Hyperplane Of Support Vector Machine Research Articles

Fused robust geometric nonparallel hyperplane support vector machine for pattern classification

Recently, introducing nonconvex loss functions in support vector machine (SVM) to improve the robustness against varies noises has been drawing much attention. In this paper, we first construct a new robust capped asymmetric elastic net (CaEN) loss function. Second, we describe a novel robust Huberized kernel-based (HK) loss function and theoretically demonstrate several important properties, such as smoothness, boundness and the trade-off between the standard least squares and the truncated least squares. Finally, we apply the CaEN loss and the HK loss into elastic net nonparallel hyperplane SVM (ENNHSVM) to develop a fused robust geometric nonparallel SVM (FRGNHSVM). The proposed FRGNHSVM not only inherits the advantages of ENNHSVM but also improves the robustness of classification problems. An efficient Pegasos-based DC (difference of convex functions) algorithm is implemented to solve the FRGNHSVM optimization problem. In comparison with four famous SVMs, including Lagrangian SVM, twin SVM, pinball SVM and C-loss twin SVM, experimental results on simulations and twelve UCI datasets show that the proposed FRGNHSVM can often improve more than 5% average prediction accuracy. Moreover, the performance of the high prediction accuracy of FRGHNSVM is more significant along with the ratio of label noise increasing, indicating its superiority in dealing with label-contaminated datasets.

Dual-energy X-ray transmission identification method of multi-thickness coal and gangue based on SVM distance transformation

By weakening the influence of dual-energy X-ray transmission (DE-XRT) thickness on the coal and gangue identification, this study aims to reveal the effect of thickness, density, and coal type on sorting. Considering the imaging law of coal and gangue in R-I two-dimensional extended space, on the basis of particle swarm optimization (PSO) and support vector machine (SVM), a distance transform image processing and identification method is provided in this study. For this method, the distance between the (R, I) coordinates of coal and gangue and the SVM hyperplane is expressed as the relative density, indicating the details of the internal density change of the coal and gangue target. The average value ME of a single target distance d and the proportion RA of positive value of d can be used as sorting parameters to adjust the sorting. Both ME and RA are verified to have high correlation with density. When the gangue density is higher than 1.8 g/cm3, ME and RA are set to 0.05 and 50%, respectively, thereby realizing the gangue pre-discharge of 5 ∼ 150 mm thick raw coal. Raw coal pre-discharge has the identification rate of 100%, and the recognition rate of different densities and coal types mixed is 96.32%. Within the thickness range of 5 ∼ 150 mm, ME and RA still depend on thickness. By adjusting ME and RA, coal with large thickness and low density may be excluded by mistake. Compared with RA, ME exhibits a higher correlation with density and a lower correlation with thickness. Hence, ME can be selected to participate in regulatory sorting, thereby obtaining more accurate results. For parameter selection and regulation of DE-XRT separation of multiple thicknesses, densities, and coal types, this study provides a new method and practical guidance.

Research on Tower Mechanical Fault Classification Method Based on Multiclass Central Segmentation Hyperplane Support Vector Machine Improvement Algorithm

In this paper, a classification recognition algorithm for tower mechanical faults is proposed, and a multiclass central segmentation hyperplane support vector machine (CSH-SVM) is proposed to improve the existing multiclass support vector machine for problems in which a certain sample satisfies multiple hyperplanes at the same time. The tilt angle change and wind direction data were extracted using the tilt sensors and anemometers attached to the tower, and the temperature and humidity sensors, as well as real-time rainfall and water accumulation information, were combined to construct a sample of the original dataset during the operation of the tower. The unbalanced samples were improved using the synthetic minority oversampling technique (SMOTE) algorithm to construct a balanced dataset suitable for machine learning and improve the prediction accuracy of machine learning. At the same time, the support vector machine hyperplane under the one-vs-all classification principle was additionally computed, and the new hyperplane was computed via the existing hyperplane not only to solve the classification problem of the transition area under the one-vs-all classification so that the samples located in this area no longer meet two hyperplane equations at the same time, but also to reduce the probability of incorrect classification to a certain extent. Through verification, CSH-SVM can classify 15 out of 77 misclassified samples into the correct category with slightly higher computational power than the traditional one-vs-all classification SVM, which can improve the classification prediction accuracy for unbalanced tower mechanical failure datasets and make an accurate judgment on the current state of the tower through the tower data as to when the tower may generate mechanical failure, thus reducing economic loss and personal safety threats.

Prediction of factors for Controlling of Green House Farming with Fuzzy based multiclass Support Vector Machine

A smart greenhouse is a scheme with the aim of allowing the plant growth optimally due to the control in temperature, soil moisture, and humidity. It is necessary to go for best possible smart greenhouse controlling system to maneuver the parameters in accordance with the climatic and seasonal changes plant. In this proposed work, the appropriate setting, monitoring of the model parameters like optimal temperature, humidity, and soil moisture in the greenhouse farm available at Modakkurichi near Erode is carried out using fuzzy logic and multiclass Support Vector Machine (SVM) techniques. It is efficiently implemented as the fuzzy trapezoidal membership function for each sample within the hyper-sphere as a linear function of the selected sample’s distance in the non-linear SVM hyperplane. Based on the simulation and experimental results, the fuzzy logic with Multi-class Support Vector Machine method is effective in selection of the rules to make decision. Simulation of the work was carried out in Python using the open source tool COLAB. Statistical parameters are evaluated for the proposed Fuzzy based SVM method. Root Mean Square Error of the proposed controller has the minimum value as 0.962E-02 when compared to other controllers which vary from 1.04 E-02 to 8.27 E-02.

The recognition of plastic bottle using linear multi hierarchical SVM classifier

Both classification rate and accuracy are crucial for the recyclable PET bottles, and the existing combination methods of SVM all simply use SVM as the unit classifier, ignoring the improvement of SVM’s classification performance in the training process of deep learning. A linear multi hierarchical deep structure based on Support Vector Machine (SVM) is proposed to cover this problem. A novel definition of the input matrix in each layer enhances the optimization of Lagrange multipliers in Sequential Minimal Optimization (SMO) algorithm, thus the datapoint in maximum interval of SVM hyperplane could be recognized, improving the classification performance of SVM classifier in this layer. The loss function defined in this paper could control the depth of Linear Multi Hierarchical SVM (LMHSVM), the generalization parameters are added in the loss function and the input matrix to enhance the generalization performance of LMHSVM. The process of creating Bottle dataset by Histogram of Oriented Gradient (HOG) and Principal Component Analysis (PCA) is introduced meanwhile, reducing the data size of bottles. Experiments are conducted on LMHSVM and multiple typical classification algorithms with Bottle dataset and UCI datasets, the results indicated that LMHSVM has excellent classification performances than FNN classifier, LIBSVM (Gaussian) and GFS-AdaBoost-C in KEEL.

A multivariate neuromonitoring approach to neuroplasticity-based computerized cognitive training in recent onset psychosis

Two decades of studies suggest that computerized cognitive training (CCT) has an effect on cognitive improvement and the restoration of brain activity. Nevertheless, individual response to CCT remains heterogenous, and the predictive potential of neuroimaging in gauging response to CCT remains unknown. We employed multivariate pattern analysis (MVPA) on whole-brain resting-state functional connectivity (rsFC) to (neuro)monitor clinical outcome defined as psychosis-likeness change after 10-hours of CCT in recent onset psychosis (ROP) patients. Additionally, we investigated if sensory processing (SP) change during CCT is associated with individual psychosis-likeness change and cognitive gains after CCT. 26 ROP patients were divided into maintainers and improvers based on their SP change during CCT. A support vector machine (SVM) classifier separating 56 healthy controls (HC) from 35 ROP patients using rsFC (balanced accuracy of 65.5%, P < 0.01) was built in an independent sample to create a naturalistic model representing the HC-ROP hyperplane. This model was out-of-sample cross-validated in the ROP patients from the CCT trial to assess associations between rsFC pattern change, cognitive gains and SP during CCT. Patients with intact SP threshold at baseline showed improved attention despite psychosis status on the SVM hyperplane at follow-up (p < 0.05). Contrarily, the attentional gains occurred in the ROP patients who showed impaired SP at baseline only if rsfMRI diagnosis status shifted to the healthy-like side of the SVM continuum. Our results reveal the utility of MVPA for elucidating treatment response neuromarkers based on rsFC-SP change and pave the road to more personalized interventions.

Characterizing Functional Connectivity Network Based on Multi-Domain Analysis for Epilepsy Classification

Epileptic is a neural disease exemplified through untypical concurrent signal discharge from the neurons present in the brain region. This abnormal brain functionality could be captured through electroencephalography (EEG) system. Generally the observed EEG signals are examined by the experienced neurologist, which may be time consuming when observing hours of EEG signal. Therefore, this proposed work provides a fully automatic epileptic seizure detection system by means of the multi-domain features along with various machine learning algorithms. Initially, the obtained EEG signals are processed to clear noise and artefacts. Subsequently, the pre-processed signals are segregated as 5 seconds epochs and for each epoch various features are extracted from frequency domain, time domain. Additionally entropy, correlation and graph theory approaches has been used for analysis the connectivity of the brain network. Subsequently, distinguishable features are chosen carefully in this regard from the immense feature set by virtue of multi-objective evolutionary method and convincingly, classification has been performed using support vector machine(SVM).A Bayesian optimization (BaO) algorithm was utilized to optimize the SVM's hyper-plane parameters. In addition, Quadratic Discriminant Analysis (QDA), Linear Discriminant Analysis (LDA),Random Forest Ensemble (RFE) and k-Nearest Neighbor Ensemble (k- NNE) was also used for comparing the proposed results. These obtained results validates by considering the performance of this work is competing along with state-of the-arts approaches. The proposed work is implemented on a CHB-MIT database .The obtained performance measure of the classifiers are 99.09%, 81.49%,80.90%,76.85% and 84.14 % in SVM , LDA, QDA, k- NNE and RFE respectively. Finally SVM with Bayesian Optimization (BaO) algorithm outperforms than other classifiers with accuracy, AUC, sensitivity and specificity, as 99.09%, 99.67%, 98.06% and 98.12%, respectively.

Cyber-Physical Integrated Intrusion Detection Scheme in SCADA System of Process Manufacturing Industry

Most Intrusion Detection System(IDS) used in Supervisory Control and Data Acquisition (SCADA) systems now are focused on the cyber field but ignored the process states in physical field of the plants. Attacks aiming at the protocol traffics can be detected but attacks aiming at the processes are difficult to be detected such as the Man In The Middle (MITM) attacks and the Replay attacks. We propose a scheme in both cyber way and physical way to detect the above attacks. Validation of process states is used to detect malicious behaviors to prevent the physical components from being damaged which can be caused by MITM, Replay, and Zero-day attacks. Nonparallel hyperplane based fuzzy classifier is presented to realize the classification of branching shaped data sets which are difficult to be classified by two parallel hyperplane of Support Vector Machine(SVM) to detect attacks caused by DoS (SYN flood) and other attacks in cyber field. Modbus/TCP traffic data are used to test the algorithm and simulation process states are used to test the validation part and the performance of this hybrid scheme is excellent.

Wrist-Worn Gesture Sensing With Wearable Intelligence

This paper presents an innovative wrist-worn device with machine learning capabilities and a wearable pressure sensor array. The device is used for monitoring different hand gestures by tracking tendon movements around the wrist. Thus, an array of PDMS-encapsulated capacitive pressure sensors is attached to the user to capture wrist movement. The sensors are embedded on a flexible substrate and their readout requires a reliable approach for measuring small changes in capacitance. This challenge was addressed by measuring the capacitance via the switched capacitor method. The values were processed using a programme on LabVIEW to visually reconstruct the gestures on a computer. In addition, to overcome limitations of tendo’s uncertainty when the wristband is re-worn, or the user is changed, a calibration step based on the support vector machine (SVM) learning technique is implemented. Sequential minimal optimization algorithm is also applied in the system to generate SVM classifiers efficiently in real-time. The working principle and the performance of the SVM algorithms demonstrate through experiments. Three discriminated gestures have been clearly separated by SVM hyperplane and correctly classified with high accuracy (>90%) during real-time gesture recognition.

Automated Detection and Segmentation of Nonmass-Enhancing Breast Tumors with Dynamic Contrast-Enhanced Magnetic Resonance Imaging.

Nonmass-enhancing (NME) lesions constitute a diagnostic challenge in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) of the breast. Computer-aided diagnosis (CAD) systems provide physicians with advanced tools for analysis, assessment, and evaluation that have a significant impact on the diagnostic performance. Here, we propose a new approach to address the challenge of NME lesion detection and segmentation, taking advantage of independent component analysis (ICA) to extract data-driven dynamic lesion characterizations. A set of independent sources was obtained from the DCE-MRI dataset of breast cancer patients, and the dynamic behavior of the different tissues was described by multiple dynamic curves, together with a set of eigenimages describing the scores for each voxel. A new test image is projected onto the independent source space using the unmixing matrix, and each voxel is classified by a support vector machine (SVM) that has already been trained with manually delineated data. A solution to the high false-positive rate problem is proposed by controlling the SVM hyperplane location, outperforming previously published approaches.

PATTERN OF CORTICAL THINNING AND SHAPE VARIABILITY RELATED TO ALZHEIMER’S DISEASE IN REGIONS AFFECTED BY EARLIEST NEUROFIBRILLARY TANGLE PATHOLOGY

The medial temporal lobe (MTL) is the site of earliest neurofibrillary tangle (NFT, Figure 1A) pathology in Alzheimer's disease (AD). Characterizing the patterns of cortical thinning and shape change in the MTL and relating them to disease progression may be useful for the staging, early detection and monitoring of AD. In addition, we hypothesize that the pattern of AD-related thinning may vary between different anatomical variants of the MTL (Figure 1B), as defined by the folding pattern of the collateral sulcus. We selected T1-weighted MRI scans of 603 subjects from ADNI (Table 1); amyloid negative (A-) controls, A+ controls, A+ early mild cognitive impairment (MCI), A+ late MCI and A+ AD. Bilateral entorhinal cortex (ERC), Brodmann areas (BA) 35 and 36 were segmented automatically. A novel multi-template shape analysis pipeline was applied to extract regional thickness, establish pointwise correspondences and quantify anatomical variability of two major MTL variants. For each MTL variant in each hemisphere, cortical thickness was compared at each point between an A- control and all other groups, yielding a t-statistic map. The effect of AD on MTL cortex shape was evaluated using principal component analysis and support vector machine on the segmentations of the A- control and A+ AD patients (opposite ends of the AD spectrum). The statistical maps in Figure 2 show a consistent pattern of disease progression: initiating in BA35 and progressing to ERC and BA36 in later stages; consistent with the NFT progression staging by Braak and Braak. The first site of cortical thinning seems to be different in variant 1 compared to variant 2; i.e. more lateral in variant 1. Moreover, Figure 3 reveals that AD is associated with decrease in overall size of the MTL, cortical thinning and widening of the CS. T-statistical maps of the contrast between amyloid-negative cognitively normal (CN) adults and the other 4 groups (amyloid-positive CN, EMCI, LMCI and AD) of both variant-templates with age and education as covariates. Left and right hemispheres are analyzed separately. Black contours outline significant clusters after cluster-level family-wise error rate correction. The corrected p-value of each cluster is indicated by the white arrow and text. The corresponding anatomical labels are shown in the first column. The Effect of AD on medial temporal lobe cortex shape of the two anatomical variants. A support vector machine (SVM) is trained to discriminate amyloid-negative cognitively normal adults and amyloid- positive AD cases (cases from the other groups were excluded). The vector orthogonal to the SVM hyperplane, which is assumed to be the direction that best discriminate the two groups, is visualized. Our novel shape analysis revealed the progression of cortical thinning and shape changes of the MTL cortex, the earliest site of NFT pathology. This effect may differ among anatomical variants. Summary thickness measurements extracted from the significant clusters (Figure 2) and the features associated with shape changes may be useful markers for early detection and tracking disease progression.

Near-surface snowmelt detection on the Greenland ice sheet from FengYun-3 MWRI data

The melt extent on the Greenland ice sheet plays an important role in energy balance, and the Arctic and global climates. The micro-wave radiation imager (MWRI) is one of the major payloads of Chinese second-generation polar-orbiting meteorological satellite, FengYun-3 (FY-3), and it is similar to the special sensor microwave/image (SSM/I). The cross-polarized gradient ratio (XPGR) is mainly applied in the scanning multichannel microwave radiometer (SMMR) (18 GHz horizontal polarization (18 H) and 37 GHz vertical polarization (37 V)), the advanced microwave scanning radiometer-earth observing system (AMSR-E) (18.7 GHz horizontal polarization (18 H) and 36.5 GHz vertical polarization (36 V)) and SSM/I (19.3 GHz horizontal polarization (19 H) and 37 GHz vertical polarization (37 V)), which increases the differences between dry and wet snow. The hyperplane of support vector machine (SVM) is used to detect the melt information based on the XPGR data on the Greenland ice sheet, which has higher detection accuracy comparing with the existing threshold methods in theory. The results were compared with the SSM/I data (threshold = − 0.0154), and the results show that the proposed method (That is XPGR combining with SVM) for MWRI data is feasible for the detection of the near-surface snowmelt information on the Greenland ice sheet.

Band Weighting via Maximizing Interclass Distance for Hyperspectral Image Classification

We present a novel band weighting strategy that exploits multiple binary support vector machines (SVMs) to maximize interclass spectral distances for multiclass hyperspectral remote image classification. Specifically, we commence by training binary SVMs based on the original training samples. We then balance the bands of training samples by maximizing the modified classification scores for SVMs. This balance scheme enlarges the distances between individual training samples and the SVM hyperplane. For each class, we reformulate the binary SVM objective function based on the balanced training samples, resulting in a weighting vector that associates a weight to each spectral band for the class. For a testing sample, we weight it and then classify it by using the binary SVM, both with respect to every individual class. The classification result is obtained from the classifier with the greatest score. Experiments on two benchmark data sets show the effectiveness of the proposed strategy.

Photometric redshift estimation for quasars by integration of KNN and SVM

The massive photometric data collected from multiple large-scale sky surveys offer significant opportunities for measuring distances of celestial objects by photometric redshifts. However, catastrophic failure is an unsolved problem with a long history and it still exists in the current photometric redshift estimation approaches (such as the k-nearest neighbor (KNN) algorithm). In this paper, we propose a novel two-stage approach by integration of KNN and support vector machine (SVM) methods together. In the first stage, we apply the KNN algorithm to photometric data and estimate their corresponding zphot. Our analysis has found two dense regions with catastrophic failure, one in the range of zphot ϵ [0.3, 1.2] and the other in the range of zphot ϵ [1.2, 2.1]. In the second stage, we map the photometric input pattern of points falling into the two ranges from their original attribute space into a high dimensional feature space by using a Gaussian kernel function from an SVM. In the high dimensional feature space, many outliers resulting from catastrophic failure by simple Euclidean distance computation in KNN can be identified by a classification hyperplane of SVM and can be further corrected. Experimental results based on the Sloan Digital Sky Survey (SDSS) quasar data show that the two-stage fusion approach can significantly mitigate catastrophic failure and improve the estimation accuracy of photometric redshifts of quasars. The percents in different |δz| ranges and root mean square (rms) error by the integrated method are 83.47%, 89.83%, 90.90% and 0.192, respectively, compared to the results by KNN (71.96%, 83.78%, 89.73% and 0.204).

PERCEIVING DIGITAL WATERMARK DETECTION AS IMAGE CLASSIFICATION PROBLEM

Digital watermark detection is treated as classification problem of image processing. For image classification that searches for a butterfly, an image can be classified as positive class that is a butterfly and negative class that is not a butterfly. Similarly, the watermarked and unwatermarked images are perceived as positive and negative class respectively. Hence, Support Vector Machine (SVM) is used as the classifier of watermarked and unwatermarked digital image due to its ability of separating both linearly and non-linearly separable data. Hyperplanes of various detectors are briefly elaborated to show how SVM's hyperplane is suitable for Stirmark attacked watermarked image. Cox’s spread spectrum watermarking scheme is used to embed the watermark into digital images. Then, Support Vector Machine is trained with both the watermarked and unwatermarked images. Training SVM eliminates the use of watermark during the detection process. Receiver Operating Characteristics (ROC) graphs are plotted to assess the false positive and false negative probability of both the correlation detector of the watermarking schemes and SVM classifier. Both watermarked and unwatermarked images are later attacked under Stirmark, and then tested on the correlation detector and SVM classifier. Remedies are suggested to preprocess the training data. The optimal setting of SVM parameters is also investigated and determined besides preprocessing. The preprocessing and optimal parameters setting enable the trained SVM to achieve substantially better results than those resulting from the correlation detector.

A second-order cone programming formulation for nonparallel hyperplane support vector machine

Expert systems often rely heavily on the performance of binary classification methods. The need for accurate predictions in artificial intelligence has led to a plethora of novel approaches that aim at correctly predicting new instances based on nonlinear classifiers. In this context, Support Vector Machine (SVM) formulations via two nonparallel hyperplanes have received increasing attention due to their superior performance. In this work, we propose a novel formulation for the method, Nonparallel Hyperplane SVM. Its main contribution is the use of robust optimization techniques in order to construct nonlinear models with superior performance and appealing geometrical properties. Experiments on benchmark datasets demonstrate the virtues in terms of predictive performance compared with various other SVM formulations. Managerial insights and the relevance for intelligent systems are discussed based on the experimental outcomes.

Machine-Learning-Based Analysis in Genome-Edited Cells Reveals the Efficiency of Clathrin-Mediated Endocytosis.

Cells internalize various molecules through clathrin-mediated endocytosis (CME). Previous live-cell imaging studies suggested that CME is inefficient, with about half of the events terminated. These CME efficiency estimates may have been confounded by overexpression of fluorescently tagged proteins and inability to filter out false CME sites. Here, we employed genome editing and machine learning to identify and analyze authentic CME sites. We examined CME dynamics in cells that express fluorescent fusions of two defining CME proteins, AP2 and clathrin. Support vector machine classifiers were built to identify and analyze authentic CME sites. From inception until disappearance, authentic CME sites contain both AP2 and clathrin, have the same degree of limited mobility, continue to accumulate AP2 and clathrin over lifetimes >∼20 s, and almost always form vesicles as assessed by dynamin2 recruitment. Sites that contain only clathrin or AP2 show distinct dynamics, suggesting they are not part of the CME pathway.

Improve the diagnosis of atrial hypertrophy with the local discriminative support vector machine.

Computer-aided diagnosis (CAD) approaches succeed in detecting a number of diseases, however, they are not good at addressing atrial hypertrophy disease due to the lack of training data. Support Vector Machine (SVM) is very popular in few CAD solutions to atrial hypertrophy. Yet the performance of SVM is moderate in atrial hypertrophy detection compared to its success in other classification problems. In this paper we propose a novel CAD algorithm, Local Discriminative SVM (LDSVM), to overcome the above-mentioned difficulty. LDSVM consists of a global SVM that is trained on the training data, and a local kNN that is trained based on the information of SVM and query. When a query arrives, SVM gives the initial decision. If the initial decision is less confident, local kNN begins to modify the initial decision. LDSVM improves the accuracy of SVM through some contributions: the risk tube, the discriminant information derived from SVM hyperplane, the new metric and the self-tuning size of neighborhood. Empirical evidence on real medical datasets show high performance of LDSVM over the peers in addressing atrial hypertrophy problems.

Prototype-Based Discriminative Feature Learning for Kinship Verification

In this paper, we propose a new prototype-based discriminative feature learning (PDFL) method for kinship verification. Unlike most previous kinship verification methods which employ low-level hand-crafted descriptors such as local binary pattern and Gabor features for face representation, this paper aims to learn discriminative mid-level features to better characterize the kin relation of face images for kinship verification. To achieve this, we construct a set of face samples with unlabeled kin relation from the labeled face in the wild dataset as the reference set. Then, each sample in the training face kinship dataset is represented as a mid-level feature vector, where each entry is the corresponding decision value from one support vector machine hyperplane. Subsequently, we formulate an optimization function by minimizing the intraclass samples (with a kin relation) and maximizing the neighboring interclass samples (without a kin relation) with the mid-level features. To better use multiple low-level features for mid-level feature learning, we further propose a multiview PDFL method to learn multiple mid-level features to improve the verification performance. Experimental results on four publicly available kinship datasets show the superior performance of the proposed methods over both the state-of-the-art kinship verification methods and human ability in our kinship verification task.

Geometric Optimum Experimental Design for Collaborative Image Retrieval

Relevance feedback (RF) schemes have been widely designed to improve the performance of content-based image retrieval. Despite the success, it is not appropriate to require the user to label a large number of samples in RF. Collaborative image retrieval (CIR) aims to reduce the labeling efforts of the user by resorting to the auxiliary information. Support vector machine (SVM) active learning can select ambiguous samples as the most informative ones for the user to label with the help of the optimal hyperplane of SVM, and thus alleviate the labeling efforts of conventional RF. However, the optimal hyperplane of SVM is usually unstable and inaccurate with small-sized training data, and this is always the case in image retrieval since the user would not like to label a large number of feedback samples and cannot label each sample accurately all the time. In this paper, we propose a novel active learning method, i.e., geometric optimum experimental design (GOED), to select multiple representative samples in the database as the most informative ones for the user to label. Especially, GOED can alleviate the small-sized training data problem by leveraging the geometric structure of unlabeled samples in the reproducing kernel Hilbert space and thus further enhance the performance of image retrieval. Different from the conventional manifold regularization framework, the new method can effectively select the most informative samples for the user to label in image retrieval. By minimizing the expected average prediction variance on the test data, GOED has a clear geometric interpretation to select a set of the most representative samples in the database iteratively with the global optimum. Compared with the popular SVM active learning, our method is label-independent and can effectively avoid various potential problems caused by insufficient and inexactly labeled samples in RF, and is more appropriate and useful for image retrieval. Extensive experiments on both synthetic datasets and a real-world image database have been conducted to show the advantages of the proposed GOED for CIR.