension reduction algorithm yields a user-friendly model that not only minimizes the information loss due to the reduction process, but also escapes data overfitting due to the lack of records.

Raab et al. introduce an application-aware approach for an explainable and hybrid deep learning-based detection of seizures in multivariate EEG time series. The deep learning models and domain knowledge are combined on seizure detection, namely (a) frequency bands, (b) location of EEG leads and (c) temporal characteristics. It is found that the visualizations of the proposed explanation module can lead to a substantially lower time for validating the predictions and leverage an increase in interpretability, trust and confidence compared to selected feature contribution plots.

Shi et al. propose a masked manifold mixup and fuzzy memory contrastive learning (M3FM) method for transfer-based few-shot learning to improve the generalization ability. A regularization technique is designed to enhance the model’s learning of local features by masking and mixing the data manifold in the hidden states of neural networks. Then, a momentum updated fuzzy memory is adopted in contrastive learning with the masked mixup manifold to help the model learn the specific distinctions of different categories. Experimental results show that the proposed method outperforms previous baseline methods on miniImageNet, CUB-200, and CIFAR-FS benchmarks.

Feng et al. propose the Pythagorean fuzzy-based distance operators, which take into account the three conventional number of parameters of Pythagorean fuzzy sets against the existing practice, and as well incorporate the whole parameters to avoid error due to exclusion as witnessed in other distance operators. The new Pythagorean fuzzy distance techniques are validated with regard to its alignment with distance operator's properties. The applications of the proposed Pythagorean fuzzy distance and its weighted version in cases involving pattern classification and disease diagnosis via deep learning approach are demonstrated, where patterns, diseases and patients are presented as Pythagorean fuzzy values.

Tang et al. propose a new object detection framework named PointDet++. The first step is to use the trained pose estimation model to obtain the local features of human body. Then, the local features and global features are reconstructed, respectively, with transformer encoder and graph convolution. In the output layer, the local features and global features are integrated according to the target to be detected, so as to improve the detection performance of the proposed model. Specifically, the proposed framework significantly outperforms state of the art by 10.3 AP scores on field operation dataset in chemical plant.