Feature Learning Research Articles

Hierarchically Recognizing Vector Graphics and A New Chart-Based Vector Graphics Dataset.

The conventional approach to image recognition has been based on raster graphics, which can suffer from aliasing and information loss when scaled up or down. In this paper, we propose a novel approach that leverages the benefits of vector graphics for object localization and classification. Our method, called YOLaT (You Only Look at Text), takes the textual document of vector graphics as input, rather than rendering it into pixels. YOLaT builds multi-graphs to model the structural and spatial information in vector graphics and utilizes a dual-stream graph neural network (GNN) to detect objects from the graph. However, for real-world vector graphics, YOLaT only models in flat GNN with vertexes as nodes ignore higher-level information of vector data. Therefore, we propose YOLaT++ to learn Multi-level Abstraction Feature Learning from a new perspective: Primitive Shapes to Curves and Points. On the other hand, given few public datasets focus on vector graphics, data-driven learning cannot exert its full power on this format. We provide a large-scale and challenging dataset for Chart-based Vector Graphics Detection and Chart Understanding, termed VG-DCU, with vector graphics, raster graphics, annotations, and raw data drawn for creating these vector charts. Experiments show that the YOLaT series outperforms both vector graphics and raster graphics-based object detection methods on both subsets of VG-DCU in terms of both accuracy and efficiency, showcasing the potential of vector graphics for image recognition tasks.

IoT-based Ubiquitous Healthcare System with Intelligent Approach to an Epidemic

Background:: The recent pandemic has shown its different shades across various solicitations, especially in the healthcare sector. It has a great impact on transforming the traditional healthcare architecture, which is based on the physical approaching model, into the modern or remote healthcare system. The remote healthcare approach is quite achievable now by utilizing multiple modern technological paradigms like AI, Cloud Computing, Feature Learning, the Internet of Things, etc. Accordingly, the pharmaceutical section is the most fascinating province to be inspected by medical experts in restoring the evolutionary healthcare approaches. COVID-19 has created chaos in the society for which many unexpected deaths occur due to delays in medication and the improper prognosis at an irreverent plan. As medical management applications have become ubiquitous in nature and technology-oriented, patient monitoring systems are getting more popular among medical actors. Method: The Internet of Things (IoT) has achieved the solution criteria for providing such a huge service across the globe at any time and in any place. A quite feasible and approachable framework has evolved through this work regarding hardware development and predictive patent analysis. The desired model illustrates various approaches to the development of a wearable sensor medium that will be directly attached to the body of the patients. These sensor mediums are mostly accountable for observing body parameters like blood pressure, heart rate, temperature, etc., and transmit these data to the cloud storage via various intermediate steps. The storage medium in the cloud will be storing the sensor-acquired data in a time-to-time manner for a detailed analysis. Further, the stored data will be normalized and processed across various predictive models. Results and Conclusion: The model with the best accuracy will be treated as the resultant model among the numerous predictive models deployed in the cloud. During the hardware development process, several hardware modules are discussed. After receiving sensor-acquired data, it will be processed by the cloud's multiple machine-learning models. Finally, thorough analytics will be developed based on a meticulous examination of the patients' cardinal, essential, and fundamental data and communicated to the appropriate physicians for action. This model will then be used for the data dissemination procedure, in which an alarm message will be issued to the appropriate authorities.

Accelerating Vertical Federated Learning

Privacy, security and data governance constraints rule out a brute force process in the integration of cross-silo data, which inherits the development of the Internet of Things. Federated learning is proposed to ensure that all parties can collaboratively complete the training task while the data is not out of the local. Vertical federated learning is a specialization of federated learning for distributed features. To preserve privacy, homomorphic encryption is applied to enable encrypted operations without decryption. Nevertheless, together with a robust security guarantee, homomorphic encryption brings extra communication and computation overhead. In this paper, we analyze the current bottlenecks of vertical federated learning under homomorphic encryption comprehensively and numerically. We propose a straggler-resilient and computation-efficient accelerating system that reduces the communication overhead in heterogeneous scenarios by 65.26% at most and reduces the computation overhead caused by homomorphic encryption by 40.66% at most. Our system can improve the robustness and efficiency of the current vertical federated learning framework without loss of security.

Biarchetype Analysis: Simultaneous Learning of Observations and Features Based on Extremes.

We introduce a novel exploratory technique, termed biarchetype analysis, which extends archetype analysis to simultaneously identify archetypes of both observations and features. This innovative unsupervised machine learning tool aims to represent observations and features through instances of pure types, or biarchetypes, which are easily interpretable as they embody mixtures of observations and features. Furthermore, the observations and features are expressed as mixtures of the biarchetypes, which makes the structure of the data easier to understand. We propose an algorithm to solve biarchetype analysis. Although clustering is not the primary aim of this technique, biarchetype analysis is demonstrated to offer significant advantages over biclustering methods, particularly in terms of interpretability. This is attributed to biarchetypes being extreme instances, in contrast to the centroids produced by biclustering, which inherently enhances human comprehension. The application of biarchetype analysis across various machine learning challenges underscores its value.

Image analysis for classifying coffee bean quality using a multi feature and machine learning approach

Price and customer satisfaction depend on coffee bean quality. The coffee industry must analyze coffee bean quality. Global demand for robusta coffee is high. Coffee industry professionals mostly understand coffee bean quality. Thus, an image analysis using a computer vision-based approach for classifying robusta coffee bean quality is required. Image acquisition, region of interest (ROI) detection, pre-processing, segmentation, feature extraction, feature selection, and classification are covered in this study. A multi-feature derived based on color, shape, and texture features was employed in feature extraction, followed by feature selection using principal component analysis (PCA). Several machine-learning methods classified the coffee beans. The method performance was assessed using precision, recall, and accuracy. The selected features using the backpropagation neural network (BPNN) classifier outperformed others with 98.54% accuracy.

Enhancing soil organic carbon prediction of LUCAS soil database using deep learning and deep feature selection

The main terrestrial carbon (C) fraction is soil organic carbon (SOC), which has a considerable effect on climate change and greenhouse gas emissions through the absorption and sequestration of carbon dioxide (CO2). This has made SOC assessment very important from both economic and environmental viewpoints. The growing count of soil spectral libraries (SSLs) from regional to global scales has brought a tremendous opportunity for the quantification of SOC through developing spectral-based prediction models. Hence, there is a need to take advantage of big data analytics for spectral data processing. The unique ability of deep learning (DL) techniques to leverage important features of high-dimensional large-scale SSLs has made them top-demanding for more sophisticated modeling. The core objective of the present study was to assess the ability of two different DL algorithms, i.e., one-dimensional convolutional neural network (1DCNN) and fully connected neural network (FCNN) coupled with stacked autoencoder (SAE) feature extraction for SOC prediction based on the data from the land use/cover area frame statistical survey (LUCAS) database. SAE extracted the high-level deep features from the visible–near-infrared–shortwave infrared (Vis–NIR–SWIR) spectra of 11441 soil samples, which were then considered as inputs to the 1DCNN and FCNN models for predicting the SOC content. Both SAE-DL feature-selected models yielded higher accuracy than those the DL developed on the entire spectra and a random forest (RF) model was constructed for comparison. The best prediction was achieved by SAE-1DCNN (R2= 0.78, RMSE = 3.94%, RPD = 4.88, RPIQ = 3.91) followed by 1DCNN (R2= 0.73, RMSE = 5.43%, RPD = 3.67, RPIQ = 2.84) proving the superiority of 1DCNN over FCNN in this study. These results supported the applicability of combined deep features extraction and regression methods for predicting SOC using high dimensional large-scale SSLs.

TMODINET: A trustworthy multi-omics dynamic learning integration network for cancer diagnostic

Multiple types of omics data contain a wealth of biomedical information which reflect different aspects of clinical samples. Multi-omics integrated analysis is more likely to lead to more accurate clinical decisions. Existing cancer diagnostic methods based on multi-omics data integration mainly focus on the classification accuracy of the model, while neglecting the interpretability of the internal mechanism and the reliability of the results, which are crucial in specific domains such as precision medicine and the life sciences. To overcome this limitation, we propose a trustworthy multi-omics dynamic learning framework (TMODINET) for cancer diagnostic. The framework employs multi-omics adaptive dynamic learning to process each sample to provide patient-centered personality diagnosis by using self-attentional learning of features and modalities. To characterize the correlation between samples well, we introduce a graph dynamic learning method which can adaptively adjust the graph structure according to the specific classification results for specific graph convolutional networks (GCN) learning. Moreover, we utilize an uncertainty mechanism by employing Dirichlet distribution and Dempster-Shafer theory to obtain uncertainty and integrate multi-omics data at the decision level, ensuring trustworthy for cancer diagnosis. Extensive experiments on four real-world multimodal medical datasets are conducted. Compared to state-of-the-art methods, the superior performance and trustworthiness of our proposed algorithm are clearly validated. Our model has great potential for clinical diagnosis.

Towards Visual-Prompt Temporal Answer Grounding in Instructional Video.

Temporal answer grounding in instructional video (TAGV) is a new task naturally derived from temporal sentence grounding in general video (TSGV). Given an untrimmed instructional video and a text question, this task aims at locating the frame span from the video that can semantically answer the question, i.e., visual answer. Existing methods tend to solve the TAGV problem with a visual span-based predictor, taking visual information to predict the start and end frames in the video. However, due to the weak correlations between the semantic features of the textual question and visual answer, current methods using the visual span-based predictor do not work well in the TAGV task. In this paper, we propose a visual-prompt text span localization (VPTSL) method, which introduces the timestamped subtitles for a text span-based predictor. Specifically, the visual prompt is a learnable feature embedding, which brings visual knowledge to the pre-trained language model. Meanwhile, the text span-based predictor learns joint semantic representations from the input text question, video subtitles, and visual prompt feature with the pre-trained language model. Thus, the TAGV is reformulated as the task of the visual-prompt subtitle span localization for the visual answer. Extensive experiments on five instructional video datasets, namely MedVidQA, TutorialVQA, VehicleVQA, CrossTalk and Coin, show that the proposed method outperforms several state-of-the-art (SOTA) methods by a large margin in terms of mIoU score, which demonstrates the effectiveness of the proposed visual prompt and text span-based predictor.

DeepMulticut: Deep Learning of Multicut Problem for Neuron Segmentation From Electron Microscopy Volume.

Superpixel aggregation is a powerful tool for automated neuron segmentation from electron microscopy (EM) volume. However, existing graph partitioning methods for superpixel aggregation still involve two separate stages-model estimation and model solving, and therefore model error is inherent. To address this issue, we integrate the two stages and propose an end-to-end aggregation framework based on deep learning of the minimum cost multicut problem called DeepMulticut. The core challenge lies in differentiating the NP-hard multicut problem, whose constraint number is exponential in the problem size. With this in mind, we resort to relaxing the combinatorial solver-the greedy additive edge contraction (GAEC)-to a continuous Soft-GAEC algorithm, whose limit is shown to be the vanilla GAEC. Such relaxation thus allows the DeepMulticut to integrate edge cost estimators, Edge-CNNs, into a differentiable multicut optimization system and allows a decision-oriented loss to feed decision quality back to the Edge-CNNs for adaptive discriminative feature learning. Hence, the model estimators, Edge-CNNs, can be trained to improve partitioning decisions directly while beyond the NP-hardness. Also, we explain the rationale behind the DeepMulticut framework from the perspective of bi-level optimization. Extensive experiments on three public EM datasets demonstrate the effectiveness of the proposed DeepMulticut.

Temporal denoising and deep feature learning for enhanced defect detection in thermography using stacked denoising convolution autoencoder

Thermal wave imaging uses the temporal temperature distribution over the object’s surface for subsurface analysis. However, the noise generated during experimentation corrupts this temporal history and hampers the detection of defect signatures. As denoising of the temporal thermal history enhances the defect detectability, this study offers a stacked denoising convolution autoencoder (SDCAE) in frequency-modulated thermal wave imaging with one-dimensional convolution layers to reduce noise in temporal thermal evolution and train high-level features resulting in improved defect signs. Experimental results on mild steel and carbon fiber reinforced polymer specimens with different sizes of defects at various depths demonstrate that integrating temporal denoising and deep feature learning techniques into a single novel framework significantly improved defect detectability. In addition, defect signal-to-noise ratios of the denoised thermal data and latent space of the proposed model compared to conventional autoencoder and dimensionality reduction techniques recommend the superiority of the proposed method.

Graph-guided imputation-free incomplete multi-view clustering

Recently, multi-view clustering methods have garnered considerable attention and have been applied in various domains. However, in practical scenarios, some samples may lack specific views, giving rise to the challenge of incomplete multi-view clustering. While some methods focus on completing missing data, incorrect completion can negatively affect representation learning. Moreover, separating completion and representation learning prevents the attainment of an optimal representation. Other methods eschew completion but singularly concentrate on either feature information or graph information, thus failing to achieve comprehensive representations. To address these challenges, we propose a graph-guided, imputation-free method for incomplete multi-view clustering. Unlike completion-based methods, our approach aims to maximize the utilization of existing information by simultaneously considering feature and graph information. This is realized through the feature learning component and the graph learning component. Introducing a degradation network, the former reconstructs view-specific representations proximate to available samples from a unified representation, seamlessly integrating feature information into the unified representation. Leveraging the semi-supervised idea, the latter utilizes reliable graph information from available samples to guide the learning of the unified representation. These two components collaborate to acquire a comprehensive unified representation for multi-view clustering. Extensive experiments conducted on real datasets demonstrate the effectiveness and competitiveness of the proposed method when compared with other state-of-the-art methods. Our code will be released on https://github.com/yff-java/GIMVC/.

Time-segment-wise feature fusion transformer for multi-modal fault diagnosis

Mechanical fault diagnosis is crucial to ensure the safe operations of equipment in intelligent manufacturing systems. Recently, deep learning based fault diagnosis methods have achieved remarkable advancements with monitored data from a single sensor. However, obtaining satisfactory diagnostic results based on a single sensor is often difficult because the complementary information between different sensors is ignored. Extracting comprehensive fault features from multi-modal data is a problem that remains to be solved. To address these challenges, a time-segment-wise feature fusion Transformer (FFTR) is proposed in this paper. First, the signals from various modalities as multiple channels are normalized channel-by-channel and form a multi-modal sample. Second, a time-segment-wise feature learning network is designed to transform a multi-modal sample into several fusion features through the sequential processes of sample segmentation, segment-level feature extraction and time-aligned feature fusion. Finally, a Transformer network is employed for comprehensive multi-modal feature analysis and fault classification. In addition, a joint loss function is designed to comprehensively train the end-to-end FFTR. The comparison experiment with other baseline methods is conducted on two multi-modal datasets. The experimental results show that FFTR achieves 3.69% and 3.93% higher diagnostic accuracy than baseline on two datasets respectively and can address real-world problems effectively.

A Curriculum-Style Self-Training Approach for Source-Free Semantic Segmentation.

Source-free domain adaptation has developed rapidly in recent years, where the well-trained source model is adapted to the target domain instead of the source data, offering the potential for privacy concerns and intellectual property protection. However, a number of feature alignment techniques in prior domain adaptation methods are not feasible in this challenging problem setting. Thereby, we resort to probing inherent domain-invariant feature learning and propose a curriculum-style self-training approach for source-free domain adaptive semantic segmentation. In particular, we introduce a curriculum-style entropy minimization method to explore the implicit knowledge from the source model, which fits the trained source model to the target data using certain information from easy-to-hard predictions. We then train the segmentation network by the proposed complementary curriculum-style self-training, which utilizes the negative and positive pseudo labels following the curriculum-learning manner. Although negative pseudo-labels with high uncertainty cannot be identified with the correct labels, they can definitely indicate absent classes. Moreover, we employ an information propagation scheme to further reduce the intra-domain discrepancy within the target domain, which could act as a standard post-processing method for the domain adaptation field. Furthermore, we extend the proposed method to a more challenging black-box source model scenario where only the source model's predictions are available. Extensive experiments validate that our method yields state-of-the-art performance on source-free semantic segmentation tasks for both synthetic-to-real and adverse conditions datasets.

Robust Domain Adaptive Object Detection With Unified Multi-Granularity Alignment.

Domain adaptive detection aims to improve the generalization of detectors on target domain. To reduce discrepancy in feature distributions between two domains, recent approaches achieve domain adaption through feature alignment in different granularities via adversarial learning. However, they neglect the relationship between multiple granularities and different features in alignment, degrading detection. Addressing this, we introduce a unified multi-granularity alignment (MGA)-based detection framework for domain-invariant feature learning. The key is to encode the dependencies across different granularities including pixel-, instance-, and category-levels simultaneously to align two domains. Specifically, based on pixel-level features, we first develop an omni-scale gated fusion (OSGF) module to aggregate discriminative representations of instances with scale-aware convolutions, leading to robust multi-scale detection. Besides, we introduce multi-granularity discriminators to identify where, either source or target domains, different granularities of samples come from. Note that, MGA not only leverages instance discriminability in different categories but also exploits category consistency between two domains for detection. Furthermore, we present an adaptive exponential moving average (AEMA) strategy that explores model assessments for model update to improve pseudo labels and alleviate local misalignment problem, boosting detection robustness. Extensive experiments on multiple domain adaption scenarios validate the superiority of MGA over other approaches on FCOS and Faster R-CNN detectors.

A lightweight multi-scale multi-angle dynamic interactive Transformer-CNN fusion model for 3D medical image segmentation

Combining Convolutional Neural Network(CNN) and Transformer has become one of the mainstream methods for three-dimensional (3D) medical image segmentation. However, the complexity and diversity of target forms in 3D medical images require models to capture complex feature information for segmentation, resulting in an excessive number of parameters which are not conducive to training and deployment. Therefore, we have developed a lightweight 3D multi-target semantic segmentation model. In order to enhance contextual texture connections and reinforce the expression of detailed feature information, we designed a multi-scale and multi-angle feature interaction module to enhance feature representation by interacting multi-scale features from different perspectives. To address the issue of attention collapse in Transformers, leading to the neglect of other detailed feature learning, we utilized local features as dynamic parameters to interact with global features, dynamically grouping and learning critical features from global features, thereby enhancing the model's ability to learn detailed features. While ensuring the segmentation capability of the model, we aimed to keep the model lightweight, resulting in a total of 9.63M parameters. Extensive experiments were conducted on public datasets ACDC and Brats2018, as well as a private dataset, Temporal Bone CT. The results indicate that our proposed model is more competitive compared to the latest techniques in 3D medical image segmentation.

Broad Distributed Game Learning for intelligent classification in rolling bearing fault diagnosis

As a new Single Layer Feedforward Network (SLFN) architecture, Broad Learning System (BLS) has been widely used in the field of fault diagnosis because of its fast-training speed and high generalization capability. However, when features in different classes of signals are similar or weak, BLS generates a large number of redundant features that may be difficult to classify accurately. In view of this, a new Broad Distributed Game Learning (BDGL) method is proposed in this paper, which maps data into the game space by constructing two non-parallel game hyperplanes to achieve game and segmentation of different similar features, thereby making the data linearly differentiable in the game space. Meanwhile, a linear distribution constraint term is designed to reduce noise fitting and weak feature learning in training data learning by limiting the complexity of model parameters, thereby making the solution of the objective function simpler and faster. By comparing the Precision, Recall, F-score, Kappa and Accuracy of BDGL and the comparison methods on the two types of rolling bearing experimental data, the results show that BDGL has a high classification accuracy. In addition, the experimental results on small and noisy samples once again demonstrate the effectiveness of BDGL, which provides an efficient solution for rolling bearing fault diagnosis.

Learning From Human Attention for Attribute-Assisted Visual Recognition.

With prior knowledge of seen objects, humans have a remarkable ability to recognize novel objects using shared and distinct local attributes. This is significant for the challenging tasks of zero-shot learning (ZSL) and fine-grained visual classification (FGVC), where the discriminative attributes of objects have played an important role. Inspired by human visual attention, neural networks have widely exploited the attention mechanism to learn the locally discriminative attributes for challenging tasks. Though greatly promoted the development of these fields, existing works mainly focus on learning the region embeddings of different attribute features and neglect the importance of discriminative attribute localization. It is also unclear whether the learned attention truly matches the real human attention. To tackle this problem, this paper proposes to employ real human gaze data for visual recognition networks to learn from human attention. Specifically, we design a unified Attribute Attention Network (A 2Net) that learns from human attention for both ZSL and FGVC tasks. The overall model consists of an attribute attention branch and a baseline classification network. On top of the image feature maps provided by the baseline classification network, the attribute attention branch employs attribute prototypes to produce attribute attention maps and attribute features. The attribute attention maps are converted to gaze-like attentions to be aligned with real human gaze attention. To guarantee the effectiveness of attribute feature learning, we further align the extracted attribute features with attribute-defined class embeddings. To facilitate learning from human gaze attention for the visual recognition problems, we design a bird classification game to collect real human gaze data using the CUB dataset via an eye-tracker device. Experiments on ZSL and FGVC tasks without/with real human gaze data validate the benefits and accuracy of our proposed model. This work supports the promising benefits of collecting human gaze datasets and automatic gaze estimation algorithms learning from human attention for high-level computer vision tasks.

Enhancing SNR in CEST imaging: A deep learning approach with a denoising convolutional autoencoder.

To develop a SNR enhancement method for CEST imaging using a denoising convolutional autoencoder (DCAE) and compare its performance with state-of-the-art denoising methods. The DCAE-CEST model encompasses an encoder and a decoder network. The encoder learns features from the input CEST Z-spectrum via a series of one-dimensional convolutions, nonlinearity applications, and pooling. Subsequently, the decoder reconstructs an output denoised Z-spectrum using a series of up-sampling and convolution layers. The DCAE-CEST model underwent multistage training in an environment constrained by Kullback-Leibler divergence, while ensuring data adaptability through context learning using Principal Component Analysis-processed Z-spectrum as a reference. The model was trained using simulated Z-spectra, and its performance was evaluated using both simulated data and in vivo data from an animal tumor model. Maps of amide proton transfer (APT) and nuclear Overhauser enhancement (NOE) effects were quantified using the multiple-pool Lorentzian fit, along with an apparent exchange-dependent relaxation metric. In digital phantom experiments, the DCAE-CEST method exhibited superior performance, surpassing existing denoising techniques, as indicated by the peak SNR and Structural Similarity Index. Additionally, in vivo data further confirm the effectiveness of the DCAE-CEST in denoising the APT and NOE maps when compared with other methods. Although no significant difference was observed in APT between tumors and normal tissues, there was a significant difference in NOE, consistent with previous findings. The DCAE-CEST can learn the most important features of the CEST Z-spectrum and provide the most effective denoising solution compared with other methods.

Gradient Harmonization in Unsupervised Domain Adaptation.

Unsupervised domain adaptation (UDA) intends to transfer knowledge from a labeled source domain to an unlabeled target domain. Many current methods focus on learning feature representations that are both discriminative for classification and invariant across domains by simultaneously optimizing domain alignment and classification tasks. However, these methods often overlook a crucial challenge: the inherent conflict between these two tasks during gradient-based optimization. In this paper, we delve into this issue and introduce two effective solutions known as Gradient Harmonization, including GH and GH++, to mitigate the conflict between domain alignment and classification tasks. GH operates by altering the gradient angle between different tasks from an obtuse angle to an acute angle, thus resolving the conflict and trade-offing the two tasks in a coordinated manner. Yet, this would cause both tasks to deviate from their original optimization directions. We thus further propose an improved version, GH++, which adjusts the gradient angle between tasks from an obtuse angle to a vertical angle. This not only eliminates the conflict but also minimizes deviation from the original gradient directions. Finally, for optimization convenience and efficiency, we evolve the gradient harmonization strategies into a dynamically weighted loss function using an integral operator on the harmonized gradient. Notably, GH/GH++ are orthogonal to UDA and can be seamlessly integrated into most existing UDA models. Theoretical insights and experimental analyses demonstrate that the proposed approaches not only enhance popular UDA baselines but also improve recent state-of-the-art models.

Geometric Understanding of Discriminability and Transferability for Visual Domain Adaptation.

To overcome the restriction of identical distribution assumption, invariant representation learning for unsupervised domain adaptation (UDA) has made significant advances in computer vision and pattern recognition communities. In UDA scenario, the training and test data belong to different domains while the task model is learned to be invariant. Recently, empirical connections between transferability and discriminability have received increasing attention, which is the key to understand the invariant representations. However, theoretical study of these abilities and in-depth analysis of the learned feature structures are unexplored yet. In this work, we systematically analyze the essentials of transferability and discriminability from the geometric perspective. Our theoretical results provide insights into understanding the co-regularization relation and prove the possibility of learning these abilities. From methodology aspect, the abilities are formulated as geometric properties between domain/cluster subspaces (i.e., orthogonality and equivalence) and characterized as the relation between the norms/ranks of multiple matrices. Two optimization-friendly learning principles are derived, which also ensure some intuitive explanations. Moreover, a feasible range for the co-regularization parameters is deduced to balance the learning of geometric structures. Based on the theoretical results, a geometry-oriented model is proposed for enhancing the transferability and discriminability via nuclear norm optimization. Extensive experiment results validate the effectiveness of the proposed model in empirical applications, and verify that the geometric abilities can be sufficiently learned in the derived feasible range.