SVM Machine Learning Tutorial - Hvad er Support Vector Machine Algorithm, forklaret med kodeeksempler

De fleste af de opgaver, som maskinindlæring håndterer lige nu, inkluderer ting som at klassificere billeder, oversætte sprog, håndtere store mængder data fra sensorer og forudsige fremtidige værdier baseret på aktuelle værdier. Du kan vælge forskellige strategier, der passer til det problem, du prøver at løse.

Den gode nyhed? Der er en algoritme i maskinlæring, der håndterer næsten alle data, du kan kaste på den. Men vi kommer der om et øjeblik.

Overvåget vs Uovervåget læring

To af de mest anvendte strategier i maskinindlæring inkluderer overvåget læring og ikke-overvåget læring.

Hvad er overvåget læring?

Supervised learning er, når du træner en maskinlæringsmodel ved hjælp af mærkede data. Det betyder, at du har data, der allerede har den rigtige klassifikation tilknyttet. En almindelig brug af overvåget læring er at hjælpe dig med at forudsige værdier for nye data.

Med overvåget læring skal du genopbygge dine modeller, da du får nye data for at sikre, at de forudsagte forudsigelser stadig er nøjagtige. Et eksempel på overvåget læring ville være mærkning af billeder af mad. Du kan have et datasæt dedikeret til kun billeder af pizza for at lære din model hvad pizza er.

Hvad er læring uden opsyn?

Uovervåget læring er, når du træner en model med umærket data. Dette betyder, at modellen bliver nødt til at finde sine egne funktioner og forudsige ud fra, hvordan den klassificerer dataene.

Et eksempel på uovervåget læring ville være at give din model billeder af flere slags mad uden etiketter. Datasættet ville have billeder af pizza, fries og andre fødevarer, og du kunne bruge forskellige algoritmer til at få modellen til at identificere bare billederne af pizza uden nogen etiketter.

Så hvad er en algoritme?

Når du hører folk tale om maskinlæringsalgoritmer, skal du huske at de taler om forskellige matematiske ligninger.

En algoritme er bare en matematisk funktion, der kan tilpasses. Derfor har de fleste algoritmer ting som omkostningsfunktioner, vægtværdier og parameterfunktioner, som du kan udveksle baseret på de data, du arbejder med. I sin kerne er maskinlæring bare en masse matematiske ligninger, der skal løses rigtig hurtigt.

Derfor er der så mange forskellige algoritmer til at håndtere forskellige slags data. En bestemt algoritme er supportvektormaskinen (SVM), og det er, hvad denne artikel vil dække detaljeret.

Hvad er en SVM?

Supportvektormaskiner er et sæt overvågede læringsmetoder, der bruges til klassificering, regression og detektering af outliers. Alle disse er almindelige opgaver i maskinindlæring.

Du kan bruge dem til at opdage kræftceller baseret på millioner af billeder, eller du kan bruge dem til at forudsige fremtidige kørselsruter med en veludstyret regressionsmodel.

Der er specifikke typer SVM'er, du kan bruge til bestemte maskinindlæringsproblemer, som f.eks. SVR (support vector regression), som er en udvidelse af supportvektorklassifikation (SVC).

Det vigtigste at huske på her er, at dette kun er matematiske ligninger, der er indstillet til at give dig det mest nøjagtige svar så hurtigt som muligt.

SVM'er adskiller sig fra andre klassificeringsalgoritmer på grund af den måde, de vælger beslutningsgrænsen på, der maksimerer afstanden fra de nærmeste datapunkter i alle klasser. Beslutningsgrænsen oprettet af SVM kaldes den maksimale marginklassifikator eller det maksimale margenhyperplan.

Sådan fungerer en SVM

En simpel lineær SVM-klassifikator fungerer ved at lave en lige linje mellem to klasser. Det betyder, at alle datapunkterne på den ene side af linjen repræsenterer en kategori, og datapunkterne på den anden side af linjen placeres i en anden kategori. Dette betyder, at der kan være et uendeligt antal linjer at vælge imellem.

Hvad der gør den lineære SVM-algoritme bedre end nogle af de andre algoritmer, som k-nærmeste naboer, er at den vælger den bedste linje til at klassificere dine datapunkter. Det vælger den linje, der adskiller dataene og er længst væk fra datapunkterne i skabet som muligt.

Et 2-D-eksempel hjælper med at give mening om alt maskinindlæringsjargon. Dybest set har du nogle datapunkter på et gitter. Du prøver at adskille disse datapunkter efter den kategori, de skal passe ind i, men du vil ikke have nogen data i den forkerte kategori. Det betyder, at du prøver at finde linjen mellem de to nærmeste punkter, der holder de andre datapunkter adskilt.

Så de to nærmeste datapunkter giver dig de supportvektorer, du vil bruge til at finde den linje. Denne linje kaldes beslutningsgrænsen.

Beslutningsgrænsen behøver ikke at være en linje. Det kaldes også et hyperplan, fordi du kan finde beslutningsgrænsen med et vilkårligt antal funktioner, ikke kun to.

Typer af SVM'er

Der er to forskellige typer SVM'er, der hver bruges til forskellige ting:

  • Simple SVM: Typisk brugt til lineære regression og klassificeringsproblemer.
  • Kernel SVM: Har mere fleksibilitet til ikke-lineære data, fordi du kan tilføje flere funktioner, så de passer til et hyperplan i stedet for et todimensionelt rum.

Hvorfor SVM'er bruges til maskinindlæring

SVM'er bruges i applikationer som genkendelse af håndskrift, indtrængen detektion, ansigtsgenkendelse, e-mail-klassificering, genklassificering og på websider. Dette er en af ​​grundene til, at vi bruger SVM'er til maskinlæring. Det kan håndtere både klassificering og regression på lineære og ikke-lineære data.

En anden grund til, at vi bruger SVM'er, er fordi de kan finde komplekse forhold mellem dine data uden at du behøver at foretage en masse transformationer alene. Det er en god mulighed, når du arbejder med mindre datasæt, der har titusinder til hundredtusinder af funktioner. De finder typisk mere nøjagtige resultater sammenlignet med andre algoritmer på grund af deres evne til at håndtere små, komplekse datasæt.

Her er nogle af fordele og ulemper ved brug af SVM'er.

Fordele

  • Effektiv på datasæt med flere funktioner, såsom økonomiske eller medicinske data.
  • Effektiv i tilfælde, hvor antallet af funktioner er større end antallet af datapunkter.
  • Bruger en delmængde af træningspunkter i beslutningsfunktionen kaldet supportvektorer, som gør det effektiv til hukommelse.
  • Different kernel functions can be specified for the decision function. You can use common kernels, but it's also possible to specify custom kernels.

Cons

  • If the number of features is a lot bigger than the number of data points, avoiding over-fitting when choosing kernel functions and regularization term is crucial.
  • SVMs don't directly provide probability estimates. Those are calculated using an expensive five-fold cross-validation.
  • Works best on small sample sets because of its high training time.

Since SVMs can use any number of kernels, it's important that you know about a few of them.

Kernel functions

Linear

These are commonly recommended for text classification because most of these types of classification problems are linearly separable.

The linear kernel works really well when there are a lot of features, and text classification problems have a lot of features. Linear kernel functions are faster than most of the others and you have fewer parameters to optimize.

Here's the function that defines the linear kernel:

f(X) = w^T * X + b

In this equation, w is the weight vector that you want to minimize, X is the data that you're trying to classify, and b is the linear coefficient estimated from the training data. This equation defines the decision boundary that the SVM returns.

Polynomial

The polynomial kernel isn't used in practice very often because it isn't as computationally efficient as other kernels and its predictions aren't as accurate.

Here's the function for a polynomial kernel:

f(X1, X2) = (a + X1^T * X2) ^ b

This is one of the more simple polynomial kernel equations you can use. f(X1, X2) represents the polynomial decision boundary that will separate your data. X1 and X2 represent your data.

Gaussian Radial Basis Function (RBF)

One of the most powerful and commonly used kernels in SVMs. Usually the choice for non-linear data.

Here's the equation for an RBF kernel:

f(X1, X2) = exp(-gamma * ||X1 - X2||^2)

In this equation, gamma specifies how much a single training point has on the other data points around it. ||X1 - X2|| is the dot product between your features.

Sigmoid

More useful in neural networks than in support vector machines, but there are occasional specific use cases.

Here's the function for a sigmoid kernel:

f(X, y) = tanh(alpha * X^T * y + C)

In this function, alpha is a weight vector and C is an offset value to account for some mis-classification of data that can happen.

Others

There are plenty of other kernels you can use for your project. This might be a decision to make when you need to meet certain error constraints, you want to try and speed up the training time, or you want to super tune parameters.

Some other kernels include: ANOVA radial basis, hyperbolic tangent, and Laplace RBF.

Now that you know a bit about how the kernels work under the hood, let's go through a couple of examples.

Examples with datasets

To show you how SVMs work in practice, we'll go through the process of training a model with it using the Python Scikit-learn library. This is commonly used on all kinds of machine learning problems and works well with other Python libraries.

Here are the steps regularly found in machine learning projects:

  • Import the dataset
  • Explore the data to figure out what they look like
  • Pre-process the data
  • Split the data into attributes and labels
  • Divide the data into training and testing sets
  • Train the SVM algorithm
  • Make some predictions
  • Evaluate the results of the algorithm

Some of these steps can be combined depending on how you handle your data. We'll do an example with a linear SVM and a non-linear SVM. You can find the code for these examples here.

Linear SVM Example

We'll start by importing a few libraries that will make it easy to work with most machine learning projects.

import matplotlib.pyplot as plt import numpy as np from sklearn import svm

For a simple linear example, we'll just make some dummy data and that will act in the place of importing a dataset.

# linear data X = np.array([1, 5, 1.5, 8, 1, 9, 7, 8.7, 2.3, 5.5, 7.7, 6.1]) y = np.array([2, 8, 1.8, 8, 0.6, 11, 10, 9.4, 4, 3, 8.8, 7.5])

The reason we're working with numpy arrays is to make the matrix operations faster because they use less memory than Python lists. You could also take advantage of typing the contents of the arrays. Now let's take a look at what the data look like in a plot:

# show unclassified data plt.scatter(X, y) plt.show()

Once you see what the data look like, you can take a better guess at which algorithm will work best for you. Keep in mind that this is a really simple dataset, so most of the time you'll need to do some work on your data to get it to a usable state.

We'll do a bit of pre-processing on the already structured code. This will put the raw data into a format that we can use to train the SVM model.

# shaping data for training the model training_X = np.vstack((X, y)).T training_y = [0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1]

Now we can create the SVM model using a linear kernel.

# define the model clf = svm.SVC(kernel='linear', C=1.0)

That one line of code just created an entire machine learning model. Now we just have to train it with the data we pre-processed.

# train the model clf.fit(training_X, training_y)

That's how you can build a model for any machine learning project. The dataset we have might be small, but if you encounter a real-world dataset that can be classified with a linear boundary this model still works.

With your model trained, you can make predictions on how a new data point will be classified and you can make a plot of the decision boundary. Let's plot the decision boundary.

# get the weight values for the linear equation from the trained SVM model w = clf.coef_[0] # get the y-offset for the linear equation a = -w[0] / w[1] # make the x-axis space for the data points XX = np.linspace(0, 13) # get the y-values to plot the decision boundary yy = a * XX - clf.intercept_[0] / w[1] # plot the decision boundary plt.plot(XX, yy, 'k-') # show the plot visually plt.scatter(training_X[:, 0], training_X[:, 1], c=training_y) plt.legend() plt.show()

Non-Linear SVM Example

For this example, we'll use a slightly more complicated dataset to show one of the areas SVMs shine in. Let's import some packages.

import matplotlib.pyplot as plt import numpy as np from sklearn import datasets from sklearn import svm

This set of imports is similar to those in the linear example, except it imports one more thing. Now we can use a dataset directly from the Scikit-learn library.

# non-linear data circle_X, circle_y = datasets.make_circles(n_samples=300, noise=0.05)

The next step is to take a look at what this raw data looks like with a plot.

# show raw non-linear data plt.scatter(circle_X[:, 0], circle_X[:, 1], c=circle_y, marker=".") plt.show()

Now that you can see how the data are separated, we can choose a non-linear SVM to start with. This dataset doesn't need any pre-processing before we use it to train the model, so we can skip that step. Here's how the SVM model will look for this:

# make non-linear algorithm for model nonlinear_clf = svm.SVC(kernel='rbf', C=1.0)

In this case, we'll go with an RBF (Gaussian Radial Basis Function) kernel to classify this data. You could also try the polynomial kernel to see the difference between the results you get. Now it's time to train the model.

# training non-linear model nonlinear_clf.fit(circle_X, circle_y)

You can start labeling new data in the correct category based on this model. To see what the decision boundary looks like, we'll have to make a custom function to plot it.

# Plot the decision boundary for a non-linear SVM problem def plot_decision_boundary(model, ax=None): if ax is None: ax = plt.gca() xlim = ax.get_xlim() ylim = ax.get_ylim() # create grid to evaluate model x = np.linspace(xlim[0], xlim[1], 30) y = np.linspace(ylim[0], ylim[1], 30) Y, X = np.meshgrid(y, x) # shape data xy = np.vstack([X.ravel(), Y.ravel()]).T # get the decision boundary based on the model P = model.decision_function(xy).reshape(X.shape) # plot decision boundary ax.contour(X, Y, P, levels=[0], alpha=0.5, linestyles=['-'])

You have everything you need to plot the decision boundary for this non-linear data. We can do that with a few lines of code that use the Matlibplot library, just like the other plots.

# plot data and decision boundary plt.scatter(circle_X[:, 0], circle_X[:, 1], c=circle_y, s=50) plot_decision_boundary(nonlinear_clf) plt.scatter(nonlinear_clf.support_vectors_[:, 0], nonlinear_clf.support_vectors_[:, 1], s=50, lw=1, facecolors="none") plt.show()

When you have your data and you know the problem you're trying to solve, it really can be this simple.

You can change your training model completely, you can choose different algorithms and features to work with, and you can fine tune your results based on multiple parameters. There are libraries and packages for all of this now so there's not a lot of math you have to deal with.

Tips for real world problems

Real world datasets have some common issues because of how large they can be, the varying data types they hold, and how much computing power they can need to train a model.

There are a few things you should watch out for with SVMs in particular:

  • Make sure that your data are in numeric form instead of categorical form. SVMs expect numbers instead of other kinds of labels.
  • Avoid copying data as much as possible. Some Python libraries will make duplicates of your data if they aren't in a specific format. Copying data will also slow down your training time and skew the way your model assigns the weights to a specific feature.
  • Watch your kernel cache size because it uses your RAM. If you have a really large dataset, this could cause problems for your system.
  • Scale your data because SVM algorithms aren't scale invariant. That means you can convert all of your data to be within the ranges of [0, 1] or [-1, 1].

Other thoughts

You might wonder why I didn't go into the deep details of the math here. It's mainly because I don't want to scare people away from learning more about machine learning.

It's fun to learn about those long, complicated math equations and their derivations, but it's rare you'll be writing your own algorithms and writing proofs on real projects.

It's like using most of the other stuff you do every day, like your phone or your computer. You can do everything you need to do without knowing the how the processors are built.

Machine learning is like any other software engineering application. There are a ton of packages that make it easier for you to get the results you need without a deep background in statistics.

Once you get some practice with the different packages and libraries available, you'll find out that the hardest part about machine learning is getting and labeling your data.

Jeg arbejder på en neurovidenskab, maskinindlæring, webbaseret ting! Du bør følge mig på Twitter for at lære mere om det og andre seje tekniske ting.