Mathematical Problems in Engineering

Volume 2018, Article ID 8243764, 13 pages

https://doi.org/10.1155/2018/8243764

## Semisupervised SVM Based on Cuckoo Search Algorithm and Its Application

School of Electronics and Information Engineering, Hebei University of Technology, Tianjin 300401, China

Correspondence should be addressed to Kewen Xia; nc.ude.tubeh@aixwk

Received 12 June 2018; Revised 15 July 2018; Accepted 14 August 2018; Published 13 September 2018

Academic Editor: Francesco Riganti-Fulginei

Copyright © 2018 Ziping He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Semisupervised support vector machine (S3VM) algorithm mainly depends on the predicted accuracy of unlabeled samples, if lots of misclassified unlabeled samples are added to the training will make the training model performance degrade. Thus, the cuckoo search algorithm (CS) is used to optimize the S3VM which also enhances the model performance of S3VM. Considering that the cuckoo search algorithm is limited to the local optimum problem, a new cuckoo search algorithm based on chaotic catfish effect optimization is proposed. First, use the chaotic mechanism with high randomness to initialize the nest for range expansion. Second, chaotic catfish nest is introduced into the effective competition coordination mechanism after falling into the local optimum, so that the candidate’s nest can jump out of the local optimal solution and accelerate the convergence ability. In the experiment, results show that the improved cuckoo search algorithm is effective and better than the particle swarm optimization (PSO) algorithm and the cuckoo search algorithm on the benchmark functions. In the end, the improved cuckoo search algorithm is used to optimize semisupervised SVM which is applied into oil layer recognition. Results show that this optimization model is superior to the semisupervised SVM in terms of recognition rate and time.

#### 1. Introduction

Semisupervised learning [1] studies how to improve learning performance by using labeled and unlabeled samples simultaneously. It has become a research focus and hotspot in pattern recognition and machine learning. In such a mixed data learning process, the sample distribution information of the unlabeled dataset is transferred to the final learning model, so that the trained learning model has better performance. Literature [2] proposes a novel graph for semisupervised discriminant analysis, which is called combined low-rank and k-nearest neighbor (LRKNN) graph, and map the data to the LR feature space and then the KNN is adopted to satisfy the algorithmic requirements of Semisupervised Discriminant Analysis (SDA). Semisupervised support vector machine is first proposed by Professor V. Vapnik [3] when the labeled samples are not enough, and it is difficult to achieve satisfactory performance; support vector machine (SVM) can use the transductive learning to improve the performance. It can be regarded as the generalization of the SVM in the unlabeled samples. S3VM has received extensive attention in recent years. Qing Wu et al. [4] described a smooth piecewise function and research smooth piecewise semisupervised SVM and used a converging linear PSO to train semisupervised SVM to get better classification accuracy. Luo et al. [5] introduced semisupervised learning for the least squares support vector machine (LSSVM) algorithm to improve the accuracy of model predictions and is used to predict the distribution of porosity and sandstone in the Jingzhou study area. Literature [6] puts forward a method with the name of Ensemble S3VM which deals with the unknown distribution by ensemble learning and applies the algorithm to ground cover classification for polarimetric synthetic aperture radar images.

Cuckoo search [7] algorithm is a new nature-inspired metaheuristic based on the obligate brood parasitic behavior of cuckoo species [8] and the Levy flight search mechanism to effectively solve the optimization problem [9]. In order to further optimize the CS algorithm, many experts and scholars have studied it. When Srivastava et al. [10] investigate local search in Levy flights, they enter tabu search idea to avoid falling into local optimum, which is successfully applied to solve the problem of automatic generation of software test data. Yang and Deb [11] proposed a multitarget cuckoo search, which was applied to engineering optimization and achieved good results. Zhang et al. [12] prescribed a modified adaptive cuckoo search (MACS) to improve the performance of CS. Wang et al. [13] used an evaluation strategy based on a dimension-by-dimension update for the progress of the iteration of the improved algorithm and proposed an enhanced CS algorithm. In literature [14], a new local-enhanced cuckoo search algorithm is designed aiming to deal with some multimodal numerical problems. Literature [15] considers utilizing multiple chaotic maps simultaneously to perform the local search within the neighborhood of the global best solution found by the chaotic cuckoo search algorithm.

The above-improved versions of CS algorithm jumped out of the local optimal or improve the convergence speed of the algorithm. In view of the fact that CS algorithm is coming to the end of the iteration, population groups tend to converge too early and lead to local optimum. First, we use chaos mapping instead of general randomization to initialize nest position, it makes the initial nest location not only has the distribution randomness but also strengthens the diversity of the bird’s nest distribution. Second, according to the literature [16], they used catfish effect to optimize artificial bee colony (ABC) algorithm in order to obtain a good ability to jump out of local optimum, we applied the catfish effect to CS algorithm, added it to the nest, and then get the chaotic catfish nest. Consequently, it improves the convergence rate of the whole population and the shortage of the algorithm into a local optimum. Finally, the CS algorithm based on the above-improved strategy is used to optimize the S3VM algorithm and apply it to the oil layer recognition and establish a new semisupervised oil layer recognition model, expecting a better recognition of oil layers.

#### 2. Cuckoo Search Algorithm and Its Improvement

##### 2.1. Cuckoo Search Algorithm Principle

###### 2.1.1. Cuckoo Breeding Behavior

According to the long-term observations of an entomologist, cuckoo has adopted a special breeding strategy parasitic brood [8]. It lays eggs in the nests of other birds and allows other birds to hatch. In order to reduce the possibility of being discovered by host birds, the cuckoo will choose the host birds that are basically alike in eating habits and easy to imitate ovately and color. When it flies to a nest, it only produces one and removes the host’s egg before spawning, or all out of the nest, forcing the host to lay eggs again. Once the cuckoo’s hatchlings hatch, it has the habit of bringing the host chicks out of the nest, thus enjoying the host bird’s tending. But when the host birds find their nests have foreign eggs, they also throw the parasitic eggs or abandon their nests and build a nest in other places.

###### 2.1.2. Levy Flights

Various studies have shown that the flight behavior of many animals and insects has demonstrated the typical characteristics of Levy flights [17–19]. A study by Reynolds and Frye shows that fruit flies or Drosophila melanogaster explore their landscape using a series of straight flight paths punctuated by a sudden turn, leading to a Levy-flight-style intermittent scale-free search pattern. Studies on human behavior such as the Ju/’hoansi hunter-gatherer foraging patterns also show the typical feature of Levy flights. Even light can be related to Levy flights [20]. And when the target location is random and sparsely distributed, Levy flight is the best search strategy for M independent search seekers.

Levy flight belongs to one type of random walk, and the walking step satisfies a stable distribution of heavy-tailed. In this form of walking, short distance exploration and occasional long distance walk alternate. Levy flight in intelligent optimization algorithm can expand search scope, increase population diversity and make it easier to jump out of local optimum.

Subsequently, such behavior has been applied to optimization and optimal search, and preliminary results show its promising capability [18].

###### 2.1.3. Cuckoo Search

The cuckoo search algorithm is based on the parasitic propagation mechanism of cuckoo bird and Levy flights search principle. It is mainly based on the following three ideal rules:(1)Each cuckoo lays one egg at one time and selects a nest randomly to hatch it.(2)The best nests will be preserved to the next generation in a randomly selected group of nests.(3)The number of nests available is fixed, and the probability that the host bird of a nest will find the exotic bird’s egg is .

On the basis of the above three ideal rules, the routing and location updating formula of cuckoo's nest is as follows:In the case, is the size of step, =1 in general. is point multiplication, and is the search path.

The Levy flight essentially provides a random walk while the random step length is drawn from a levy distribution as shown in the following formula:which has an infinite variance with an infinite mean. Here the steps essentially form a random walk process with a power-law step-length distribution with a heavy tail. Some of the new solutions should be generated by Levy walk around the best solution obtained so far; this will speed up the local search. However, a substantial fraction of the new solutions should be generated by far-field randomization and whose location should be far enough from the current best solution, this will make sure the system will not be trapped in a local optimum.

To sum up, the main steps of the CS algorithm can be described as follows.

*Step 1. *The objective function is , initialization group, and generates the initial position of N bird's nest randomly.

*Step 2. *Calculate the objective function value of each nest and record the current best solution.

*Step 3. *Keep the location of the best nest in the previous generation, and update the position of other bird's nest according to formula (1).

*Step 4. *Comparing the existing bird’s nest with the previous generation, if it is better, it takes it as the best position at present.

*Step 5. *Using a random number R compare with , if , then change the nest position randomly, and get a new set of nest position.

*Step 6. *If the end condition is not met, return Step 2.

*Step 7. *Output global optimal position.

##### 2.2. The Cuckoo Search Algorithm Based on Chaotic Catfish Effect

###### 2.2.1. Initial Chaotic Nest

The initial nest location of the bird’s nest is an important link in the CS algorithm. It not only affects the convergence speed of the algorithm but also restricts the quality of the final solution of the problem. According to the randomness, regularity, and mutual correlation of chaotic systems, we use chaos mapping to extract and capture information in the solution space to enhance the diversity of the initial bird nest location. In this paper, the logistic chaotic mapping is adopted, and its mathematical iterative equation is as follows:Among them, T is a presupposed maximum number of chaotic iterations and is a random number distributed uniformly on the interval , because the initial value cannot take any of the fixed points; otherwise it is a stable orbit and cannot generate chaos, so . is chaos control parameters; the system will be in a state of complete chaos when =4.

Firstly, a set of chaotic variables is produced by using formula (3); secondly, we map the location of n, d dimension nest to the chaotic interval by the chaotic sequence once according to formula (4). and represent the largest and the smallest boundary of , respectively. The average accuracy is the fitness function, which is based on the k-fold cross-validation approach. The distribution of nest is shown in Figure 1.