Feature-level Fusion Approach Research Articles

Research on model transfer strategies based on the fusion of NIR-MIR spectral data

This study investigated the impact of different data fusion strategies on the performance of soluble solids content (SSC) prediction models based on near-infrared and mid-infrared spectroscopic techniques. In the data-level fusion approach, we applied standard normal variate and multiplicative scatter correction for pre-processing the NIR and MIR data. For the feature-level fusion, we utilized successive projections algorithm and competitive adaptive reweighted sampling to select informative wavelengths, and then applied direct orthogonal projection (DOP) for model transfer. The study employed a dataset of 150 honey samples to evaluate the impact of different data fusion strategies on model performance. To effectively evaluate model performance, we utilized the coefficient of R2 and RMSEP as evaluation metrics. By comparing the results of data-level fusion, feature-level fusion and single-spectrum model transfer, the results showed that spectral data fusion improved the model transfer performance compared to the single-spectrum approach, with feature-level fusion exhibiting the most significant advantages. The effective variable selection techniques in feature-level fusion successfully removed a substantial amount of interfering data and significantly reduced noise influence, thereby improving the model accuracy. Specifically, the use of feature-level fusion improved the predictive model’s R2 from 0.319 to 0.878 and reduced the RMSEP from 1.974 to 0.613°Brix, demonstrating the significant advantages of this approach in enhancing model transfer performance. The research findings provide important reference and theoretical support for future studies in the field of food quality assessment and other near-infrared spectroscopic data applications. This not only validates the effectiveness of the feature-level fusion approach, but also lays the foundation for establishing efficient and reliable predictive models.

Rapid and accurate quantification of trypsin activity using integrated infrared and ultraviolet spectroscopy with data fusion techniques

Proteases play a crucial role in industrial enzyme formulations, with activity fluctuations significantly impacting product quality and yield. Therefore, developing a method for precise and rapid detection of protease activity is paramount. This study aimed to develop a rapid and accurate method for quantifying trypsin activity using integrated infrared (IR) and ultraviolet (UV) spectroscopy combined with data fusion techniques. The developed method evaluates the enzymatic activity of trypsin under varying conditions, including temperature, pH, and ionic strength. By comparing different data fusion methods, the study identifies the optimal model for accurate enzyme activity prediction. The results demonstrated significant improvements in predictive performance using the feature-level data fusion approach. Additionally, substituting the spectral data of the samples in the validation sets into the best prediction model resulted in a minimal residual difference between predicted and true values, further verifying the model's accuracy and reliability. This innovative approach offers a practical solution for the efficient and precise quantification of enzyme activity, with broad applications in industrial processes.

Chatter Identification in Milling of Titanium Alloy Using Machine Learning Approaches with Non-Linear Features of Cutting Force and Vibration Signatures

The generation of chatter during machining operations is extremely detrimental to the cutting tool life and the surface quality of the workpiece. The present study aims to identify chatter conditions during the end milling of Ti6Al4V alloy. Experimental modal analysis is carried out, and stability lobe diagrams (SLDs) are developed to identify machining parameters under stable and chatter conditions. Experiments are conducted to acquire cutting force and vibration signatures corresponding to machining conditions selected from the SLD. Non-linear chatter features, such as Approximate Entropy, Holder Exponent, and Lyapunov Exponent extracted from the sensor signatures, are used to build Machine Learning (ML) models to identify chatter using Decision Trees (DTs), Support Vector Machines (SVMs) and DT-based Ensembles. A feature-level fusion approach is adopted to improve the classification performance of the ML models. The DT-based Adaboost model trained using dominant non-linear features classifies chatter with an accuracy of 96.8%. The non-linear features extracted from the sensor signatures offer a direct indication of the chatter and are found to be effective in identifying the machining chatter with good accuracy.

Text-Independent Speaker Recognition System Using Feature-Level Fusion for Audio Databases of Various Sizes

To improve the speaker recognition rate, we propose a speaker recognition model based on the fusion of different kinds of speech features. A new type of feature aggregation methodology with a total of 18 features is proposed and includes mel frequency cepstral coefficient (MFCC), linear predictive coding (LPC), perceptual linear prediction (PLP), root mean square (RMS), centroid, and entropy features along with their delta (Δ) and delta–delta (ΔΔ) feature vectors. The proposed approach is tested on five different sizes of speech datasets, namely the NIST-2008, voxforge, ELSDSR, VCTK, and voxceleb1 speech corpora. The results are evaluated using the MATLAB classification learner application with the linear discriminant (LD), K nearest neighbor (KNN), and ensemble classifiers. For the NIST-2008 and voxforge datasets, the best SI accuracy of 96.9% and 100% and the lowest speaker verification (SV) equal error rate (EER) values of 0.2% and 0% are achieved with the LD and KNN classifiers, respectively. For the VCTK and ELSDSR datasets, the best SI accuracy of 100% and the lowest SV EER of 0% are achieved with all three classifiers using different feature-level fusion approaches, while the highest SI accuracy and lowest EER achieved on the voxceleb1 database are 90% and 4.07%, respectively, using the KNN classifier. From the experimental results, it is observed that the fusion of different features with their delta and delta–delta values shows an increase in speaker identification accuracy of 10–50%, and the EER value for SV is reduced compared to the value obtained with a single feature.

Statistical Machine Learning Strategy and Data Fusion for Detecting Incipient ITSC Faults in IM

The new technological developments have allowed the evolution of the industrial process to this new concept called Industry 4.0, which integrates power machines, robotics, smart sensors, communication systems, and the Internet of Things to have more reliable automation systems. However, electrical rotating machines like the Induction Motor (IM) are still widely used in several industrial applications because of their robust elements, high efficiency, and versatility in industrial applications. Nevertheless, the occurrence of faults in IMs is inherent to their operating conditions; hence, Inter-turn short-circuit (ITSC) is one of the most common failures that affect IMs, and its appearance is due to electrical stresses leading to the degradation of the stator winding insulation. In this regard, this work proposes a diagnosis methodology capable of performing the assessment and automatic detection of incipient electric faults like ITSC in IMs; the proposed method is supported through the processing of different physical magnitudes such as vibration, stator currents and magnetic stray-flux and their fusion of information. Certainly, the novelty and contribution include the characterization of different physical magnitudes by estimating a set of statistical time domain features, as well as their fusion following a feature-level fusion approach and their reduction through the Linear discriminant Analysis technique. Furthermore, the fusion and reduction of information from different physical magnitudes lead to performing automatic fault detection and identification by a simple Neural-Network (NN) structure since all considered conditions can be represented in a 2D plane. The proposed method is evaluated under a complete set of experimental data, and the obtained results demonstrate that the fusion of information from different sources (physical magnitudes) can lead to achieving a global classification ratio of up to 99.4% during the detection of ITSC in IMs and an improvement higher than 30% in comparison with classical approaches that consider the analysis of a unique physical magnitude. Additionally, the results make this proposal feasible to be incorporated as a part of condition-based maintenance programs in the industry.

Multimodal Emotion Recognition Framework Using a Decision-Level Fusion and Feature-Level Fusion Approach

ABSTRACT In this manuscript, multimodal emotion recognition using a decision-level fusion and feature-level fusion approach is proposed. In the first approach, decision-level fusion approach is proposed, which is considered a late fusion, where fine-tuned models are developed for each modality. For that, the input is taken from IEMOCAP Database, initially, it is tokenized to a length of 128 tokens and given to a transformer-based BERT model. In the second approach, a feature-level fusion approach is proposed which is considered an early fusion where features from each modality are combined and then fed to the attention-based LSTM. For that, the input is taken from IEMOCAP Database, which contains three modalities: text, speech and Video. Here, text features are extracted with the CNN model, speech features are extracted using the OPENSMILE toolkit and Video features are extracted using a 3D-CNN architecture. Then the proposed approaches are simulated with python. The performance metrics, such as accuracy, sensitivity, specificity, precision, and recall, are evaluated. Then the performance of the proposed first approach is compared with the second approach. The simulation results of the second approach provide a higher accuracy of 0.98%; a higher sensitivity of 0.96%, and a higher sensitivity of 0.75% than the first approach.

A feature-level multi-sensor fusion approach for in-situ quality monitoring of selective laser melting

Selective laser melting (SLM) is a commonly used technique in additive manufacturing to produce metal components with complex geometries and high precision. However, the poor process reproducibility and unstable product reliability has hindered its wide adoption in practice. Hence, there is a pressing demand for in-situ quality monitoring and real-time process control. In this paper, a feature-level multi-sensor fusion approach is proposed to combine acoustic emission signals with photodiode signals to realize in-situ quality monitoring for intelligence-driven production of SLM. An off-axial in-situ monitoring system featuring a microphone and a photodiode is developed to capture the process signatures during the building process. According to the 2D porosity and 3D density measurements, the collected acoustic and optical signals are grouped into three categories to indicate the quality of the produced parts. In consideration of the laser scanning information, an approach to transform the 1D signal to 2D image is developed. The converted images are then used to train a convolutional neural network so as to extract and fuse the features derived from the two individual sensors. In comparison with several baseline models, the proposed multi-sensor fusion approach achieves the best performance in quality monitoring.

Feature level fusion framework for multimodal biometric system based on CCA with SVM classifier and cosine similarity measure

ABSTRACT The multimodal biometric system using feature level fusion offers more accurate and reliable recognition performance than the unimodal system. But in practice, feature level fusion is challenging to perform when biometric modalities have heterogeneous and incompatible feature representation and enforce the final decision more confidently. One of the main concerns in the fusion of features is to drive the highly discriminatory representation amongst different biometric modalities. This paper aims to design a framework for an efficient feature level fusion based on canonical correlation analysis (CCA) with a support vector machine (SVM) classifier to get a highly discriminant and affine invariant fused feature vector. The principal component analysis (PCA) + CCA subspace approach is used to achieve dimensionality reduction and feature fusion in a coherent manner, This approach eliminates the need for a complex matcher/classifier design to process a fused feature vector and also reduces computational complexity. The experimental findings for the SDUMLA-HMT multimodal database demonstrate that CCA on the extracted feature sets of iris and fingerprint modalities results in reasonably better multimodal classification accuracy with a substantial reduction in the feature dimensions. Using SVM, we achieved a classification accuracy of 100%. In this paper furthermore, three different distance measures are explored to test the efficacy of the proposed CCA-based feature level fusion approach. The best recognition performance is achieved in terms of an equal error rate (EER) of 0.176% for the cosine similarity measure. We also compared the proposed approach with the match score level fusion method. The proposed feature level fusion approach excels the recognition performance in contrast to the other literature approaches.

Establishing Statistical Correlation Between Sensor Signature Features and Lubricant Solid Particle Contamination in a Spur Gearbox

This paper aims to predict the severity of solid particle contaminants present in the lubricant in a Spur Gearbox using Vibration, Acoustic Emission, and Sound Signature features. Sensor signatures are acquired at various contaminant conditions of lubricant with different speed and load conditions. Statistical Features are extracted in the time domain, and feature ranking is carried out using the analysis of variance approach. Statistical models are developed using the selected features of Sound, Acoustic Emission, and Vibration separately and fusing the features in the feature level. Decision Trees and Support Vector Machine algorithms are used in this study to build statistical models. AE features have a good correlation with lubricant conditions compared to sound and vibration features. The feature-level fusion approach predicts the lubricant conditions with an accuracy of more than 99%. The feature-level fusion models built using dominant features are computationally efficient without compromising the prediction ability.

Fusion of Skeleton and Inertial Data for Human Action Recognition Based on Skeleton Motion Maps and Dilated Convolution

Human activity recognition (HAR) has become a hot research topic, due to its wide application prospect. Fusion-based methods can be used to complement single sensing modality methods. This paper presents the simultaneous utilization of skeleton data and inertial signals—which are captured at the same time using a Kinect depth camera and ten wearable inertial sensors —within a fusion framework, in order to achieve more robust human action recognition, compared to situations where each sensing modality is used individually. Skeleton data captured by the Kinect depth camera are transformed into a weighted front-view skeleton motion map (WF-SMM), a weighted multi-view skeleton motion map (WM-SMM), and a 3D weighted skeleton motion map (3DW-SMM), which are then fed as inputs into a convolutional neural network. Meanwhile, the inertial data are transformed into 2D inertial images, then fed into a 2D dilated convolutional neural network. Two types of fusion are considered: decision-level fusion and feature-level fusion. Experiments were conducted using the publicly available Changzhou University Multimodal Human Action Data set (CZU-MHAD), in which simultaneous skeleton sequence and inertial signals were captured for a total of 22 actions. The results obtained indicate that both the decision- and feature-level fusion approaches generate higher recognition accuracies, compared to the approaches where each sensing modality is used individually. The highest accuracy (of 98.90%) was obtained with the decision-level fusion approach using 3DW-SMM. In addition, some experiments are conducted on the continuous action streams generated based on the CZU-MHAD with different score threshold. And the highest f1 score 82.05 % is obtained with the threshold of 0.4.

User recognition based on periocular biometrics and touch dynamics

• We proposed a multimodal biometric recognition system. • Two sources of behavioural biometric data are analyzed. • Eye movements and touch dynamics improve the performance of recognition systems. • Feature-level fusion approach. • The proposed approach allows to obtain an accuracy of over 92%. Web user behavioural recognition is the process by which web users are identified and distinguished through behavioural features. In this work, two sources of behavioural biometric data are analyzed for the development of this web user identification model, touch dynamics and the characteristics extracted from the periocular area related to the pupils, blinks and fixations. The approach adopted used to improve the overall performance of the multimodal biometric recognition system is based on a fusion at the Feature level to which different distance measure techniques (Euclidean, Bray-Curtis, Manhattan, Canberra, Chebyshev, Cosine) are applied to determine if the test sample belongs to the target subject. To further improve the system performance, we have applied multi-data processing methods such as Canonical Correlation Analysis (CCA) and Principal Component Analysis (PCA). The results obtained demonstrate the promise of these two different biometric traits and, above all, of their fusion. In fact, the fusion approach allows obtaining an accuracy higher than that of individual biometrics, reaching an accuracy of over 92%.

An Optimized Feature Selection Technique in Diversified Natural Scene Text for Classification Using Genetic Algorithm

Natural scene text classification is considered to be a challenging task because of diversified set of image contents, presence of degradations including noise, low contrast/resolution and the random appearance of foreground (font, style, sizes and orientations) and background properties. Above all, the high dimension of the input image’s feature space is another major problem in such tasks. This work is aimed to tackle these problems and remove redundant and irrelevant features to improve the generalization properties of the classifier. In other words, the selection of a qualitative and discriminative set of features, aiming to reduce dimensionality that helps to achieve a successful pattern classification. In this work, we use a biologically inspired genetic algorithm because crossover employed in such algorithm significantly improve the quality of multimodal discriminative set of features and hence improve the classification accuracy for diversified natural scene text images. The Support Vector Machine (SVM) algorithm is used for classification and the average F-Score is used as fitness function and target condition. First after preprocessing input images, the whole feature space (population) is built using a multimodal feature representation technique. Second, a feature level fusion approach is used to combine the features. Third, to improve the average F-score of the classifier, we apply a meta-heuristic optimization technique using a GA for feature selection. The proposed algorithm is tested on five publically available datasets and the results are compared with various state-of-the-art methods. The obtained results proved that the proposed algorithm performs well while classifying textual and non-textual region with better accuracy than benchmark state-of-the-art algorithms.

Speech Emotion Recognition Considering Nonverbal Vocalization in Affective Conversations

In real-life communication, nonverbal vocalization such as laughter, cries or other emotion interjections, within an utterance play an important role for emotion expression. In previous studies, only few emotion recognition systems consider nonverbal vocalization, which naturally exists in our daily conversation. In this work, both verbal and nonverbal sounds within an utterance are considered for emotion recognition of real-life affective conversations. Firstly, a support vector machine (SVM)-based verbal and nonverbal sound detector is developed. A prosodic phrase auto-tagger is further employed to extract the verbal/nonverbal sound segments. For each segment, the emotion and sound feature embeddings are respectively extracted using the deep residual networks (ResNets). Finally, a sequence of the extracted feature embeddings for the entire dialog turn are fed to an attentive long short-term memory (LSTM)-based sequence-to-sequence model to output an emotional sequence as recognition result. The NNIME corpus (The NTHU-NTUA Chinese interactive multimodal emotion corpus), which consists of verbal and nonverbal sounds, was adopted for system training and testing. 4766 single speaker dialogue turns in the audio data of the NNIME corpus were selected for evaluation. The experimental results showed that nonverbal vocalization was helpful for speech emotion recognition. For comparison, the proposed method based on decision-level fusion achieved an accuracy of 61.92% for speech emotion recognition outperforming the traditional methods as well as the feature-level and model-level fusion approaches.

Deep Learning Approach for Multimodal Biometric Recognition System Based on Fusion of Iris, Face, and Finger Vein Traits.

With the increasing demand for information security and security regulations all over the world, biometric recognition technology has been widely used in our everyday life. In this regard, multimodal biometrics technology has gained interest and became popular due to its ability to overcome a number of significant limitations of unimodal biometric systems. In this paper, a new multimodal biometric human identification system is proposed, which is based on a deep learning algorithm for recognizing humans using biometric modalities of iris, face, and finger vein. The structure of the system is based on convolutional neural networks (CNNs) which extract features and classify images by softmax classifier. To develop the system, three CNN models were combined; one for iris, one for face, and one for finger vein. In order to build the CNN model, the famous pertained model VGG-16 was used, the Adam optimization method was applied and categorical cross-entropy was used as a loss function. Some techniques to avoid overfitting were applied, such as image augmentation and dropout techniques. For fusing the CNN models, different fusion approaches were employed to explore the influence of fusion approaches on recognition performance, therefore, feature and score level fusion approaches were applied. The performance of the proposed system was empirically evaluated by conducting several experiments on the SDUMLA-HMT dataset, which is a multimodal biometrics dataset. The obtained results demonstrated that using three biometric traits in biometric identification systems obtained better results than using two or one biometric traits. The results also showed that our approach comfortably outperformed other state-of-the-art methods by achieving an accuracy of 99.39%, with a feature level fusion approach and an accuracy of 100% with different methods of score level fusion.

Multidomain Feature Level Fusion for Classification of Lumbar Intervertebral Disc Using Spine MR Images

Grading of discs is essential for the assessment of degeneration progression which subsequently plays a vital role in decision making in the removal of a disc. In particular, Pfirrmann’s five-scale (1–5) scoring system is widely used in MR image modality for grading the discs. In this study, we have presented a contemporary semiautomatic feature level fusion approach for the classification of inter-vertebral discs. The data of T2-weighted lumbar MR scans in sagittal plane were collected from 120 distinct subjects. In total, 1123 inter-vertebral disc images were obtained upon performing image augmentation. The experts have segregated the discs into five categories as per Pfirrmann’s criteria. This segregation is utilized as ground truth label data for classification. Furthermore, two feature extraction techniques are exploited, one from spatial domain and other follows deep learning process. A popular Local Binary Pattern (LBP) texture descriptor extracts features from spatial domain. In addition, a popular pre-trained Convolution Neural Network (CNN), which acts as a feature extractor, extracts deep features. The training procedure using SVM classifier yields a model built from post-fusion feature vectors. Furthermore, to estimate the model’s performance, a 5-fold cross-validation is performed by computing principal component analysis as well as without dimensionality reduction. Experiment results obtained on our dataset indicate that after dimensionality reduction, SVM classifier with various kernel functions yields the accuracy up to 92%. A quantitative analysis of the classifier model is presented for parameters, namely – Accuracy, Area Under Curve (AUC), Specificity, Sensitivity, and F1 measure.

Feature-level fusion approaches based on multimodal EEG data for depression recognition

This study aimed to construct a novel multimodal model by fusing different electroencephalogram (EEG) data sources, which were under neutral, negative and positive audio stimulation, to discriminate between depressed patients and normal controls. The EEG data of different modalities were fused using a feature-level fusion technique to construct a depression recognition model. The EEG signals of 86 depressed patients and 92 normal controls were recorded simultaneously while receiving different audio stimuli. Then, from the EEG signals of each modality, linear and nonlinear features were extracted and selected to obtain features of each modality. In addition, a linear combination technique was used to fuse the EEG features of different modalities to build a global feature vector and find several powerful features. Furthermore, genetic algorithms were used to perform feature weighting to improve the overall performance of the recognition framework. The classification accuracy of each classifier, namely the k-nearest neighbor (KNN), decision tree (DT), and support vector machine (SVM), was compared, and the results were encouraging. The highest classification accuracy of 86.98% was obtained by the KNN classifier in the fusion of positive and negative audio stimuli, demonstrating that the fusion modality could achieve higher depression recognition accuracy rate compared with the individual modality schemes. This study may provide an additional tool for identifying depression patients.

Estimating Remaining Useful Life of Turbofan Engine Using Data-Level Fusion and Feature-Level Fusion

Degradation of systems is a natural and inevitable process which widely happens in industries. Therefore, prognostics is used to prevent unexpected failures of complex engineering systems by evaluating the health status of the system and estimating the remaining useful life, using multiple sensors that simultaneously monitor the degradation process of the system. Since these sensor signals often have usable and effective information about a degradation process, data fusion methods are used to obtain more precise and reliable prognostic results. In this paper, the problem of prognostic modeling and remaining useful life estimation of the turbofan engine is considered and a methodology is proposed using data-level and feature-level fusion approaches to better characterize the degradation process of the system. A degradation model for the engine fault is developed by combining a physics-based model and a Wiener process with positive drift. The maximum likelihood estimation method is used to estimate the unknown parameters of the model. Eventually, the remaining useful life is estimated for testing data of a case study involving the degradation of a turbofan engine, and the results are evaluated.

Sub-band-based feature fusion and hybrid fusion approaches for multimodal biometric identification

A multimodal biometric system using feature fusion and hybrid fusion of face and iris is proposed. A novel feature level fusion of face and iris features, using both low and high frequency sub-bands of discrete wavelet transform (DWT), and principal component analysis (PCA) is designed. The redundant data resulted from feature fusion of face and iris is overcome by feature transformation through linear discriminant analysis (LDA). The proposed feature level fusion is tested for face databases (ORL and Yale), and iris databases (CASIA and UBIRIS). The performance of the proposed feature level fusion approach is superior to DWT, PCA and Gabor+PCA-based fusion methods by exhibiting highest recognition rate of 97% with low dimensionality. Further, a hybrid fusion of feature level and score level fusion methods is proposed to improve the performance of the multimodal biometric system. In comparison to feature level and score level fusion methods, the hybrid fusion method attains highest recognition rate of 99.6% and least equal error rate (EER) of 0.086 for ORL+CASIA database.

Sub-band-based feature fusion and hybrid fusion approaches for multimodal biometric identification

A multimodal biometric system using feature fusion and hybrid fusion of face and iris is proposed. A novel feature level fusion of face and iris features, using both low and high frequency sub-bands of discrete wavelet transform (DWT), and principal component analysis (PCA) is designed. The redundant data resulted from feature fusion of face and iris is overcome by feature transformation through linear discriminant analysis (LDA). The proposed feature level fusion is tested for face databases (ORL and Yale), and iris databases (CASIA and UBIRIS). The performance of the proposed feature level fusion approach is superior to DWT, PCA and Gabor+PCA-based fusion methods by exhibiting highest recognition rate of 97% with low dimensionality. Further, a hybrid fusion of feature level and score level fusion methods is proposed to improve the performance of the multimodal biometric system. In comparison to feature level and score level fusion methods, the hybrid fusion method attains highest recognition rate of 99.6% and least equal error rate (EER) of 0.086 for ORL+CASIA database.

Remote Sensing Scene Classification Using Heterogeneous Feature Extraction and Multi-Level Fusion

Understanding the scenes provided by remote sensing (RS) images has drawn increasing attention in the last decade. It is to automatically classify a RS scene image by feature extraction and label assignment. Although much effort has been dedicated to developing discriminative feature extraction as well as automatic classification techniques, it is still very challenging owing to the complex distributions of the ground objects in high spatial resolution scenes. To enhance the ability to represent the RS scenes, an integration of multiple types of features for remote sensing scenes is considered as an effective way. Nevertheless, different kinds of features possess different characteristics, and how to fuse them together is a critical problem. In this paper, to fuse three different but complementary types of features that are extracted to characterize global attributes of scenes together, a discriminant correlation analysis based feature-level fusion approach is proposed, which maximizes the correlation of corresponding features across the two feature sets and in addition de-correlates features that belong to different classes within each feature set. In addition, to further improve the scene classification performance, another kind of information fusion form, called decision-level fusion is adopted in the classification stage. In our proposed decision-level fusion technique, the final results of multiple classifiers are combined via majority voting. Extensive experiments results conducted on the well-known SIRI-WHU dataset, the WHU-RS dataset and the UC Merced Land Use dataset have demonstrated that the proposed remote sensing scene classification method based on heterogeneous feature extraction and multi-level fusion is superior to many state-of-the-art scene classification algorithms.