Updates to the documentation (linguistic corrections) (#414)

* Fix typo in Features list

* Update distance.md documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

* Fix grammatical mistakes in documentation

docs/machine-learning/association/apriori.md

@@ -15,7 +15,7 @@ $associator = new Apriori($support = 0.5, $confidence = 0.5);
 
 ### Train
 
-To train a associator simply provide train samples and labels (as `array`). Example:
+To train an associator, simply provide train samples and labels (as `array`). Example:
 
 ```
 $samples = [['alpha', 'beta', 'epsilon'], ['alpha', 'beta', 'theta'], ['alpha', 'beta', 'epsilon'], ['alpha', 'beta', 'theta']];
@@ -31,7 +31,7 @@ You can train the associator using multiple data sets, predictions will be based
 
 ### Predict
 
-To predict sample label use `predict` method. You can provide one sample or array of samples:
+To predict sample label use the `predict` method. You can provide one sample or array of samples:
 
 ```
 $associator->predict(['alpha','theta']);
@@ -43,7 +43,7 @@ $associator->predict([['alpha','epsilon'],['beta','theta']]);
 
 ### Associating
 
-Get generated association rules simply use `rules` method.
+To get generated association rules, simply use the `rules` method.
 
 ```
 $associator->getRules();
@@ -52,7 +52,7 @@ $associator->getRules();
 
 ### Frequent item sets
 
-Generating k-length frequent item sets simply use `apriori` method.
+To generate k-length frequent item sets, simply use the `apriori` method.
 
 ```
 $associator->apriori();

docs/machine-learning/classification/k-nearest-neighbors.md

@@ -14,7 +14,7 @@ $classifier = new KNearestNeighbors($k=3, new Minkowski($lambda=4));
 
 ## Train
 
-To train a classifier simply provide train samples and labels (as `array`). Example:
+To train a classifier, simply provide train samples and labels (as `array`). Example:
 
 ```
 $samples = [[1, 3], [1, 4], [2, 4], [3, 1], [4, 1], [4, 2]];
@@ -28,7 +28,7 @@ You can train the classifier using multiple data sets, predictions will be based
 
 ## Predict
 
-To predict sample label use `predict` method. You can provide one sample or array of samples:
+To predict sample label use the `predict` method. You can provide one sample or array of samples:
 
 ```
 $classifier->predict([3, 2]);

docs/machine-learning/classification/naive-bayes.md

@@ -4,7 +4,7 @@ Classifier based on applying Bayes' theorem with strong (naive) independence ass
 
 ### Train
 
-To train a classifier simply provide train samples and labels (as `array`). Example:
+To train a classifier, simply provide train samples and labels (as `array`). Example:
 
 ```
 $samples = [[5, 1, 1], [1, 5, 1], [1, 1, 5]];
@@ -18,7 +18,7 @@ You can train the classifier using multiple data sets, predictions will be based
 
 ### Predict
 
-To predict sample label use `predict` method. You can provide one sample or array of samples:
+To predict sample label use the `predict` method. You can provide one sample or array of samples:
 
 ```
 $classifier->predict([3, 1, 1]);

docs/machine-learning/classification/svc.md

@@ -21,7 +21,7 @@ $classifier = new SVC(Kernel::RBF, $cost = 1000, $degree = 3, $gamma = 6);
 
 ### Train
 
-To train a classifier simply provide train samples and labels (as `array`). Example:
+To train a classifier, simply provide train samples and labels (as `array`). Example:
 
 ```
 use Phpml\Classification\SVC;
@@ -38,7 +38,7 @@ You can train the classifier using multiple data sets, predictions will be based
 
 ### Predict
 
-To predict sample label use `predict` method. You can provide one sample or array of samples:
+To predict sample label use the `predict` method. You can provide one sample or array of samples:
 
 ```
 $classifier->predict([3, 2]);
@@ -74,7 +74,7 @@ $classifier = new SVC(
 $classifier->train($samples, $labels);
 ```
 
-Then use `predictProbability` method instead of `predict`:
+Then use the `predictProbability` method instead of `predict`:
 
 ```
 $classifier->predictProbability([3, 2]);

docs/machine-learning/clustering/dbscan.md

@@ -16,12 +16,12 @@ $dbscan = new DBSCAN($epsilon = 2, $minSamples = 3, new Minkowski($lambda=4));
 
 ### Clustering
 
-To divide the samples into clusters simply use `cluster` method. It's return the `array` of clusters with samples inside.
+To divide the samples into clusters, simply use the `cluster` method. It returns the `array` of clusters with samples inside.
 
 ```
 $samples = [[1, 1], [8, 7], [1, 2], [7, 8], [2, 1], [8, 9]];
 
 $dbscan = new DBSCAN($epsilon = 2, $minSamples = 3);
 $dbscan->cluster($samples);
-// return [0=>[[1, 1], ...], 1=>[[8, 7], ...]] 
+// return [0=>[[1, 1], ...], 1=>[[8, 7], ...]]
 ```

docs/machine-learning/clustering/k-means.md

@@ -1,6 +1,6 @@
 # K-means clustering
 
-The K-Means algorithm clusters data by trying to separate samples in n groups of equal variance, minimizing a criterion known as the inertia or within-cluster sum-of-squares. 
+The K-Means algorithm clusters data by trying to separate samples in n groups of equal variance, minimizing a criterion known as the inertia or within-cluster sum-of-squares.
 This algorithm requires the number of clusters to be specified.
 
 ### Constructor Parameters
@@ -15,11 +15,11 @@ $kmeans = new KMeans(4, KMeans::INIT_RANDOM);
 
 ### Clustering
 
-To divide the samples into clusters simply use `cluster` method. It's return the `array` of clusters with samples inside.
+To divide the samples into clusters, simply use the `cluster` method. It returns the `array` of clusters with samples inside.
 
 ```
 $samples = [[1, 1], [8, 7], [1, 2], [7, 8], [2, 1], [8, 9]];
-Or if you need to keep your indentifiers along with yours samples you can use array keys as labels.
+Or if you need to keep your identifiers along with yours samples you can use array keys as labels.
 $samples = [ 'Label1' => [1, 1], 'Label2' => [8, 7], 'Label3' => [1, 2]];
 
 $kmeans = new KMeans(2);
@@ -32,8 +32,8 @@ $kmeans->cluster($samples);
 #### kmeans++ (default)
 
 K-means++ method selects initial cluster centers for k-mean clustering in a smart way to speed up convergence.
-It use the DASV seeding method consists of finding good initial centroids for the clusters.
+It uses the DASV seeding method consists of finding good initial centroids for the clusters.
 
 #### random
 
-Random initialization method chooses completely random centroid. It get the space boundaries to avoid placing clusters centroid too far from samples data.
+Random initialization method chooses completely random centroid. It gets the space boundaries to avoid placing cluster centroids too far from samples data.

docs/machine-learning/cross-validation/random-split.md

@@ -1,20 +1,20 @@
 # Random Split
 
-One of the simplest methods from Cross-validation is implemented as `RandomSpilt` class. Samples are split to two groups: train group and test group. You can adjust number of samples in each group.
+One of the simplest methods from Cross-validation is implemented as `RandomSpilt` class. Samples are split to two groups: train group and test group. You can adjust the number of samples in each group.
 
 ### Constructor Parameters
 
 * $dataset - object that implements `Dataset` interface
 * $testSize - a fraction of test split (float, from 0 to 1, default: 0.3)
 * $seed - seed for random generator (e.g. for tests)
- 
+
 ```
 $randomSplit = new RandomSplit($dataset, 0.2);
 ```
 
 ### Samples and labels groups
 
-To get samples or labels from test and train group you can use getters:
+To get samples or labels from test and train group, you can use getters:
 
 ```
 $dataset = new RandomSplit($dataset, 0.3, 1234);

docs/machine-learning/cross-validation/stratified-random-split.md

@@ -1,22 +1,22 @@
 # Stratified Random Split
 
-Analogously to `RandomSpilt` class samples are split to two groups: train group and test group.
+Analogously to `RandomSpilt` class, samples are split to two groups: train group and test group.
 Distribution of samples takes into account their targets and trying to divide them equally.
-You can adjust number of samples in each group.
+You can adjust the number of samples in each group.
 
 ### Constructor Parameters
 
 * $dataset - object that implements `Dataset` interface
 * $testSize - a fraction of test split (float, from 0 to 1, default: 0.3)
 * $seed - seed for random generator (e.g. for tests)
- 
+
 ```
 $split = new StratifiedRandomSplit($dataset, 0.2);
 ```
 
 ### Samples and labels groups
 
-To get samples or labels from test and train group you can use getters:
+To get samples or labels from test and train group, you can use getters:
 
 ```
 $dataset = new StratifiedRandomSplit($dataset, 0.3, 1234);
@@ -41,4 +41,4 @@ $dataset = new ArrayDataset(
 $split = new StratifiedRandomSplit($dataset, 0.5);
 ```
 
-Split will have equals amount of each target. Two of the target `a` and two of `b`.
+Split will have equal amounts of each target. Two of the target `a` and two of `b`.

docs/machine-learning/datasets/array-dataset.md

@@ -2,7 +2,7 @@
 
 Helper class that holds data as PHP `array` type. Implements the `Dataset` interface which is used heavily in other classes.
 
-### Constructors Parameters
+### Constructor Parameters
 
 * $samples - (array) of samples
 * $labels - (array) of labels
@@ -15,7 +15,7 @@ $dataset = new ArrayDataset([[1, 1], [2, 1], [3, 2], [4, 1]], ['a', 'a', 'b', 'b
 
 ### Samples and labels
 
-To get samples or labels you can use getters:
+To get samples or labels, you can use getters:
 
 ```
 $dataset->getSamples();
@@ -24,7 +24,7 @@ $dataset->getTargets();
 
 ### Remove columns
 
-You can remove columns by index numbers, for example:
+You can remove columns by their index numbers, for example:
 
 ```
 use Phpml\Dataset\ArrayDataset;

docs/machine-learning/datasets/csv-dataset.md

@@ -2,11 +2,11 @@
 
 Helper class that loads data from CSV file. It extends the `ArrayDataset`.
 
-### Constructors Parameters
+### Constructor Parameters
 
 * $filepath - (string) path to `.csv` file
 * $features - (int) number of columns that are features (starts from first column), last column must be a label
-* $headingRow - (bool) define is file have a heading row (if `true` then first row will be ignored)
+* $headingRow - (bool) define if the file has a heading row (if `true` then first row will be ignored)
 
 ```
 $dataset = new CsvDataset('dataset.csv', 2, true);

docs/machine-learning/datasets/files-dataset.md

@@ -2,7 +2,7 @@
 
 Helper class that loads dataset from files. Use folder names as targets. It extends the `ArrayDataset`.
 
-### Constructors Parameters
+### Constructor Parameters
 
 * $rootPath - (string) path to root folder that contains files dataset
 
@@ -42,7 +42,7 @@ data
         ...
 ```
 
-Load files data with `FilesDataset`: 
+Load files data with `FilesDataset`:
 
 ```
 use Phpml\Dataset\FilesDataset;

docs/machine-learning/datasets/mnist-dataset.md

@@ -1,6 +1,6 @@
 # MnistDataset
 
-Helper class that load data from MNIST dataset: [http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)
+Helper class that loads data from MNIST dataset: [http://yann.lecun.com/exdb/mnist/](http://yann.lecun.com/exdb/mnist/)
 
 > The MNIST database of handwritten digits, available from this page, has a training set of 60,000 examples, and a test set of 10,000 examples. It is a subset of a larger set available from NIST. The digits have been size-normalized and centered in a fixed-size image.
   It is a good database for people who want to try learning techniques and pattern recognition methods on real-world data while spending minimal efforts on preprocessing and formatting.
@@ -18,7 +18,7 @@ $trainDataset = new MnistDataset('train-images-idx3-ubyte', 'train-labels-idx1-u
 
 ### Samples and labels
 
-To get samples or labels you can use getters:
+To get samples or labels, you can use getters:
 
 ```
 $dataset->getSamples();

docs/machine-learning/datasets/svm-dataset.md

@@ -2,7 +2,7 @@
 
 Helper class that loads data from SVM-Light format file. It extends the `ArrayDataset`.
 
-### Constructors Parameters
+### Constructor Parameters
 
 * $filepath - (string) path to the file
 

docs/machine-learning/feature-extraction/tf-idf-transformer.md

@@ -19,7 +19,7 @@ $transformer = new TfIdfTransformer($samples);
 
 ### Transformation
 
-To transform a collection of text samples use `transform` method. Example:
+To transform a collection of text samples, use the `transform` method. Example:
 
 ```
 use Phpml\FeatureExtraction\TfIdfTransformer;
@@ -28,7 +28,7 @@ $samples = [
     [0 => 1, 1 => 1, 2 => 2, 3 => 1, 4 => 0, 5 => 0],
     [0 => 1, 1 => 1, 2 => 0, 3 => 0, 4 => 2, 5 => 3],
 ];
-        
+
 $transformer = new TfIdfTransformer($samples);
 $transformer->transform($samples);
 
@@ -38,5 +38,5 @@ $samples = [
    [0 => 0, 1 => 0, 2 => 0, 3 => 0, 4 => 0.602, 5 => 0.903],
 ];
 */
-        
+
 ```

docs/machine-learning/feature-extraction/token-count-vectorizer.md

@@ -16,7 +16,7 @@ $vectorizer = new TokenCountVectorizer(new WhitespaceTokenizer());
 
 ### Transformation
 
-To transform a collection of text samples use `transform` method. Example:
+To transform a collection of text samples, use the `transform` method. Example:
 
 ```
 $samples = [
@@ -42,7 +42,7 @@ $vectorizer->transform($samples);
 
 ### Vocabulary
 
-You can extract vocabulary using `getVocabulary()` method. Example:
+You can extract vocabulary using the `getVocabulary()` method. Example:
 
 ```
 $vectorizer->getVocabulary();

docs/machine-learning/feature-selection/selectkbest.md

@@ -5,7 +5,7 @@
 ## Constructor Parameters
 
 * $k (int) - number of top features to select, rest will be removed (default: 10)
-* $scoringFunction (ScoringFunction) - function that take samples and targets and return array with scores (default: ANOVAFValue)
+* $scoringFunction (ScoringFunction) - function that takes samples and targets and returns an array with scores (default: ANOVAFValue)
 
 ```php
 use Phpml\FeatureSelection\SelectKBest;
@@ -27,13 +27,13 @@ $selector->fit($samples = $dataset->getSamples(), $dataset->getTargets());
 $selector->transform($samples);
 
 /*
-$samples[0] = [1.4, 0.2]; 
+$samples[0] = [1.4, 0.2];
 */
 ```
 
 ## Scores
 
-You can get a array with the calculated score for each feature. 
+You can get an array with the calculated score for each feature.
 A higher value means that a given feature is better suited for learning.
 Of course, the rating depends on the scoring function used.
 
@@ -56,7 +56,7 @@ $selector->scores();
   float(1179.0343277002)
   [3]=>
   float(959.32440572573)
-} 
+}
 */
 ```
 
@@ -70,11 +70,11 @@ For classification:
    The test is applied to samples from two or more groups, possibly with differing sizes.
 
 For regression:
- - **UnivariateLinearRegression**  
+ - **UnivariateLinearRegression**
    Quick linear model for testing the effect of a single regressor, sequentially for many regressors.
    This is done in 2 steps:
      - 1. The cross correlation between each regressor and the target is computed, that is, ((X[:, i] - mean(X[:, i])) * (y - mean_y)) / (std(X[:, i]) *std(y)).
-     - 2. It is converted to an F score 
+     - 2. It is converted to an F score
 
 ## Pipeline
 

docs/machine-learning/feature-selection/variance-threshold.md

@@ -1,7 +1,7 @@
 # Variance Threshold
 
-`VarianceThreshold` is a simple baseline approach to feature selection. 
+`VarianceThreshold` is a simple baseline approach to feature selection.
-It removes all features whose variance doesn’t meet some threshold. 
+It removes all features whose variance doesn’t meet some threshold.
 By default, it removes all zero-variance features, i.e. features that have the same value in all samples.
 
 ## Constructor Parameters
@@ -16,10 +16,10 @@ $transformer = new VarianceThreshold(0.15);
 
 ## Example of use
 
-As an example, suppose that we have a dataset with boolean features and 
+As an example, suppose that we have a dataset with boolean features and
 we want to remove all features that are either one or zero (on or off)
-in more than 80% of the samples. 
+in more than 80% of the samples.
-Boolean features are Bernoulli random variables, and the variance of such 
+Boolean features are Bernoulli random variables, and the variance of such
 variables is given by
 ```
 Var[X] = p(1 - p)

docs/machine-learning/metric/accuracy.md

@@ -1,10 +1,10 @@
 # Accuracy
 
-Class for calculate classifier accuracy.
+Class for calculating classifier accuracy.
 
 ### Score
 
-To calculate classifier accuracy score use `score` static method. Parameters:
+To calculate classifier accuracy score, use the `score` static method. Parameters:
 
 * $actualLabels - (array) true sample labels
 * $predictedLabels - (array) predicted labels (e.x. from test group)

docs/machine-learning/metric/classification-report.md

@@ -1,6 +1,6 @@
 # Classification Report
 
-Class for calculate main classifier metrics: precision, recall, F1 score and support.
+Class for calculating main classifier metrics: precision, recall, F1 score and support.
 
 ### Report
 

docs/machine-learning/metric/confusion-matrix.md

@@ -1,6 +1,6 @@
 # Confusion Matrix
 
-Class for compute confusion matrix to evaluate the accuracy of a classification.
+Class for computing confusion matrix to evaluate the accuracy of a classification.
 
 ### Example (all targets)
 

docs/machine-learning/neural-network/multilayer-perceptron-classifier.md

@@ -39,8 +39,7 @@ $mlp = new MLPClassifier(4, [$layer1, $layer2], ['a', 'b', 'c']);
 
 ## Train
 
-To train a MLP simply provide train samples and labels (as array). Example:
+To train a MLP, simply provide train samples and labels (as array). Example:
-
 
 ```
 $mlp->train(
@@ -71,7 +70,7 @@ $mlp->setLearningRate(0.1);
 
 ## Predict
 
-To predict sample label use predict method. You can provide one sample or array of samples:
+To predict sample label use the `predict` method. You can provide one sample or array of samples:
 
 ```
 $mlp->predict([[1, 1, 1, 1], [0, 0, 0, 0]]);

docs/machine-learning/preprocessing/imputation-missing-values.md

@@ -49,7 +49,7 @@ $data = [
 
 ```
 
-You can also use `$samples` constructer parameter instead of `fit` method:
+You can also use the `$samples` constructor parameter instead of the `fit` method:
 
 ```
 use Phpml\Preprocessing\Imputer;

docs/machine-learning/regression/least-squares.md

@@ -1,10 +1,10 @@
 # LeastSquares Linear Regression
 
-Linear model that use least squares method to approximate solution. 
+Linear model that uses least squares method to approximate solution.
 
 ### Train
 
-To train a model simply provide train samples and targets values (as `array`). Example:
+To train a model, simply provide train samples and targets values (as `array`). Example:
 
 ```
 $samples = [[60], [61], [62], [63], [65]];
@@ -18,7 +18,7 @@ You can train the model using multiple data sets, predictions will be based on a
 
 ### Predict
 
-To predict sample target value use `predict` method with sample to check (as `array`). Example:
+To predict sample target value, use the `predict` method with sample to check (as `array`). Example:
 
 ```
 $regression->predict([64]);
@@ -27,8 +27,8 @@ $regression->predict([64]);
 
 ### Multiple Linear Regression
 
-The term multiple attached to linear regression means that there are two or more sample parameters used to predict target. 
+The term multiple attached to linear regression means that there are two or more sample parameters used to predict target.
-For example you can use: mileage and production year to predict price of a car.  
+For example you can use: mileage and production year to predict the price of a car.
 
 ```
 $samples = [[73676, 1996], [77006, 1998], [10565, 2000], [146088, 1995], [15000, 2001], [65940, 2000], [9300, 2000], [93739, 1996], [153260, 1994], [17764, 2002], [57000, 1998], [15000, 2000]];
@@ -42,7 +42,7 @@ $regression->predict([60000, 1996])
 
 ### Intercept and Coefficients
 
-After you train your model you can get the intercept and coefficients array.
+After you train your model, you can get the intercept and coefficients array.
 
 ```
 $regression->getIntercept();

docs/machine-learning/regression/svr.md

@@ -21,7 +21,7 @@ $regression = new SVR(Kernel::LINEAR, $degree = 3, $epsilon=10.0);
 
 ### Train
 
-To train a model simply provide train samples and targets values (as `array`). Example:
+To train a model, simply provide train samples and targets values (as `array`). Example:
 
 ```
 use Phpml\Regression\SVR;
@@ -38,7 +38,7 @@ You can train the model using multiple data sets, predictions will be based on a
 
 ### Predict
 
-To predict sample target value use `predict` method. You can provide one sample or array of samples:
+To predict sample target value, use the `predict` method. You can provide one sample or array of samples:
 
 ```
 $regression->predict([64])

docs/machine-learning/workflow/pipeline.md

@@ -5,13 +5,12 @@ In machine learning, it is common to run a sequence of algorithms to process and
     * Split each document’s text into tokens.
     * Convert each document’s words into a numerical feature vector ([Token Count Vectorizer](machine-learning/feature-extraction/token-count-vectorizer/)).
     * Learn a prediction model using the feature vectors and labels.
-    
-PHP-ML represents such a workflow as a Pipeline, which consists sequence of transformers and a estimator.
 
+PHP-ML represents such a workflow as a Pipeline, which consists of a sequence of transformers and an estimator.
 
 ### Constructor Parameters
 
-* $transformers (array|Transformer[]) - sequence of objects that implements Transformer interface
+* $transformers (array|Transformer[]) - sequence of objects that implements the Transformer interface
 * $estimator (Estimator) - estimator that can train and predict
 
 ```
@@ -29,7 +28,8 @@ $pipeline = new Pipeline($transformers, $estimator);
 
 ### Example
 
-First our pipeline replace missing value, then normalize samples and finally train SVC estimator. Thus prepared pipeline repeats each transformation step for predicted sample.
+First, our pipeline replaces the missing value, then normalizes samples and finally trains the SVC estimator.
+Thus prepared pipeline repeats each transformation step for predicted sample.
 
 ```
 use Phpml\Classification\SVC;

docs/math/distance.md

@@ -4,7 +4,7 @@ Selected algorithms require the use of a function for calculating the distance.
 
 ### Euclidean
 
-Class for calculation Euclidean distance.
+Class for calculating Euclidean distance.
 
 ![euclidean](https://upload.wikimedia.org/math/8/4/9/849f040fd10bb86f7c85eb0bbe3566a4.png "Euclidean Distance")
 
@@ -13,7 +13,7 @@ To calculate Euclidean distance:
 ```
 $a = [4, 6];
 $b = [2, 5];
-   
+
 $euclidean = new Euclidean();
 $euclidean->distance($a, $b);
 // return 2.2360679774998
@@ -21,7 +21,7 @@ $euclidean->distance($a, $b);
 
 ### Manhattan
 
-Class for calculation Manhattan distance.
+Class for calculating Manhattan distance.
 
 ![manhattan](https://upload.wikimedia.org/math/4/c/5/4c568bd1d76a6b15e19cb2ac3ad75350.png "Manhattan Distance")
 
@@ -30,7 +30,7 @@ To calculate Manhattan distance:
 ```
 $a = [4, 6];
 $b = [2, 5];
-   
+
 $manhattan = new Manhattan();
 $manhattan->distance($a, $b);
 // return 3
@@ -38,7 +38,7 @@ $manhattan->distance($a, $b);
 
 ### Chebyshev
 
-Class for calculation Chebyshev distance.
+Class for calculating Chebyshev distance.
 
 ![chebyshev](https://upload.wikimedia.org/math/7/1/2/71200f7dbb43b3bcfbcbdb9e02ab0a0c.png "Chebyshev Distance")
 
@@ -47,7 +47,7 @@ To calculate Chebyshev distance:
 ```
 $a = [4, 6];
 $b = [2, 5];
-   
+
 $chebyshev = new Chebyshev();
 $chebyshev->distance($a, $b);
 // return 2
@@ -55,7 +55,7 @@ $chebyshev->distance($a, $b);
 
 ### Minkowski
 
-Class for calculation Minkowski distance.
+Class for calculating Minkowski distance.
 
 ![minkowski](https://upload.wikimedia.org/math/a/a/0/aa0c62083c12390cb15ac3217de88e66.png "Minkowski Distance")
 
@@ -64,7 +64,7 @@ To calculate Minkowski distance:
 ```
 $a = [4, 6];
 $b = [2, 5];
-   
+
 $minkowski = new Minkowski();
 $minkowski->distance($a, $b);
 // return 2.080
@@ -83,7 +83,7 @@ $minkowski->distance($a, $b);
 
 ### Custom distance
 
-To apply your own function of distance use `Distance` interface. Example
+To apply your own function of distance use the `Distance` interface. Example:
 
 ```
 class CustomDistance implements Distance
@@ -103,7 +103,7 @@ class CustomDistance implements Distance
             $distance[] = $a[$i] * $b[$i];
         }
 
-        return min($distance);    
+        return min($distance);
     }
 }
 ```

docs/math/statistic.md

@@ -7,7 +7,7 @@ Selected statistical methods.
 Correlation coefficients are used in statistics to measure how strong a relationship is between two variables. There are several types of correlation coefficient.
 
 ### Pearson correlation
- 
+
 Pearson’s correlation or Pearson correlation is a correlation coefficient commonly used in linear regression.
 
 Example: