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17,000 | has very active user community it contains number of state-of-the-art machine learning algorithmsas well as comprehensive documentation about each algorithm scikit-learn is very popular tooland the most prominent python library for machine learning it is widely used in industry and academiaand wealth of tutorials and c... |
17,001 | packagespip install numpy scipy matplotlib ipython scikit-learn pandas essential libraries and tools understanding what scikit-learn is and how to use it is importantbut there are few other libraries that will enhance your experience scikit-learn is built on top of the numpy and scipy scientific python libraries in add... |
17,002 | [[ [ ]we will be using numpy lot in this bookand we will refer to objects of the numpy ndarray class as "numpy arraysor just "arrays scipy scipy is collection of functions for scientific computing in python it providesamong other functionalityadvanced linear algebra routinesmathematical function optimizationsignal proc... |
17,003 | not fit into memory)so we need to create sparse representations directly here is way to create the same sparse matrix as beforeusing the coo formatin[ ]data np ones( row_indices np arange( col_indices np arange( eye_coo sparse coo_matrix((data(row_indicescol_indices))print("coo representation:\ {}format(eye_coo)out[ ]c... |
17,004 | pandas pandas is python library for data wrangling and analysis it is built around data structure called the dataframe that is modeled after the dataframe simply puta pandas dataframe is tablesimilar to an excel spreadsheet pandas provides great range of methods to modify and operate on this tablein particularit allows... |
17,005 | age location name new york john paris anna berlin peter london linda there are several possible ways to query this table for examplein[ ]select all rows that have an age column greater than display(data_pandas[data_pandas age ]this produces the following resultage location name berlin peter london linda mglearn this bo... |
17,006 | there are two major versions of python that are widely used at the momentpython (more precisely and python (with the latest release being at the time of writingthis sometimes leads to some confusion python is no longer actively developedbut because python contains major changespython code usually does not run on python... |
17,007 | python version|anaconda ( -bit)(defaultjul [gcc (red hat - )pandas versionmatplotlib versionnumpy versionscipy versionipython versionscikit-learn version : : while it is not important to match these versions exactlyyou should have version of scikit-learn that is as least as recent as the one we used now that we have ev... |
17,008 | because we have measurements for which we know the correct species of iristhis is supervised learning problem in this problemwe want to predict one of several options (the species of iristhis is an example of classification problem the possible outputs (different species of irisesare called classes every iris in the da... |
17,009 | print("keys of iris_dataset\ {}format(iris_dataset keys())out[ ]keys of iris_datasetdict_keys(['target_names''feature_names''descr''data''target']the value of the key descr is short description of the dataset we show the beginning of the description here (feel free to look up the rest yourself)in[ ]print(iris_dataset['... |
17,010 | print("type of data{}format(type(iris_dataset['data']))out[ ]type of datathe rows in the data array correspond to flowerswhile the columns represent the four measurements that were taken for each flowerin[ ]print("shape of data{}format(iris_dataset['data'shape)out[ ]shape of data( we see that the array contains measure... |
17,011 | print("shape of target{}format(iris_dataset['target'shape)out[ ]shape of target( ,the species are encoded as integers from to in[ ]print("target:\ {}format(iris_dataset['target'])out[ ]target[ the meanings of the numbers are given by the iris['target_names'array means setosa means versicolorand means virginica measurin... |
17,012 | what arbitrarybut using test set containing of the data is good rule of thumb in scikit-learndata is usually denoted with capital xwhile labels are denoted by lowercase this is inspired by the standard formulation ( )= in mathematicswhere is the input to function and is the output following more conventions from mathem... |
17,013 | print("x_test shape{}format(x_test shape)print("y_test shape{}format(y_test shape)out[ ]x_test shape( y_test shape( ,first things firstlook at your data before building machine learning model it is often good idea to inspect the datato see if the task is easily solvable without machine learningor if the desired informa... |
17,014 | from the plotswe can see that the three classes seem to be relatively well separated using the sepal and petal measurements this means that machine learning model will likely be able to learn to separate them building your first modelk-nearest neighbors now we can start building the actual machine learning model there ... |
17,015 | to the new data pointwe can consider any fixed number of neighbors in the training (for examplethe closest three or five neighborsthenwe can make prediction using the majority class among these neighbors we will go into more detail about this in for nowwe'll use only single neighbor all machine learning models in sciki... |
17,016 | we can now make predictions using this model on new data for which we might not know the correct labels imagine we found an iris in the wild with sepal length of cma sepal width of cma petal length of cmand petal width of cm what species of iris would this bewe can put this data into numpy arrayagain by calculating the... |
17,017 | y_pred knn predict(x_testprint("test set predictions:\ {}format(y_pred)out[ ]test set predictions[ in[ ]print("test set score{ }format(np mean(y_pred =y_test))out[ ]test set score we can also use the score method of the knn objectwhich will compute the test set accuracy for usin[ ]print("test set score{ }format(knn sco... |
17,018 | data point and one column per feature the array is one-dimensional arraywhich here contains one class labelan integer ranging from to for each of the samples we split our dataset into training setto build our modeland test setto evaluate how well our model will generalize to newpreviously unseen data we chose the -near... |
17,019 | supervised learning as we mentioned earliersupervised machine learning is one of the most commonly used and successful types of machine learning in this we will describe supervised learning in more detail and explain several popular supervised learning algorithms we already saw an application of supervised machine lear... |
17,020 | tive class and the other class being the negative class herepositive doesn' represent having benefit or valuebut rather what the object of the study is sowhen looking for spam"positivecould mean the spam class which of the two classes is called positive is often subjective matterand specific to the domain the iris exam... |
17,021 | training set if the training and test sets have enough in commonwe expect the model to also be accurate on the test set howeverthere are some cases where this can go wrong for exampleif we allow ourselves to build very complex modelswe can always be as accurate as we like on the training set let' take look at made-up e... |
17,022 | rules that work well on this dataremember that we are not interested in making predictions for this datasetwe already know the answers for these customers we want to know if new customers are likely to buy boat we therefore want to find rule that will work well for new customersand achieving percent accuracy on the tra... |
17,023 | relation of model complexity to dataset size it' important to note that model complexity is intimately tied to the variation of inputs contained in your training datasetthe larger variety of data points your dataset containsthe more complex model you can use without overfitting usuallycollecting more data points will y... |
17,024 | nesses of each algorithmand what kind of data they can best be applied to we will also explain the meaning of the most important parameters and options many algorithms have classification and regression variantand we will describe both it is not necessary to read through the descriptions of each algorithm in detailbut ... |
17,025 | as you can see from shapethis dataset consists of data pointswith features to illustrate regression algorithmswe will use the synthetic wave dataset the wave dataset has single input feature and continuous target variable (or responsethat we want to model the plot created here (figure - shows the single feature on the ... |
17,026 | showing the regression target we are using these very simplelow-dimensional datasets because we can easily visualize them-- printed page has two dimensionsso data with more than two features is hard to show any intuition derived from datasets with few features (also called low-dimensional datasetsmight not hold in data... |
17,027 | cancer keys()dict_keys(['feature_names''data''descr''target''target_names']datasets that are included in scikit-learn are usually stored as bunch objectswhich contain some information about the dataset as well as the actual data all you need to know about bunch objects is that they behave like dictionarieswith the adde... |
17,028 | we will also be using real-world regression datasetthe boston housing dataset the task associated with this dataset is to predict the median value of homes in several boston neighborhoods in the susing information such as crime rateproximity to the charles riverhighway accessibilityand so on the dataset contains data p... |
17,029 | the -nn algorithm is arguably the simplest machine learning algorithm building the model consists only of storing the training dataset to make prediction for new data pointthe algorithm finds the closest data points in the training dataset--its "nearest neighbors -neighbors classification in its simplest versionthe -nn... |
17,030 | numberkof neighbors this is where the name of the -nearest neighbors algorithm comes from when considering more than one neighborwe use voting to assign label this means that for each test pointwe count how many neighbors belong to class and how many neighbors belong to class we then assign the class that is more frequ... |
17,031 | from sklearn model_selection import train_test_split xy mglearn datasets make_forge(x_trainx_testy_trainy_test train_test_split(xyrandom_state= nextwe import and instantiate the class this is when we can set parameterslike the number of neighbors to use herewe set it to in[ ]from sklearn neighbors import kneighborsclas... |
17,032 | threeand nine neighbors shown in figure - in[ ]figaxes plt subplots( figsize=( )for n_neighborsax in zip([ ]axes)the fit method returns the object selfso we can instantiate and fit in one line clf kneighborsclassifier(n_neighbors=n_neighborsfit(xymglearn plots plot_ d_separator(clfxfill=trueeps= ax=axalpha mglearn disc... |
17,033 | the results are shown in figure - in[ ]from sklearn datasets import load_breast_cancer cancer load_breast_cancer(x_trainx_testy_trainy_test train_test_splitcancer datacancer targetstratify=cancer targetrandom_state= training_accuracy [test_accuracy [try n_neighbors from to neighbors_settings range( for n_neighbors in n... |
17,034 | -neighbors regression there is also regression variant of the -nearest neighbors algorithm againlet' start by using the single nearest neighborthis time using the wave dataset we've added three test data points as green stars on the -axis the prediction using single neighbor is just the target value of the nearest neig... |
17,035 | againwe can use more than the single closest neighbor for regression when using multiple nearest neighborsthe prediction is the averageor meanof the relevant neighbors (figure - )in[ ]mglearn plots plot_knn_regression(n_neighbors= supervised machine learning algorithms |
17,036 | the -nearest neighbors algorithm for regression is implemented in the kneighbors regressor class in scikit-learn it' used similarly to kneighborsclassifierin[ ]from sklearn neighbors import kneighborsregressor xy mglearn datasets make_wave(n_samples= split the wave dataset into training and test set x_trainx_testy_trai... |
17,037 | test set predictions[- - - - - - we can also evaluate the model using the score methodwhich for regressors returns the score the scorealso known as the coefficient of determinationis measure of goodness of prediction for regression modeland yields score between and value of corresponds to perfect predictionand value of... |
17,038 | values of n_neighbors as we can see from the plotusing only single neighboreach point in the training set has an obvious influence on the predictionsand the predicted values go through all of the data points this leads to very unsteady prediction considering more neighbors leads to smoother predictionsbut these do not ... |
17,039 | linear models are class of models that are widely used in practice and have been studied extensively in the last few decadeswith roots going back over hundred years linear models make prediction using linear function of the input featureswhich we will explain shortly linear models for regression for regressionthe gener... |
17,040 | we added coordinate cross into the plot to make it easier to understand the line looking at [ we see that the slope should be around which we can confirm visually in the plot the intercept is where the prediction line should cross the -axisthis is slightly below zerowhich you can also confirm in the image linear models... |
17,041 | skewed perspective for datasets with many featureslinear models can be very powerful in particularif you have more features than training data pointsany target can be perfectly modeled (on the training setas linear function there are many different linear models for regression the difference between these models lies i... |
17,042 | of coef_ and intercept_ scikit-learn always stores anything that is derived from the training data in attributes that end with trailing underscore that is to separate them from parameters that are set by the user the intercept_ attribute is always single float numberwhile the coef_ attribute is numpy array with one ent... |
17,043 | training set score test set score this discrepancy between performance on the training set and the test set is clear sign of overfittingand therefore we should try to find model that allows us to control complexity one of the most commonly used alternatives to standard linear regression is ridge regressionwhich we will... |
17,044 | coefficientsand its performance on the training set how much importance the model places on simplicity versus training set performance can be specified by the userusing the alpha parameter in the previous examplewe used the default parameter alpha= there is no reason why this will give us the best trade-offthough the o... |
17,045 | plt plot(ridge coef_' 'label="ridge alpha= "plt plot(ridge coef_'^'label="ridge alpha= "plt plot(ridge coef_' 'label="ridge alpha= "plt plot(lr coef_' 'label="linearregression"plt xlabel("coefficient index"plt ylabel("coefficient magnitude"plt hlines( len(lr coef_)plt ylim(- plt legend(figure - comparing coefficient ma... |
17,046 | but vary the amount of training data available for figure - we subsampled the boston housing dataset and evaluated linearregression and ridge(alpha= on subsets of increasing size (plots that show model performance as function of dataset size are called learning curves)in[ ]mglearn plots plot_ridge_n_samples(figure - le... |
17,047 | when using the full dataset is just by chanceanother interesting aspect of figure - is the decrease in training performance for linear regression if more data is addedit becomes harder for model to overfitor memorize the data lasso an alternative to ridge for regularizing linear regression is lasso as with ridge regres... |
17,048 | we increase the default setting of "max_iter"otherwise the model would warn us that we should increase max_iter lasso lasso(alpha= max_iter= fit(x_trainy_trainprint("training set score{ }format(lasso score(x_trainy_train))print("test set score{ }format(lasso score(x_testy_test))print("number of features used{}format(np... |
17,049 | of alpha and ridge regression for alpha= we not only see that most of the coefficients are zero (which we already knew)but that the remaining coefficients are also small in magnitude decreasing alpha to we obtain the solution shown as the green dotswhich causes most features to be exactly zero using alpha= we get model... |
17,050 | linear models are also extensively used for classification let' look at binary classification first in this casea prediction is made using the following formulay [ [ [ [ [px[pb the formula looks very similar to the one for linear regressionbut instead of just returning the weighted sum of the featureswe threshold the p... |
17,051 | from sklearn linear_model import logisticregression from sklearn svm import linearsvc xy mglearn datasets make_forge(figaxes plt subplots( figsize=( )for modelax in zip([linearsvc()logisticregression()]axes)clf model fit(xymglearn plots plot_ d_separator(clfxfill=falseeps= ax=axalpha mglearn discrete_scatter( [: ] [: ]... |
17,052 | ticregression and linearsvc try to fit the training set as best as possiblewhile with low values of the parameter cthe models put more emphasis on finding coefficient vector (wthat is close to zero there is another interesting aspect of how the parameter acts using low values of will cause the algorithms to try to adju... |
17,053 | tant when considering more features let' analyze linearlogistic in more detail on the breast cancer datasetin[ ]from sklearn datasets import load_breast_cancer cancer load_breast_cancer(x_trainx_testy_trainy_test train_test_splitcancer datacancer targetstratify=cancer targetrandom_state= logreg logisticregression(fit(x... |
17,054 | an already underfit modelboth training and test set accuracy decrease relative to the default parameters finallylet' look at the coefficients learned by the models with the three different settings of the regularization parameter (figure - )in[ ]plt plot(logreg coef_ ' 'label=" = "plt plot(logreg coef_ '^'label=" = "pl... |
17,055 | different values of supervised machine learning algorithms |
17,056 | its the model to using only few features here is the coefficient plot and classification accuracies for regularization (figure - )in[ ]for cmarker in zip([ ][' ''^'' '])lr_l logisticregression( =cpenalty=" "fit(x_trainy_trainprint("training accuracy of logreg with ={ }{ }formatclr_l score(x_trainy_train))print("test ac... |
17,057 | cancer dataset for different values of linear models for multiclass classification many linear classification models are for binary classification onlyand don' extend naturally to the multiclass case (with the exception of logistic regressiona common technique to extend binary classification algorithm to multiclass cla... |
17,058 | and one intercept (bfor each class the class for which the result of the classification confidence formula given here is highest is the assigned class labelw[ [ [ [ [px[pb the mathematics behind multiclass logistic regression differ somewhat from the onevs -rest approachbut they also result in one coefficient vector an... |
17,059 | in[ ]linear_svm linearsvc(fit(xyprint("coefficient shape"linear_svm coef_ shapeprint("intercept shape"linear_svm intercept_ shapeout[ ]coefficient shape( intercept shape( ,we see that the shape of the coef_ is ( )meaning that each row of coef_ contains the coefficient vector for one of the three classes and each column... |
17,060 | the following example (figure - shows the predictions for all regions of the spacein[ ]mglearn plots plot_ d_classification(linear_svmxfill=truealpha mglearn discrete_scatter( [: ] [: ]yline np linspace(- for coefinterceptcolor in zip(linear_svm coef_linear_svm intercept_[' '' '' '])plt plot(line-(line coef[ interceptc... |
17,061 | strengthsweaknessesand parameters the main parameter of linear models is the regularization parametercalled alpha in the regression models and in linearsvc and logisticregression large values for alpha or small values for mean simple models in particular for the regression modelstuning these parameters is quite importa... |
17,062 | the number of samples they are also often used on very large datasetssimply because it' not feasible to train other models howeverin lower-dimensional spacesother models might yield better generalization performance we will look at some examples in which linear models fail in "kernelized support vector machineson page ... |
17,063 | any continuous datawhile bernoullinb assumes binary data and multinomialnb assumes count data (that isthat each feature represents an integer count of somethinglike how often word appears in sentencebernoullinb and multinomialnb are mostly used in text data classification the bernoullinb classifier counts how often eve... |
17,064 | multinomialnb and bernoullinb have single parameteralphawhich controls model complexity the way alpha works is that the algorithm adds to the data alpha many virtual data points that have positive values for all the features this results in "smoothingof the statistics large alpha means more smoothingresulting in less c... |
17,065 | in this illustrationeach node in the tree either represents question or terminal node (also called leafthat contains the answer the edges connect the answers to question with the next question you would ask in machine learning parlancewe built model to distinguish between four classes of animals (hawkspenguinsdolphinsa... |
17,066 | to build treethe algorithm searches over all possible tests and finds the one that is most informative about the target variable figure - shows the first test that is picked splitting the dataset vertically at [ ]= yields the most informationit best separates the points in class from the points in class the top nodeals... |
17,067 | figure - decision boundary of tree with depth (leftand corresponding decision tree (rightthis recursive process yields binary tree of decisionswith each node containing test alternativelyyou can think of each test as splitting the part of the data that is currently being considered along one axis this yields view of th... |
17,068 | tree (right)the full tree is quite large and hard to visualize prediction on new data point is made by checking which region of the partition of the feature space the point lies inand then predicting the majority target (or the single target in the case of pure leavesin that region the region can be found by traversing... |
17,069 | decisiontreeclassifier classes scikit-learn only implements pre-pruningnot post-pruning let' look at the effect of pre-pruning in more detail on the breast cancer dataset as alwayswe import the dataset and split it into training and test part then we build model using the default setting of fully developing the tree (g... |
17,070 | accuracy on training set accuracy on test set analyzing decision trees we can visualize the tree using the export_graphviz function from the tree module this writes file in the dot file formatwhich is text file format for storing graphs we set an option to color the nodes to reflect the majority class in each node and ... |
17,071 | makes predictionsand is good example of machine learning algorithm that is easily explained to nonexperts howevereven with tree of depth fouras seen herethe tree can become bit overwhelming deeper trees ( depth of is not uncommonare even harder to grasp one method of inspecting the tree that may be helpful is to find o... |
17,072 | cancer dataset here we see that the feature used in the top split ("worst radius"is by far the most important feature this confirms our observation in analyzing the tree that the first level already separates the two classes fairly well howeverif feature has low feature_importanceit doesn' mean that this feature is uni... |
17,073 | notonous relationship with the class labeland the decision boundaries found by decision tree figure - decision tree learned on the data shown in figure - the plot shows dataset with two features and two classes hereall the information is contained in [ ]and [ is not used at all but the relation between [ and supervised... |
17,074 | means class and low value means class (or vice versawhile we focused our discussion here on decision trees for classificationall that was said is similarly true for decision trees for regressionas implemented in decision treeregressor the usage and analysis of regression trees is very similar to that of classification ... |
17,075 | seems to be quite linear and so should be relatively easy to predictapart from some bumps we will make forecast for the years after using the historical data up to that pointwith the date as our only feature we will compare two simple modelsa decisiontreeregressor and linearregression we rescale the prices using logari... |
17,076 | by regression tree on the ram price data the difference between the models is quite striking the linear model approximates the data with lineas we knew it would this line provides quite good forecast for the test data (the years after )while glossing over some of the finer variations in both the training and the test d... |
17,077 | ting decision trees have two advantages over many of the algorithms we've discussed so farthe resulting model can easily be visualized and understood by nonexperts (at least for smaller trees)and the algorithms are completely invariant to scaling of the data as each feature is processed separatelyand the possible split... |
17,078 | number of trees to build (the n_estimators parameter of randomforestregressor or randomforestclassifierlet' say we want to build trees these trees will be built completely independently from each otherand the algorithm will make different random choices for each tree to make sure the trees are distinct to build treewe ... |
17,079 | highest probability is predicted analyzing random forests let' apply random forest consisting of five trees to the two_moons dataset we studied earlierin[ ]from sklearn ensemble import randomforestclassifier from sklearn datasets import make_moons xy make_moons(n_samples= noise= random_state= x_trainx_testy_trainy_test... |
17,080 | sion boundary obtained by averaging their predicted probabilities as another examplelet' apply random forest consisting of trees on the breast cancer datasetin[ ]x_trainx_testy_trainy_test train_test_splitcancer datacancer targetrandom_state= forest randomforestclassifier(n_estimators= random_state= forest fit(x_trainy... |
17,081 | plot_feature_importances_cancer(forestfigure - feature importances computed from random forest that was fit to the breast cancer dataset as you can seethe random forest gives nonzero importance to many more features than the single tree similarly to the single decision treethe random forest also gives lot of importance... |
17,082 | modern computers do)you can use the n_jobs parameter to adjust the number of cores to use using more cpu cores will result in linear speed-ups (using two coresthe training of the random forest will be twice as fast)but specifying n_jobs larger than the number of cores will not help you can set n_jobs=- to use all the c... |
17,083 | context known as weak learners)like shallow trees each tree can only provide good predictions on part of the dataand so more and more trees are added to iteratively improve performance gradient boosted trees are frequently the winning entries in machine learning competitionsand are widely used in industry they are gene... |
17,084 | gbrt gradientboostingclassifier(random_state= max_depth= gbrt fit(x_trainy_trainprint("accuracy on training set{ }format(gbrt score(x_trainy_train))print("accuracy on test set{ }format(gbrt score(x_testy_test))out[ ]accuracy on training set accuracy on test set in[ ]gbrt gradientboostingclassifier(random_state= learnin... |
17,085 | fit to the breast cancer dataset we can see that the feature importances of the gradient boosted trees are somewhat similar to the feature importances of the random foreststhough the gradient boosting completely ignored some of the features as both gradient boosting and random forests perform well on similar kinds of d... |
17,086 | model of similar complexity in contrast to random forestswhere higher n_esti mators value is always betterincreasing n_estimators in gradient boosting leads to more complex modelwhich may lead to overfitting common practice is to fit n_estimators depending on the time and memory budgetand then search over different lea... |
17,087 | linear model for classification can only separate points using lineand will not be able to do very good job on this dataset (see figure - )in[ ]from sklearn svm import linearsvc linear_svm linearsvc(fit(xymglearn plots plot_ d_separator(linear_svmxmglearn discrete_scatter( [: ] [: ]yplt xlabel("feature "plt ylabel("fea... |
17,088 | in[ ]add the squared first feature x_new np hstack([xx[: :* ]from mpl_toolkits mplot import axes daxes figure plt figure(visualize in ax axes (figureelev=- azim=- plot first all the points with = then all with = mask = ax scatter(x_new[mask ]x_new[mask ]x_new[mask ] =' 'cmap=mglearn cm = ax scatter(x_new[~mask ]x_new[~... |
17,089 | feature derived from feature in the new representation of the datait is now indeed possible to separate the two classes using linear modela plane in three dimensions we can confirm this by fitting linear model to the augmented data (see figure - )in[ ]linear_svm_ linearsvc(fit(x_newycoefintercept linear_svm_ coef_ rave... |
17,090 | as function of the original featuresthe linear svm model is not actually linear anymore it is not linebut more of an ellipseas you can see from the plot created here (figure - )in[ ]zz yy * dec linear_svm_ decision_function(np c_[xx ravel()yy ravel()zz ravel()]plt contourf(xxyydec reshape(xx shape)levels=[dec min() dec... |
17,091 | features the kernel trick the lesson here is that adding nonlinear features to the representation of our data can make linear models much more powerful howeveroften we don' know which features to addand adding many features (like all possible interactions in dimensional feature spacemight make computation very expensiv... |
17,092 | decreases for higher degrees in practicethe mathematical details behind the kernel svm are not that importantthoughand how an svm with an rbf kernel makes decision can be summarized quite easily--we'll do so in the next section understanding svms during trainingthe svm learns how important each of the training data poi... |
17,093 | in this casethe svm yields very smooth and nonlinear (not straight lineboundary we adjusted two parameters herethe parameter and the gamma parameterwhich we will now discuss in detail tuning svm parameters the gamma parameter is the one shown in the formula given in the previous sectionwhich controls the width of the g... |
17,094 | eters and gamma going from left to rightwe increase the value of the parameter gamma from to small gamma means large radius for the gaussian kernelwhich means that many points are considered close by this is reflected in very smooth decision boundaries on the leftand boundaries that focus more on single points further ... |
17,095 | gamma= /n_featuresin[ ]x_trainx_testy_trainy_test train_test_splitcancer datacancer targetrandom_state= svc svc(svc fit(x_trainy_trainprint("accuracy on training set{ }format(svc score(x_trainy_train))print("accuracy on test set{ }format(svc score(x_testy_test))out[ ]accuracy on training set accuracy on test set the mo... |
17,096 | arithmic scalepreprocessing data for svms one way to resolve this problem is by rescaling each feature so that they are all approximately on the same scale common rescaling method for kernel svms is to scale the data such that all features are between and we will see how to do this using the minmaxscaler preprocessing ... |
17,097 | minimum for each feature maximum for each feature in[ ]use the same transformation on the test setusing min and range of the training set (see for detailsx_test_scaled (x_test min_on_trainingrange_on_training in[ ]svc svc(svc fit(x_train_scaledy_trainprint("accuracy on training set{ }formatsvc score(x_train_scaledy_tra... |
17,098 | kernelized support vector machines are powerful models and perform well on variety of datasets svms allow for complex decision boundarieseven if the data has only few features they work well on low-dimensional and high-dimensional data ( few and many features)but don' scale very well with the number of samples running ... |
17,099 | [ [ [ [ [px[pb in plain englishy is weighted sum of the input features [ to [ ]weighted by the learned coefficients [ to [pwe could visualize this graphically as shown in figure - in[ ]display(mglearn plots plot_logistic_regression_graph()figure - visualization of logistic regressionwhere input features and predictions... |
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