Review of Domain-Based Novelty Detection Using One Class Support Vector Machine

One of the primary problems with machine learning and data mining is novelty detection (ND), sometimes referred to as anomaly detection, outlier detection, or one-class classification. Differentiating recognized items (regular patterns) from samples that are abnormal (outliers) is ND's primary duty [1]. The capability to identify novel classes could possess a substantial and favorable outcome, wherein the test data (or unlabelled data) might comprise details regarding items not known at the time of the training process [2]. ND encompasses learning a model that can recognize any departure from normalcy by absorbing the characteristics of the training dataset's normal data samples. Real-world applications include, among other things, currency validation, machine failure detection, medical diagnostics, and user verification in computer systems. Normal data samples are usually abundant in ND-related applications, but abnormal data samples are sometimes scarce or, in certain situations, nonexistent. As a result, the majority of ND algorithms prioritize the typical data and primarily use it to create a data description [3].

The predictive performance in ND is determined by measuring the model’s ability to classify samples belonging to the normal category, i.e., elements that have properties alike the elements used for training, and distinguish those samples, referred to as novel, outliers, or abnormal [4]. The novelty detection technique is employed to devise a model that isolates new patterns from a specified dataset. The model must be formulated in a manner that inputs having features different from those used during training should have the inputs classified as novel patterns, while those matching the training inputs should be classified accordingly [5]. In recent years, numerous fields have focused on the function of one-class categorization in pattern recognition. The approach of simulating a widely dispersed class to categorize an unknown testing class is known as one-class classification, and it is frequently employed for ND. When there is just one known class available to train the model (i.e., classifier) rather than two or more, it is regarded as a specific case of a classification problem. The ability of the constructed model to differentiate samples of the normal class that is, samples with traits comparable to those used in training from the other examples, which are referred to be abnormal or novel, or outliers, is the basis for measuring prediction performance in ND [6].

ND can also be viewed as much like novel class detection [1, 7, 8]. Two circumstances should be substantiated to affirm the advent of a novel class: the threshold condition and the cohesion-separation condition. Cluster-specific assumptions are made for the first condition, where elements of the novel class are assumed to be like the other elements of the class; however, those elements are different from the elements belonging to other classes. The second condition indicates that the novel class element count must exceed a specified threshold. The threshold is employed for differentiating between the novel class and outlier’s cases; when the quantity of applicants is fewer than the stated level, we presume that they represent anomalies in the current classes. Experts determine the requisite threshold value, and it is specific to the application [9]. In the wake of the specified criteria, a learner must evaluate sets of instances to ascertain the creation of an additional class. Thus, current techniques are either based on chunks [10-12] or according to timing limitations [13, 14].

Although terms such as anomaly detection, outlier detection, novelty detection, and one-class classification have nuanced differences in the literature, this review treats them interchangeably, focusing on their shared objective of identifying deviations from learned normal data using domain-based methods.

With a focus on domain-based methods for novelty detection in the machine learning literature, this survey attempts to present an up-to-date and organized summary of recent research and approaches to novelty detection using a semi-supervised learning approach using One-Class Support Vector Machines (OCSVM). The rest of the paper is organized in this manner: Section 2 discusses the novelty detection methodologies, including various categories of approaches from the literature. Meanwhile, Section 3 delves into Support Vector Machines (SVM), where this section details a support vector data description review (SVDD) and OCSVM are presented. This is followed by a detailed technical review of the fundamental algorithmic improvement made to OCSVM from the literature, and a review of real-world applications of novelty detection using OCSVM. At the end, the review is summarized in Section 4 and followed by the concluding remarks.

SVM is a widely used classifier for generating decision boundaries that divide data into various classes. For binary pattern classification of linearly separable data, the original SVM network is a perfect fit. A hyperplane that maximizes the distance between two classes is used by the SVM. Support vectors are the training points that are located close to the border, establishing this dividing edge. Numerous adjustments and enhancements have been made to the original concept since it was first proposed. A technique called Robust Support Vector Machines (RSVM) deals with the over-fitting issue that noise in the training dataset causes. With this method, the standard SVM is combined with an averaging technique (class centre) to smooth the decision surface and regulate the degree of regularization [21].

3.1 Support Vector Data Description

One commonly used method of a one-class classifier is SVDD. This technique maps target data into a high-dimensional feature space, intending to identify a set of support vectors (SV) representing the spherical border of the target data. The procedure takes place in feature space; hence, the description boundary of SVDD is adjustable. To make up for shortcomings in earlier one-class classifier research, SVM served as the model for the development of SVDD. Numerous classification techniques before the usage of support vectors relied on estimating the target data set's probability distribution [15].

Recently, certain SVDD technique extensions have been put forth to enhance the hyper-spherically shaped novelty boundary's boundaries. The first extension is proposed in the previous study [22], where a new SVDD incorporates the idea of density weighting—that is, assigning each data point a weight based on its relative density, as determined by applying the k-nearest neighbor (k-NN) method to the target data's density distribution. This novel approach emphasizes data points in high-density regions by incorporating the additional weight into the SVDD search for an ideal description. Eventually, the optimal description moves to these places.

Recent studies further extend Deep SVDD by integrating representation learning with contrastive objectives, improving feature compactness for normal samples while enhancing separability from abnormal patterns. For example, contrastive Deep SVDD frameworks combine contrastive learning and SVDD loss to strengthen anomaly discrimination in complex feature spaces [23].

On the other hand, Yin et al. [24] introduced an SVDD technique for robust novelty detection that is based on active learning. It may lessen the quantity of labelled data by utilizing a framework for active learning, generalize the data spread, and lessen the effect of noise by directing the selection process with the help of the local density.

A deep learning neural network model that adopts the SVDD was proposed by Kim et al. [25]. A variation of the SVM, the SVDD achieves a maximal margin in one-class classification tasks, resulting in great generalization performance. The goal of the suggested model is to achieve deep learning's representational power. With the SVDD, generalization performance is preserved. In the study by Wang and Cha [26], according to the multivariate statistics known as Stahel-Donoho (SD) outlying-ness in an arbitrary kernel space, the authors have suggested giving each observation a weight. Weighted penalties, whose weights depend smoothly on the outlying-ness criteria, were presented as a novel robust SVDD. By assigning a weight to each data item based on a few chosen weight function families. In order to find the minimum-sized hypersphere, SVDD down-weights observations containing a lot of outliers, which could be mistakes, recordings from unusual situations, or members of a different population. To create a better model for the regular data, it is crucial to be able to identify these observations during SVDD training.

A two-phase intelligent fault detection approach for rotating equipment that combines optimized SVDD and optimized SVM was proposed by Zhang et al. [27]. To be more precise, SVM is used for fault identification, and SVDD is used for fault detection. The grasshopper optimization algorithm (GOA) optimizes the parameters of SVM and SVDD. The input feature vector for SVDD and SVM is extracted using multiscale entropy (ME). The advantages and disadvantages of eight distinct entropy-based indicators for feature extraction are examined within the parameters of the suggested methodology. A technique for selecting features when building the SVDD model with only normal samples is shown.

Meanwhile, to efficiently monitor the nonlinear plantwide processes, a decentralized fault detection and diagnosis technique was suggested by Wang et al. [28]. It has two main themes: fault diagnosis based on SVDD and mutual information-Louvain-based process decomposition. First, the plantwide process is first mapped as an undirected graph that matches the process structure and mechanism knowledge. A Louvain algorithm with MI correlation is suggested to finely break down the process into manageable sub-blocks. Mutual Information (MI) is provided to illustrate the degree of correlation between various nodes (i.e., process variables). For each sub-block, a decentralized defect detection technique based on SVDD is then introduced, and the associated variable contribution rate is calculated. Decentralized SVDD (DSVDD), which identifies the abnormal status and pinpoints the variable causing this fault, is the basis for local fault diagnosis and detection. The DSVDD model is used to identify faults and determine their causes by calculating the corresponding contribution rate.

In the study by Rahimzadeh Arashloo [29], the author has introduced a dual norm into the goal function, demonstrating a way for managing the intrinsic sparsity or consistency of the issue to improve descriptive capacity. By generalizing the model to ${{\ell }_{p}}$-norm where $p\ge 1$, the proposed approach enables formulating a non-linear cost for slacks. Also, extend the proposed works of ${{\ell }_{p}}$-norm concept from a strictly one-class environment to the training situation and demonstrate the benefits of the suggested extension by include marked negative objects.

DR-SVDD, or dynamic radius support vector data description, is a new fault diagnosis technique. was proposed by Lu et al. [30] to efficiently identify the fuel cell system with proton exchange membranes faults. Compared to the classic SVDD and enhanced SVDDs, this approach takes into account the distribution properties of the training set sample as well as the SVDD hypersphere radius information to provide a more sufficient and accurate description of the sample data. New slack variables are added to the model to improve its generalization performance, resilience, fault-tolerance, and computational complexity.

The Sparrow Search Algorithm (SSA) was introduced by Pan et al. [31] into the parameter optimization process of SVDD. This method reads the training data then determines and arranges the fitness values for every sparrow based on the characteristics that correspond to its location. The training samples are divided into two groups when SVDD is trained using a single group at random; While the other group conducts the test, one group trains the SVDD model determine how many samples are not in the hypersphere. This is known as the fitness value. The sparrow that has the lowest fitness was chosen as the elite, and its position data was recorded to ascertain whether the fitness was below or equal to the error rate threshold. The computed error rate is then used as the fitness value.

In the study by Wu et al. [32], the authors have proposed the Part Interval Stacked Auto-encoder and Support Vector Data Description (PISAE-SVDD), a new process monitoring and fault diagnosis algorithm. This algorithm improves the Stacked Auto-encoder's (SAE) loss function. The mean square error of the initial input and output data is the reconstruction error value in certain measurement data. In contrast, a specific acceptable range for the reconstruction error value is provided by uncertain measurement data. Within this range, the measurement data's error value is regarded as zero. In the same manner as for specific measurement data, the reconstruction error value of measurement data that exceeds the permitted range is computed. Meanwhile, SAE's powerful nonlinear characterization capability is used to retrieve the distinctive information of the industrial process. Then, using the SAE feature information data taken from normal samples, SVDD is utilized to determine the control limit of the fluctuation range of the normal functioning state.

A Broad Learning Systems (BLS)-based weighted SVDD algorithm was proposed by Huang et al. [33], this increases the SVDD model's robustness during training by introducing reconstruction of a few atypical samples and error weights. SVDD was utilized to address issues where the proportion of sample categories of data is highly uneven, and the BLS was enhanced to produce a new model for data reconstruction.

On the other hand, a novel approach of a pinball loss SVDD was suggested in order to find outliers in the previous study [34]. In this approach, the sphere classifier uses all the training data, including the ones that are located inside the sphere. Because a little quantity of noisy data has minimal effect regarding the classifier, this technique is more resistive to noise and achieves dispersion minimization in the sphere center. This technique is superior in two ways: first, it employs the pinball loss, which improves our approach's robustness and reduces scatter in the sphere center, in contrast to the traditional SVDD, which uses the hinge loss function and is noise-sensitive; second, it can be distinguished from the existing weight-varying anti-noise SVDD techniques, which take more pre-processing time to produce.

In industrial anomaly detection, recent improvements to Deep SVDD emphasize robust feature extraction and patch-level representation to handle localized defects, demonstrating improved detection stability in real deployment contexts [35].

3.1.1 Summary

Overall, the reviewed SVDD extensions reveal a clear research trend toward improving robustness and adaptability of the hypersphere boundary under real-world data imperfections. Density-weighted and active-learning-based SVDD variants consistently enhance sensitivity to local data structure, particularly in noisy or imbalanced datasets. Meanwhile, integration with deep learning models enables SVDD to handle high-dimensional and nonlinear feature representations more effectively. However, these improvements often introduce increased computational complexity and additional hyperparameters, which can limit scalability and hinder deployment in real-time systems. Despite performance gains, most SVDD variants remain sensitive to kernel and parameter selection, highlighting the need for adaptive or self-tuning mechanisms in future research.

3.2 One-Class Support Vector Machines

OCSVM is a popular method that is a reliable classifier for unsupervised anomaly detection. However, in some cases, it is not resistant to outliers. A few of its variations have recently been put forth to increase the resilience against outliers. The fundamental concept of OCSVM is to locate in the feature space a hyperplane $\left( w\cdot \phi \left( x \right) \right)-\rho =0$ that, with the greatest possible margin, divides sample images from the origin. The following is the primal optimization problem [36].

$\underset{w,\xi ,\rho }{\mathop{\min }}\,\frac{1}{2}{{w}^{2}}-\rho +\frac{1}{\nu l}\underset{i=1}{\overset{n}{\mathop \sum }}\,{{\xi }_{i}}\\ \text{s}\text{.t}\text{. }\!\!~\!\!\text{ }\left( w.\varphi ~\left( {{x}_{i}} \right) \right)\ge ~\rho ~{{\xi }_{i}},~{{\xi }_{i}}~\ge 0,~i=1,\ldots ,n$                        (1)

where, $l$ represents all of the training samples, $\nu $ is a trade-off parameter, and $\xi $ are slack variables. Meanwhile, $w$, $\rho $, and $\xi $ are the weight vector, offset parameter, and $i$-th training sample, respectively. This is a convex optimization problem, and its dual problem, which is represented below, can be used to solve it.

$\underset{\alpha }{\mathop{\max }}\,-\frac{1}{2}\underset{i,j,=1}{\overset{n}{\mathop \sum }}\,{{\alpha }_{i}}{{\alpha }_{j}}\kappa \left( {{x}_{i}},{{x}_{j}} \right)\\\text{s}\text{.t}\text{.}~0\le {{\alpha }_{i}}\le \frac{1}{\nu l},~\sum {{\alpha }_{i}}=1$                       (2)

where, $\kappa \left( {{x}_{i}},{{x}_{j}} \right)$ denotes a kernel function. A typical kernel function adopted by researchers is the Gaussian Radial Basis Function (RBF), which is given as follows:

$\kappa \left( {{x}_{i}},~{{x}_{j}} \right)=\text{exp}\left( -\frac{1}{2{{\sigma }^{2}}}{{x}_{i}}-{{x}_{j}}^{2} \right)$                 (3)

where, $\sigma $ is a Gaussian function parameter. Because of its capacity to represent intricate and non-linear decision boundaries, this RBF is employed as the kernel function. The RBF kernel calculates the relationship between two data points' similarity and the Euclidean distance between them [37].

Let's say sample ${{x}_{i}}$ lies outside of the classification hyperplane, ${{\xi }_{i}}$ is greater than 0, and the Karush-Kuhn-Tucker (KKT) condition states that ${{\alpha }_{i}}=1/\nu l$. This indicates that in traditional OCSVM, samples outside of the surface are defined by SVs. It is well known that the normal vector $w=\mathop{\sum }_{i=1}^{l}{{\alpha }_{i}}\phi \left( {{x}_{i}} \right)$ can be written in terms of the mappings of SVs. When $\nu $ is set large to create outliers that are outside the surface, these outliers become SVs and their respective ${{\alpha }_{i}}$ are equal to $1/\nu l$, which gives them more magnitude control over the normal vector and the surface; conversely, when $\nu $ is set small, the surface surrounds the outliers, thereby influencing the surface.

There are two components to the strategy suggested by Schölkopf et al. [36]; getting the surface around the target cluster core is the first step; using this surface and find outliers and remove them from the training set so that the final OCSVM model may be trained. It is anticipated that the surface will identify the outliers outside and, more crucially, will not be affected by these outside-located outliers to better contain the cluster core of the target class. By adjusting $\nu $, the first expectation can be fulfilled since this value represents the upper bound for training samples that are situated outside of the surface or hyperplane.

3.2.1 Algorithmic improvements to the OCSVM

Anomaly detection makes considerable use of a OCSVM. To detect anomalies, OCSVM looks for the ideal hyperplane in high-dimensional data that can maximally separate the data from anomalies. However, conventional OCSVM' hinge loss is unlimited, leading to greater loss from outliers and impairing their ability to detect anomalies. Outlier influence is decreased using the bounding hinge loss function [38].

In this section, the most recent development in the fundamental research on OCSVM at the algorithmic level is discussed. The implementation of the OCSVM in the earlier research is always centered around the original formulation, such as in Eqs. (1) and (2). However, recently, more research found in the literature has made significant changes to the OCSVM formulation at the algorithmic level.

For example, a new OCSVM algorithm based on hidden information was proposed by Zhu and Zhong [39]. They proposed a modified OCSVM that exploits so-called “hidden” or group information present in the training data. Unlike the standard OCSVM, which models all training samples using a single set of slack variables, their approach assumes that samples can be meaningfully partitioned into groups (e.g., based on demographic, acquisition, or contextual attributes). The key motivation is that deviations from the learned boundary may have different significance across groups, and a single global slack mechanism may bias the novelty boundary, particularly when training data are limited or heterogeneous. To address this, the method introduces a second learning space, referred to as the correcting space, in addition to the conventional decision space. While all samples contribute to defining the decision boundary in the decision space, group-specific correcting functions are learned in the correcting space to model slack variables. These correcting functions regulate how much each group is allowed to violate the boundary, effectively imposing group-dependent constraints on the slack variables. Importantly, the correcting space does not perform classification; instead, it modulates the influence of training errors during optimization. This two-space formulation enables the OCSVM to incorporate auxiliary group information, improving generalization by preventing dominant or noisy groups from disproportionately shaping the novelty boundary.

In another approach, an algorithm for resilient and sparse anomaly detection was put forth by Tian et al. [40]. They have added the ramp loss function with comparison to the initial implementation of OCSVM. The primary goal of this work is to create a sparse and robust semi-supervised method by using the non-convexity aspects of the ramp loss function. Additionally, the derived model was solved using the Concave-Convex Procedure (CCCP), which solves a non-differentiable non-convex optimization problem. The authors have introduced a ramp loss function in this manner:

${{R}_{\rho ,s}}=\left\{ \begin{array}{*{35}{l}}   0, & z\ge \rho   \\   \rho -z, & \rho -s<z<\rho   \\   s, & z\le \rho -s  \\ \end{array} \right.$                    (4)

where, $z$ and $s$ are the loss function score and pre-defined parameter, respectively. Therefore, the ramp loss function as in Eq. (4) was employed to strengthen the resilience of OCSVM and prevent the outliers from being excluded as support vectors. Based on this function, for those $z\le \rho -s$, the ramp loss will be flat, and its value will be a constant $s$. Ramp loss OCSVM can be reformulated as:

$\underset{w,\rho ,s}{\mathop{\min }}\,\frac{1}{2}w_{2}^{2}+\frac{1}{\nu l}\underset{i=1}{\overset{l}{\mathop \sum }}\,{{R}_{\rho ,s}}\left( {{w}^{T}}\phi \left( {{x}_{i}} \right) \right)$                         (5)

To accurately categorize samples that resemble training data, OCSVM seeks to choose an appropriate region from an unknown probability distribution that includes the majority of the input samples. This algorithm can be used to locate the hypersphere with the smallest radius to discover outliers. However, a conventional OCSVM’s hinge loss is unlimited, leading to greater loss from outliers and impairing their ability to detect anomalies, which in turn results in the lessened outlier’s influence [40].

On the other hand, a new method for detecting anomalies in big amounts of data using randomized nonlinear features in SVM was proposed [38]. This method reduces computing complexity by doing away with the requirement to handle enormous kernel matrices for large datasets. Instead of looking for support vectors that are optimized using an unlimited loss function, the authors have proposed an iterative approach with a bounded loss function using a half-quadratic optimization technique.

In this case, the random projection can reduce the optimization method's computational cost needed for large nonlinear kernels. Hence, a similar effect can be observed when using nonlinear features. Considering these issues, the authors in the research [38] proposed OCSVM's optimization issue with a bounded loss function as:

$\underset{w,\rho }{\mathop{\max }}\,\frac{1}{2}w_{2}^{2}-\frac{1}{\nu l}\underset{i=1}{\overset{l}{\mathop \sum }}\,\xi _{i}^{r}-\rho $                     (6)

where, randomized slack variables, $\xi _{i}^{r}=\beta \left( 1-{{e}^{-\eta {{\xi }_{i}}}} \right)$. , with normalization constant, $\beta $ given as follows:

$\beta =\frac{1}{1-{{e}^{-\eta }}}$                        (7)

where, the scaling constant is $\eta \ge 0$. The fundamental goal of constraining the loss function of $\xi _{i}^{r}=1$ is ensured by the normalizing constant $\beta $. The scale constant, $\eta $. , sets the upper bound, and the loss function becomes conventional hinge loss when $\eta =0$ The above formula demonstrates that the bounded loss function OCSVM is convex and monotonic, just like conventional OCSVM. It is evident that $\eta $.  regulates the limit of the loss function, substituting the unbounded loss function of the conventional SVM with a bounded one. Greater $\eta $ values indicate higher degrees of scaling, and vice versa [38].

In terms of kernel parameters, for example $\text{ }\!\!\sigma\!\!\text{ }$ in Eq. (3), whose selection is not simple for anomaly detection situations, has a significant role in OCSVM's performance. Furthermore, in certain complex and unequal data distributions, the densities and shapes of distinct data regions can differ significantly, which makes it challenging for OCSVM to use a global kernel parameter to generate good boundaries in every region. Hence, in the study by Pang et al. [41], they have suggested a hybrid technique combining vector quantization and OCSVM, known as VQ-OCSVM, to address the problems.

To be more precise, distribution information about normal data is extracted via vector quantization, and the resulting information is utilized to build a clear mapping function that creates a high-dimensional feature space from data. The classifier is then constructed within the feature space using OCSVM. Through the addition of the explicit mapping to OCSVM, two regularization hyperparameters exist, ${{\lambda }_{1}}$ and ${{\lambda }_{2}}$ have been introduced in VQ-OCSVM. For ${{\lambda }_{2}}$, the traditional OCSVM algorithm is referred to, and it is suggested to be fixed to the value of 1. As for ${{\lambda }_{1}}$, they have introduced the subsequent practical yet empirical approach to determine its value.

In order to achieve feature auto-selection and model sparsity, keep in mind that ${{\lambda }_{1}}~$regulates the weight of the ${{L}_{1}}$-norm regularization in the objective function. It makes sense that a model with a ${{\lambda }_{1}}~$that is too small will overfit the typical training data and be too complex, whereas a model with a ${{\lambda }_{1}}~$that is too large will be too simple and underfit the typical training data [41].

The dual problem, which is a quadratic programming problem, is solved using the conventional OCSVM in order to solve the primal problem. Nevertheless, quadratic programming is ineffective for training large-scale problems since its computation is cubic and its storage complexity increases quadratically with problem scale. Therefore, Zhu et al. [42] proposed to directly train OCSVM in primordial space. Unfortunately, the gradient-based optimization approach, a first-order method that converges quickly, cannot solve it because of the non-differentiability of hinge loss utilized in OCSVM.

Furthermore, the OCSVM is less resilient to outliers because of the unbounded hinge loss. Because of the outliers, the decision boundary will diverge greatly from the ideal hyperplane. A nonconvex differentiable function, a Huberized truncated loss function, was suggested as a solution to the problems to increase the OCSVM's resilience [42]. As an alternative to hinge loss in conventional OCSVM, the Huberized truncated loss function was proposed to be used due to its insensitiveness to outliers. Unlike regular OCSVM, robust OCSVM has a differentiable primal objective function. The primordial space's resilient OCSVM can be solved using a method for rapid proximal gradients. The following are the two Huber loss functions that the authors have suggested:

${{H}_{1}}\left( r \right)=\left\{ \begin{array}{*{35}{l}}   \rho -r-\frac{\delta }{2}, & r\le \rho -\delta   \\   \frac{{{\left( \rho -r \right)}^{2}}}{2\delta }, & \rho -\delta <r\le \rho   \\   0, & r>\rho   \\ \end{array} \right.$                          (8)

$\kappa {{H}_{s}}\left( r \right)=\left\{ \begin{array}{*{35}{l}}   s-r-\frac{\delta }{2}, & r\le \rho -\delta   \\   \frac{{{\left( s-r \right)}^{2}}}{2\delta }, & s-\delta <r\le s  \\   0, & r>s  \\ \end{array} \right.$                                (9)

The continuous and differentiable nature of ${{H}_{1}}\left( r \right)$ and ${{H}_{s}}\left( r \right)$ was readily apparent. It can be observed that these functions diminish to the hinge loss when $\delta \to 0$ and expand linearly as $i$ lowers. Following the combination of ${{H}_{1}}\left( r \right)$ and $-{{H}_{s}}\left( r \right)$, the Huberized truncated loss function, ${{T}_{s}}\left( r \right)={{H}_{1}}\left( r \right)-{{H}_{s}}\left( r \right)$ can be written as follows:

${{T}_{s}}\left( r \right)={{H}_{1}}\left( r \right)-{{H}_{s}}\left( r \right)=\left\{ \begin{array}{*{35}{l}}   \rho -s, & r\le s-\delta   \\   \rho -r-\frac{\delta }{2}-\frac{{{\left( s-r \right)}^{2}}}{2\delta }, & s-\delta <r\le s  \\   \rho -r-\frac{\delta }{2}, & s<r\le \rho -\delta   \\   \frac{{{\left( \rho -r \right)}^{2}}}{2\delta }, & \rho -\delta <r\le \rho   \\   0, & r>\rho   \\ \end{array} \right.$                       (10)

As presented above, the development of OCSVM began with a modification that added further restrictions to the slack variables for the instances belonging to various groups. Then, later, the ramp loss function was introduced, where this loss function's non-convexity properties were used to create a robust, sparse semi-supervised method. After that bounded loss function was integrated utilizing OCSVM's randomized nonlinear characteristics, removing the requirement to handle big kernel matrices for big datasets, which lowers the complexity in terms of time and space. In another method, it was developed by utilizing the vector quantization technique combined with the OCSVM, which is more capable of generalization complex data distribution. Later, a Huberized truncated loss function was proposed to overcome the hinge loss function's drawbacks and increase the OCSVM's robustness.

(1) Synthesis of algorithmic advancesment in OCSVM

Algorithmic improvements to OCSVM can be broadly categorized into three dominant directions: loss-function modification, integration with auxiliary learning models, and computational acceleration. Loss-based approaches, such as ramp, bounded, and Huberized loss functions, consistently improve robustness against outliers by limiting the influence of extreme samples; however, they often introduce non-convex optimization challenges and heightened parameter sensitivity. Hybrid approaches that combine OCSVM with deep learning or vector quantization enhance representational power but increase model complexity and training cost. Efforts aimed at accelerating OCSVM through randomized features or primal-space optimization improve scalability for large datasets, yet may trade off accuracy in highly heterogeneous data distributions. Overall, existing methods exhibit a recurring tension between robustness, computational efficiency, and generalization capability.

3.2.2 Applications of OCSVM

There are many areas or fields of applications that have made use of OCSVM in dealing with the challenge of novelty detection. In this section, some of the recent research that has applied OCSVM is discussed. For example, Delgado-Prieto et al. [20] proposed a multi-modal strategy to enhance the effectiveness of novelty detection. The approach used in this work is broken down into three primary steps. The first step is a specific feature calculation and reduction over all accessible physical magnitudes. Next, a group of OCSVM-based novelty detection models was developed to detect previously unconsidered events. Lastly, a diagnosis model that consists of a feature fusion scheme was introduced to classify faults accurately.

A new scheme was proposed to be utilized for denoising, which displays the optimal thresholding rule and mother wavelet combination for every signal [43]. This scheme requires features to be collected from the time-frequency and time-domains, and the energy-to-frequency analysis shows the optimal mother wavelet for feature extraction from each signal. The criterion of the Shannon entropy ratio. In this work, it is also demonstrated because by making the signals more nonlinear, the statistical traditional or mixtures of statistical traditional and solely nonlinear features have the ability to fully classify data; nonlinear features are unable to do so. Hence, three rotating systems' vibration data are detected using OC-SVM; nevertheless, the focus is on data pre-processing techniques such denoising, dimension reduction, vectorization, feature extraction, and normalization. In particular, for the first time, the impact of both classical and nonlinear statistical feature extraction on novelty detection.

Saari et al. [44] have used OCSVM to use fault-specific characteristics taken from vibration signals in order to detect and identify wind turbine bearing problems. By training models using these attributes as input for a OCSVM, automatic identification was accomplished. By adjusting the model tuning settings, detection models with varying sensitivity were trained concurrently. Additionally, efforts were made to determine a process for choosing the model tuning parameters by first determining the system's criticality and then using that information to estimate the detection model's accuracy.

An unsupervised deep learning method was proposed founded on an OCSVM-based deep auto-encoder, where the classifier was used in the measurement of the reaction data obtained from baseline or intact structures as training data, making it possible to identify structural degradation in the future [45]. The well-crafted deep auto-encoder, which is utilized as an extractor to extract damage-sensitive features from the observed acceleration response data, and the OCSVM, which is employed as a damage detector, are the main innovations and contributions of the suggested approach.

On the other hand, Cardoso and Poppi [46] suggested a novel technique that uses one-class modeling and Raman spectroscopy to examine the adulteration in cassava starch. OCSVM was found to have achieved higher accuracy than other techniques. This study evaluated two methods for one-class classifier models: OC-SVM and soft independent modelling by class analogy (SIMCA).

A new hybrid model was proposed in the previous study [47] that combines an unsupervised deep belief network (DBN) and OCSVM to solve the difficulty of detecting high-dimensional geochemical abnormalities. This model uses DBN to initially extract the pertinent features, which are then fed into the OCSVM. The hybrid method's decision function values are used to map the geochemical patterns associated with iron deposits. The OCSVM is then trained using the features discovered from the original data in order to successfully distinguish the multivariate geochemical anomaly from the geochemical background. Ramp OC-SVM, a robust and nonconvex semi-supervised technique, was proposed by Tian et al. [48]. OCSVM was used to handle the lack of labelled data for deceptive opinions and by utilizing the Ramp loss functions, non-convex features to its advantage, where it removes the impact of non-reviewed opinions and outliers.

In the other work, the large building land area was able to be retrieved from Landsat image data using an OCSVM-based approach [49]. Their works have demonstrated that OCSVM is appropriate for the research of remote sensing image classification when only one class of features is extracted, and expanding the use of OCSVM in remote sensing picture building recognition, demonstrating its effectiveness and precision in this context. In the study by Yin and Wang [50], a new strategy was put forward to detect the outliers of unhealthy leaf images from the massive leaf images dataset using OCSVM. They have established that their modified OCSVM has produced very efficient and robust results in detecting the anomalous data from the extensive dataset of leaf images.

The decision tree classifier and OCSVM were used to create a hybrid intrusion detection system [51]. This system is designed to detect both known Very highly accurate zero-day cyberattacks with low false alarm rates. Using OCSVM as the classifier inside their ensemble learning model, the experimental results have shown that this system outperforms traditional single classifier approaches and proves to be more effective than other machine learning techniques.

On the other hand, a novel personalized federated learning method based on OCSVM was proposed by Anaissi et al. [52]. In this work, the method aims to address the transmission and data privacy concerns raised by central machine learning models by customizing the support vectors that are generated at each client in the distributed learning model structure. Their results have shown that the proposed OCSVM-based personalized federated learning method has achieved significant accuracy and can precisely generalize the clients’ models compared to the other techniques.

Recently, an OCSVM-based algorithm was proposed by Karami and Niaki [53] to overcome the limited sensitivity of fast change point detection, high computing costs, poor scalability with large networks, and excessive reliance on case-based features. It is adaptable to a variety of social network applications and efficiently identifies network disruptions by utilizing both nodal and network-level characteristics. The approach reduces the processing of input data by using a well-defined training data dictionary with an evolutionary network update procedure, improving memory and time efficiency.

Recent application studies also demonstrate the practicality of one-class classification for structural health monitoring using online anomaly detection, emphasizing real-time deployment under limited anomaly labels and evolving operating conditions [54].

(1) Summary of application-oriented implementation

Across diverse application domains, including fault diagnosis, medical analysis, remote sensing, and cybersecurity, OCSVM-based novelty detection demonstrates strong adaptability and consistent performance when labeled anomaly data are scarce. Application-driven studies highlight the importance of domain-specific feature engineering and preprocessing pipelines, which often play a decisive role in detection accuracy. Nevertheless, reliance on handcrafted features or expert knowledge reduces portability across domains. Furthermore, many application-oriented models require careful parameter tuning and exhibit sensitivity to operating conditions, limiting robustness under data drift or evolving environments. These observations suggest that future application-focused research should emphasize adaptive feature learning and automated parameter calibration to improve long-term reliability.

Recent comparative studies continue to include OC-SVM as a primary baseline for unsupervised anomaly detection. For example, Agyemang [55] evaluated OC-SVM against Isolation Forest, Local Outlier Factor, Robust Covariance, and an SGD-based OC-SVM variant, reporting that OC-SVM remains among the most effective methods for identifying outliers, achieving strong recall performance, while highlighting trade-offs with precision depending on the dataset characteristics.

This review examined novelty detection from the perspective of domain-description learning, focusing on SVM-based formulations, particularly SVDD and OCSVM. Unlike probabilistic, distance-based, and reconstruction-based methods, domain-description approaches directly model the boundary of normal data, which explains their broad adoption in scenarios where abnormal samples are rare, unknown, or difficult to label.

The reviewed literature shows that recent progress in SVDD/OCSVM development follows several consistent directions. First, robust loss designs (e.g., ramp, bounded, pinball, or Huberized losses) reduce the influence of outliers and contaminated training data; however, they often introduce non-convex optimization or additional hyperparameters, increasing training complexity and sensitivity. Second, hybrid and deep integration strategies enhance representation learning and improve detection accuracy in high-dimensional domains, but they commonly require extensive tuning and can increase computational cost, limiting practicality in real-time applications. Third, acceleration and scalability techniques, including randomized features and primal-space optimization, reduce computational and memory burdens for large datasets; nonetheless, these improvements may trade off boundary precision in heterogeneous or dynamically evolving environments.

Despite these developments a number of unresolved issues are still present in all of the studies that were surveyed. The sensitivity of OCSVM/SVDD performance to kernel parameters loss settings and threshold selection is a major problem that frequently necessitates expert-driven tuning and decreases portability across domains. The decreased dependability of static decision boundaries under concept drift data drift and non-stationary circumstances particularly in streaming or long-term monitoring settings is another persistent drawback. Lastly while many studies show good empirical performance, they offer few theoretical assurances about generalization and robustness under contamination and distribution shift.

Future research should therefore prioritize: (i) self-tuning and adaptive domain-description models that can update boundaries under drift while maintaining stability, (ii) scalable optimization frameworks that preserve robustness without high computational overhead, and (iii) hybrid methods that combine domain-description learning with modern feature learning while minimizing parameter sensitivity. Addressing these directions will significantly improve the deployability of OCSVM/SVDD-based novelty detection in real-world systems.