Tech

# SVM Vs. Neural Network 1. ## Overview

This post will explore the main similarities and differences between two popular algorithms in machine learning: support vector machines (SVM) and neural networks (NN).

Let’s start with a brief explanation of both, examine their most essential characteristics, and then note the differences between SVM and NN.

Finally, we will explore several scenarios or use cases that require a choice between neural networks and support vector machines.

At the end of this post, we’ll learn what makes support vector machines different from neural networks and when to use one over the other.

1. ## Highlighting the boundaries of the problem

### 2.1 General classification

The logic of the narrative requires that we begin the consideration of the material with a brief discussion of the problem of classification. Usually, to solve it, specialists resort to both auxiliary vector machines (from now on: SVM) and neural networks (NN).

Any classification task will be to study a function of the form y = f(x), where x is the feature vector, and y is the vector corresponding to the classes associated with the observations.

Both SVMs and NNs are good at this task. The advantage of SVM is having an appropriate choice of kernel. In the case of NNs, we often deal with the most efficient product activation function. Thus, the difference between programs is not in the types of tasks they are capable of solving; but in the difference in the characteristics of their theoretical foundations and the realization of the possibilities inherent in them.

They both can also, just as significantly, approximate linear and non-linear functions:

This means that both versions of the algorithm are equally capable of solving all types of classification problems; therefore, the decision to use one instead of the other has nothing to do with the problem itself. One final note: both the SVM and NNs we are discussing here refer solely to the difference in classification options. However, these are not the only possible forms of SVM or NNs.

### 2.2. Approximating the Decision Boundary With NNs

Let’s start considering the issues of interest to us with single-layer networks. It follows from the universal approximation theorem that a neural network with only one hidden layer can approximate almost any continuous function with a rational choice of weights.

Let’s start considering the issues of interest to us with single-layer networks. It follows from the universal approximation theorem that a neural network with only one hidden layer can approximate almost any continuous function with a rational choice of weights.

Suppose we define the boundaries of the solution of classification problems as a continuous function. In this case, it can also be defined as a continuous feature space mapping. And the universal approximation theorem guarantees that NNs can approximate it.

### 2.3. Approximating the Decision Boundary With SVMs

If we are talking about SVM, then the principle of the system will be slightly different. Support Vector Machines, during operation, identify the hyperplane that corresponds like nothing else to the best possible separation among the nearest observations belonging to 2 different classes. These observations are called “support vectors”; for a properly named SVM, they are a small subset of the system’s entire set of data.

1. ## Comparative analysis of SVMs and NNs

### 3.1Parametric function

Now we can compare two algorithms, between which there are many similarities. The first similarity comes from the fact that both of them are parametric. The reasons for this are quite different from each other. But the fact remains.

Neural networks also tend to use parameters, although their requirements can be much more significant. The most critical parameters of this algorithm regulate the density and number of layers and their size. Thus, there is an apparent similarity between the models since they are both parametric but differ by type and number of parameters required.

### 3.2 Embedded non-linearity

SVM uses non-linearity thanks to the kernel method. Neural networks, in turn, are sharpened to use a non-linear activation function. One of the main reasons for developing neural networks is the need to overcome the problem of classifying nonlinear observations. This means that non-linearity is their fundamental characteristic.

The fundamental difference between the two algorithms concerns their basic structure. SVM has many options. One of them is related to the linear increase in the input data size in NNs.

Even though this article focuses on single-layer networks, we should not forget that a neural network can have many layers. As a rule, their number will depend solely on the developer’s desire. As a result, a NN with the same number of parameters as an SVM will always have a higher complexity than the latter.

This is due to the more complex interaction between model parameters. In NNs, it is limited to those belonging to neighboring layers. Instead, SVM has parameter C that regulates the overfitting for soft-margin.

### 3.3 Algorithm learning methods

One of the most essential differences between SVM and NNs concerns the time required to train the algorithm. If you wish, you can learn how to work with SVM in the shortest possible time. This does not apply to planting neural networks. The process of learning to work with them can take much more of your time.

Learning how to work with neural networks of a high degree of complexity usually takes several days and sometimes weeks. This means that restarting training and initialization of work for SVM and NNs occurs entirely differently.

### Brief conclusions

Above, we briefly noted the similarities and differences between support vector machines and neural networks. A clear understanding of the main similarities and differences between the two algorithms for solving classification problems is crucial for working effectively with them. If you have difficulties with introduction of AI technology to your business project, get professional consultation from this ML team. Only having the whole amount of theoretical knowledge about the operation of algorithms you will be able to work effectively with both SVM Vs. Neural networks.