SVM Vodič za strojno učenje - Što je algoritam strojnog vektora podrške, objašnjen s primjerima koda

Većina zadataka koje obrađuje strojno učenje trenutno uključuje stvari poput klasificiranja slika, prevođenja jezika, rukovanja velikim količinama podataka sa senzora i predviđanja budućih vrijednosti na temelju trenutnih vrijednosti. Možete odabrati različite strategije kako bi odgovarale problemu koji pokušavate riješiti.

Dobre vijesti? Postoji algoritam u strojnom učenju koji će obrađivati ​​gotovo sve podatke koje na njega možete baciti. Ali stići ćemo tamo za minutu.

Nadzirano i nenadzirano učenje

Dvije najčešće korištene strategije u strojnom učenju uključuju učenje pod nadzorom i učenje bez nadzora.

Što je učenje pod nadzorom?

Nadzirano učenje je kada trenirate model strojnog učenja koristeći označene podatke. To znači da imate podatke koji već imaju odgovarajuću klasifikaciju. Jedna od uobičajenih upotreba nadziranog učenja je pomoć u predviđanju vrijednosti za nove podatke.

Uz nadzirano učenje morat ćete izraditi svoje modele dok dobivate nove podatke kako biste bili sigurni da su vraćena predviđanja i dalje točna. Primjer učenja pod nadzorom bilo bi označavanje slika hrane. Mogli biste imati skup podataka posvećen samo slikama pizze kako biste naučili svoj model što je pizza.

Što je učenje bez nadzora?

Učenje bez nadzora je kad trenirate model s neobilježenim podacima. To znači da će model morati pronaći vlastite značajke i prognozirati na temelju načina na koji klasificira podatke.

Primjer učenja bez nadzora bio bi davanje slika vašem modelu više vrsta hrane bez naljepnica. Skup podataka sadržavao bi slike pizze, pomfrita i druge hrane, a vi biste mogli koristiti različite algoritme kako biste dobili model da identificira samo slike pizze bez ikakvih naljepnica.

Pa, koji je algoritam?

Kad čujete kako ljudi govore o algoritmima strojnog učenja, sjetite se da govore o različitim matematičkim jednadžbama.

Algoritam je samo prilagodljiva matematička funkcija. Zbog toga većina algoritama ima stvari poput funkcija troškova, vrijednosti težine i parametarskih funkcija koje možete međusobno razmijeniti na temelju podataka s kojima radite. U svojoj osnovi, strojno učenje samo je hrpa matematičkih jednadžbi koje treba riješiti vrlo brzo.

Zbog toga postoji toliko različitih algoritama za obradu različitih vrsta podataka. Poseban algoritam je stroj za vektorske potpore (SVM) i to je ono što će ovaj članak detaljno pokriti.

Što je SVM?

Strojevi za vektorske potpore skup su nadziranih metoda učenja koje se koriste za klasifikaciju, regresiju i otkrivanje izvanrednih vrijednosti. Sve su to uobičajeni zadaci u strojnom učenju.

Pomoću njih možete otkriti stanice raka na temelju milijuna slika ili ih možete upotrijebiti za predviđanje budućih ruta vožnje dobro opremljenim regresijskim modelom.

Postoje određene vrste SVM-ova koje možete koristiti za određene probleme strojnog učenja, poput regresije vektora podrške (SVR) koja je produženje klasifikacije vektora podrške (SVC).

Ovdje morate imati na umu da su ovo samo matematičke jednadžbe podešene kako bi vam pružile najtočniji mogući odgovor što je brže moguće.

SVM se razlikuju od ostalih klasifikacijskih algoritama zbog načina na koji odabiru granicu odluke koja maksimizira udaljenost od najbližih podatkovnih točaka svih klasa. Granica odluke koju kreiraju SVM-ovi naziva se klasifikator maksimalne margine ili hiperravnina maksimalne margine.

Kako SVM radi

Jednostavni linearni SVM klasifikator djeluje tako da napravi ravnu liniju između dvije klase. To znači da će sve podatkovne točke na jednoj strani crte predstavljati kategoriju, a podatkovne točke na drugoj strani crte stavit će se u drugu kategoriju. To znači da možete odabrati neograničen broj redaka.

Ono što linearni SVM algoritam čini boljim od nekih drugih algoritama, poput k-najbližih susjeda, jest to što odabire najbolju liniju za klasifikaciju vaših podatkovnih točaka. Odabire liniju koja razdvaja podatke i najudaljenija je od točaka podataka ormara.

Dvodimenzionalni primjer pomaže razumjeti sve žargone strojnog učenja. U osnovi imate neke podatkovne točke na mreži. Pokušavate razdvojiti ove podatkovne točke prema kategoriji u koju bi se trebali uklopiti, ali ne želite imati podatke u pogrešnoj kategoriji. To znači da pokušavate pronaći liniju između dviju najbližih točaka koja drži ostale podatkovne točke odvojenima.

Dakle, dvije najbliže podatkovne točke daju vam vektore podrške pomoću kojih ćete pronaći tu liniju. Ta se crta naziva granicom odluke.

Granica odluke ne mora biti crta. Također se naziva hiperravan jer granicu odluke možete pronaći s bilo kojim brojem značajki, a ne samo s dvije.

Vrste SVM-ova

Postoje dvije različite vrste SVM-ova, koji se koriste za različite stvari:

  • Jednostavni SVM: Tipično se koristi za probleme linearne regresije i klasifikacije.
  • Kernel SVM: Ima veću fleksibilnost za nelinearne podatke jer možete dodati više značajki kako bi se uklopilo u hiperravan umjesto u dvodimenzionalni prostor.

Zašto se SVM koriste u strojnom učenju

SVM se koriste u aplikacijama poput prepoznavanja rukopisa, otkrivanja upada, otkrivanja lica, klasifikacije e-pošte, klasifikacije gena i na web stranicama. To je jedan od razloga što SVM-ove koristimo u strojnom učenju. Može se nositi s klasifikacijom i regresijom linearnih i nelinearnih podataka.

Još jedan razlog zbog kojeg koristimo SVM-ove jest zato što oni mogu pronaći složene odnose između vaših podataka, a da sami ne morate obaviti puno transformacija. To je izvrsna opcija kada radite s manjim skupovima podataka koji imaju desetke do stotine tisuća značajki. Oni obično pronalaze preciznije rezultate u usporedbi s drugim algoritmima zbog svoje sposobnosti rukovanja malim složenim skupovima podataka.

Evo nekoliko prednosti i nedostataka upotrebe SVM-ova.

Pros

  • Učinkovito u skupovima podataka s više značajki, poput financijskih ili medicinskih podataka.
  • Učinkovito u slučajevima kada je broj značajki veći od broja točaka podataka.
  • Koristi podskup točaka treninga u funkciji donošenja odluke nazvanu vektori podrške što je čini memorijski učinkovitom.
  • 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.

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