SVM-i masinõppe õpetus - mis on tugivektori masina algoritm, mida on selgitatud koodinäidetega

Enamik masinõppe ülesannetest sisaldab praegu selliseid asju nagu piltide klassifitseerimine, keelte tõlkimine, anduritest suure hulga andmete käitlemine ja tulevaste väärtuste ennustamine praeguste väärtuste põhjal. Võite valida erinevad strateegiad, mis sobivad probleemiga, mida proovite lahendada.

Hea uudis? Masinaõppes on algoritm, mis käsitleb peaaegu kõiki andmeid, mida saate sellesse visata. Kuid me jõuame sinna minutiga.

Juhendatud vs järelevalveta õppimine

Kaks masinõppes kõige sagedamini kasutatavat strateegiat hõlmavad juhendatud õppimist ja järelevalveta õppimist.

Mis on juhendatud õppimine?

Juhendatud õppimine on see, kui koolitate masinõppemudelit sildistatud andmete abil. See tähendab, et teil on andmeid, millel on juba õige klassifikatsioon seotud. Juhendatud õppe üks levinud kasutusviis on aidata teil uute andmete väärtusi ennustada.

Juhendatud õppimise korral peate uute andmete saamisel oma mudelid uuesti üles ehitama, et veenduda, et tagastatud ennustused on ikka õiged. Juhendatud õppe näide oleks toidupiltide sildistamine. Teil võiks olla andmekogum, mis on pühendatud lihtsalt pitsa piltidele, et õpetada oma mudelit, mis pizza on.

Mis on järelevalveta õppimine?

Järelevalveta õppimine on see, kui koolitate sildistamata andmetega mudelit. See tähendab, et mudel peab leidma oma funktsioonid ja tegema ennustusi andmete klassifitseerimise põhjal.

Järelevalveta õppimise näide on see, kui annate oma mudelile pilte mitut liiki toidust, millel pole silte. Andmekogumil oleks pitsa, friikartulite ja muude toitude kujutised ning võite kasutada erinevaid algoritme, et mudel tuvastaks ainult pitsapildid ilma siltideta.

Mis on algoritm?

Kui kuulete inimesi rääkimas masinõppe algoritmidest, pidage meeles, et nad räägivad erinevatest matemaatikavõrranditest.

Algoritm on lihtsalt kohandatav matemaatikafunktsioon. Seetõttu on enamikul algoritmidel sellised funktsioonid nagu kulufunktsioonid, kaalu väärtused ja parameetrifunktsioonid, mida saate vahetada nende andmete põhjal, millega töötate. Põhimõtteliselt on masinõpe vaid hunnik matemaatilisi võrrandeid, mis tuleb tõesti kiiresti lahendada.

Seetõttu on erinevat tüüpi andmete töötlemiseks nii palju erinevaid algoritme. Üks konkreetne algoritm on tugivektorimasin (SVM) ja seda see artikkel üksikasjalikult kajastab.

Mis on SVM?

Tugivektorimasinad on juhendatud õppemeetodite kogum, mida kasutatakse liigitamisel, regressioonil ja kõrvalekallete tuvastamisel. Kõik need on masinõppes tavalised ülesanded.

Võite kasutada neid vähirakkude tuvastamiseks miljonite piltide põhjal või kasutada neid hästi paigaldatud regressioonimudeli abil tulevaste sõiduteede ennustamiseks.

Konkreetsete masinõppeprobleemide jaoks saate kasutada teatud tüüpi SVM-e, näiteks tugivektori regressioon (SVR), mis on tugivektorite klassifikatsiooni (SVC) laiendus.

Peamine, mida siin silmas pidada, on see, et need on vaid matemaatilised võrrandid, mis on häälestatud nii, et saaksite võimalikult täpse vastuse.

SVM-id erinevad teistest klassifitseerimisalgoritmidest sellepärast, et nad valivad otsuse piiri, mis maksimeerib kauguse kõigi klasside lähimatest andmepunktidest. SVM-ide loodud otsuste piiri nimetatakse maksimaalse marginaali klassifikaatoriks või maksimaalse marginaali hüpertasandiks.

Kuidas SVM töötab

Lihtne lineaarne SVM-i klassifikaator töötab kahe klassi vahel sirgjoonena. See tähendab, et kõik joone ühel küljel olevad andmepunktid esindavad kategooriat ja rea ​​teisel poolel olevad andmepunktid liigitatakse teise kategooriasse. See tähendab, et valida võib lõpmatu arv ridu.

Mis teeb lineaarse SVM-i algoritmi mõnest teisest algoritmist, näiteks k-lähimatest naabritest, paremaks, on see, et see valib teie andmepunktide klassifitseerimiseks parima rea. See valib rea, mis eraldab andmeid ja asub kapi andmepunktidest kõige kaugemal.

2-D näide aitab kogu masinõppe žargooni mõtestada. Põhimõtteliselt on teil võrgus mõned andmepunktid. Püüate eraldada need andmepunktid kategooria järgi, millesse need peaksid sobima, kuid te ei soovi, et andmed oleksid vales kategoorias. See tähendab, et proovite leida joont kahe lähima punkti vahel, mis hoiab teised andmepunktid eraldatud.

Nii et kaks lähimat andmepunkti annavad teile tugivektorid, mida saate selle joone leidmiseks kasutada. Seda joont nimetatakse otsustamispiiriks.

Otsuse piir ei pea olema joon. Seda nimetatakse ka hüperlennukiks, sest otsustuspiiri leiate mis tahes arvu funktsioonidega, mitte ainult kahega.

SVM-ide tüübid

On kahte erinevat tüüpi SVM-e, mida kasutatakse erinevateks asjadeks:

  • Lihtne SVM: kasutatakse tavaliselt lineaarse regressiooni ja klassifitseerimise probleemide korral.
  • Kerneli SVM: Mittelineaarsete andmete jaoks on suurem paindlikkus, kuna saate lisada rohkem funktsioone, et mahutada kahemõõtmelise ruumi asemel hüpertasapind.

Miks kasutatakse masinõppes SVM-e

SVM-e kasutatakse sellistes rakendustes nagu käekirja tuvastamine, sissetungi tuvastamine, näotuvastus, e-posti klassifikatsioon, geenide klassifikatsioon ja veebilehtedel. See on üks põhjus, miks me kasutame masinõppes SVM-e. See saab hakkama nii lineaarsete kui mittelineaarsete andmete klassifitseerimise ja regressiooniga.

Teine põhjus, miks me SVM-e kasutame, on see, et nad leiavad teie andmete vahel keerukad seosed ilma, et peaksite ise palju teisendusi tegema. See on suurepärane võimalus, kui töötate väiksemate andmekogumitega, millel on kümneid kuni sadu tuhandeid funktsioone. Tavaliselt leiavad nad teiste algoritmidega võrreldes täpsemaid tulemusi, kuna neil on võimalus käituda väikeste ja keeruliste andmekogumitega.

Siin on mõned plussid ja miinused SVM-ide kasutamiseks.

Plussid

  • Mõjutab mitme funktsiooniga andmekogumitele, näiteks finants- või meditsiiniandmetele.
  • Tõhus juhtudel, kui funktsioonide arv on suurem kui andmepunktide arv.
  • Kasutab otsustamisfunktsioonis treeningpunktide alamhulka, mida nimetatakse tugivektoriteks, mis muudab selle mälutõhusaks.
  • 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.

Töötan neuroteaduse, masinõppe, veebipõhise asja kallal! Peaksite mind Twitteris jälgima, et rohkem teada saada selle ja muu laheda tehnika kohta.