The K in the name of this classifier represents the k nearest neighbors, where k is an integer value specified by the user. Hence as the name suggests, this classifier implements learning based on the k nearest neighbors. The choice of the value of k is dependent on data. Lets understand it more with the help if an implementation example
This answer says no, but on the documentation for KNeighborsClassifier, it says the metrics mentioned in DistanceMetrics are available. Distance metrics don't include an explicit cosine distance, probably because it's not really a distance, but supposedly it's possible to input a function into the metric. I tried inputting the scikit learn linear kernel into KNeighborsClassifier but it gives me an error that the function needs two arrays as arguments. Anyone else tried this?
The cosine similarity is generally defined as xT y / (||x|| * ||y||), and outputs 1 if they are the same and goes to -1 if they are completely different. This definition is not technically a metric, and so you can't use accelerating structures like ball and kd trees with it. If you force scikit learn to use the brute force approach, you should be able to use it as a distance if you pass it your own custom distance metric object. There are methods of transforming the cosine similarity into a valid distance metric if you would like to use ball trees (you can find one in the JSAT library)
Notice though, that xT y / (||x|| * ||y||) = (x/||x||)T (y/||y||). The euclidean distance can be equivalently written as sqrt(xTx + yTy 2 xTy). If we normalize every datapoint before giving it to the KNeighborsClassifier, then x^T x = 1 for all x. So the euclidean distance will degrade to sqrt(2 2x^T y). For completely the same inputs, we would get sqrt(2-2*1) = 0 and for complete opposites sqrt(2-2*-1)= 2. And it is clearly a simple shape, so you can get the same ordering as the cosine distance by normalizing your data and then using the euclidean distance. So long as you use the uniform weights option, the results will be identical to having used a correct Cosine Distance.
KNN family class constructors have a parameter called metric, you can switch between different distance metrics you want to use in nearest neighbour model. A list of available distance metrics can be found here
If you want to use cosine metric for ranking and classification problem, you can use norm 2 Euclidean distance on normalized feature vector, that gives you same ranking/classification (predictions that made by argmax or argmin operations) results.
In order to arrive at the most accurate prediction, machine learning models are built, tuned and compared against each other. The reader can get can click on the links below to assess the models or sections of the exercise. Each section has a short explanation of theory, and a description of applied machine learning with Python:
This blog is part of a series of models showcasing applied machine learning models in a classification setting. By clicking on any of the tabs above, the reader can navigate to other methods of analysis applied to the same data. This was designed so that one could see what a data scientist would do from soup to nuts when faced with a problem like the one presented here. Note that the overall focus of this blog is K-Nearest Neighbors. More specifically,
There are several statistics text books available showing that the test error rate in machine learning is minimized when using the Bayes classifier, which assigns observations to a class based on predictor values. For example, when we have two classes, the Bayes classifier assigns an observation to one of the classes if
A hundred observations are classified into two classes represented by orange and blue. The orange dots represent the area where a test observation will be assigned to the orange class while the blue dots represent the area where an observation will be assigned to the blue class. The dashed line is the Bayes Classifier.
Unfortunately, the real decision boundary is rarely known in real world problems and the computing of the Bayes classifier is impossible. One of the most frequently cited classifiers introduced that does a reasonable job instead is called K-Nearest Neighbors (KNN) Classifier.
Provided a positive integer K and a test observation of , the classifier identifies the K points in the data that are closest to x0. Therefore if K is 5, then the five closest observations to observation x0 are identified. These points are typically represented by N0. The KNN classifier then computes the conditional probability for class j as the fraction of points in observations in N0 whose response equals j. The mathematical representation of this is:
It is not surprising that altering K produces dramatically different results. When K=1, the decision boundary is minimally restricted, KNN models are said to produce low bias but high variance. As we increase K, the flexibility of the classifier gets reduced and the decision boundary gets closer and closer to linear. These models produce low variance but high bias. Neither perform particularly well based on test accuracy so we need to find a model with well balanced variance and bias, and we can find that model through parameter tuning.
So let us tune a KNN model with GridSearchCV. The first step is to load all libraries and the charity data for classification. Note that I created three separate datasets: 1.) the original data set wit 21 variables that were partitioned into train and test sets, 2.) a dataset that contains second order polynomials and interaction terms also partitioned, and 3.) a a dataset that contains third order polynomials and interaction terms - partitioned into train and test sets. Each dataset was standardized and the variables with VIF scores greater than 5 were removed. All datasets were pickled and those pickles are called and loaded below. The pre-work described above can be seen by navigating to the Linear and Quadratic Discriminant Analysis blog.
We use cross validation and grid search to find the best model. Scikit-Learn affords us with several tunable parameters. For a complete list of tunable parameters click on the link for KNeighborsClassifier.The list of tunable parameters are is also embedded (and coded out) in the chunk below. Further, I set the algorithm used to auto, although there are other parameters levels that one can decide on. Note that there are four options for algorithm:
Now we can see how accurate teach of the four models performed based on test data. The first model was our default model without any tuning. Indeed, tuning parameters can get us significant gains over the accuracy of our default model. In fact, the model fitted on the original training data without interaction terms performed will and had an 86% accuracy.
Additional statistics are also available about the accuracy of the winning model. Take a look at the recall of our winning model for example. It will be really interesting to compare these results to the output of other methods.
k-NN (k-Nearest Neighbor), one of the simplest machine learning algorithms, is non-parametric and lazy in nature. Non-parametric means that there is no assumption for the underlying data distribution i.e. the model structure is determined from the dataset. Lazy or instance-based learning means that for the purpose of model generation, it does not require any training data points and whole training data is used in the testing phase.
The unsupervised nearest neighbors implement different algorithms (BallTree, KDTree or Brute Force) to find the nearest neighbor(s) for each sample. This unsupervised version is basically only step 1, which is discussed above, and the foundation of many algorithms (KNN and K-means being the famous one) which require the neighbor search. In simple words, it is Unsupervised learner for implementing neighbor searches.
As discussed, there exist many algorithms like KNN and K-Means that requires nearest neighbor searches. That is why Scikit-learn decided to implement the neighbor search part as its own learner. The reason behind making neighbor search as a separate learner is that computing all pairwise distance for finding a nearest neighbor is obviously not very efficient. Lets see the module used by Sklearn to implement unsupervised nearest neighbor learning along with example.
sklearn.neighbors.NearestNeighbors is the module used to implement unsupervised nearest neighbor learning. It uses specific nearest neighbor algorithms named BallTree, KDTree or Brute Force. In other words, it acts as a uniform interface to these three algorithms.
This parameter will take the algorithm (BallTree, KDTree or Brute-force) you want to use to compute the nearest neighbors. If you will provide auto, it will attempt to decide the most appropriate algorithm based on the values passed to fit method.
It can affect the speed of the construction & query as well as the memory required to store the tree. It is passed to BallTree or KDTree. Although the optimal value depends on the nature of the problem, its default value is 30.
It is the metric to use for distance computation between points. We can pass it as a string or callable function. In case of callable function, the metric is called on each pair of rows and the resulting value is recorded. It is less efficient than passing the metric name as a string.
[braycurtis,canberra,chebyshev,dice,hamming,jaccard, correlation,kulsinski,mahalanobis,minkowski,rogerstanimoto,russellrao, sokalmicheme,sokalsneath, seuclidean, sqeuclidean, yule].
Once we fit the unsupervised NearestNeighbors model, the data will be stored in a data structure based on the value set for the argument algorithm. After that we can use this unsupervised learners kneighbors in a model which requires neighbor searches.
The K in the name of this classifier represents the k nearest neighbors, where k is an integer value specified by the user. Hence as the name suggests, this classifier implements learning based on the k nearest neighbors. The choice of the value of k is dependent on data.
The Radius in the name of this classifier represents the nearest neighbors within a specified radius r, where r is a floating-point value specified by the user. Hence as the name suggests, this classifier implements learning based on the number neighbors within a fixed radius r of each training point.
The K in the name of this regressor represents the k nearest neighbors, where k is an integer value specified by the user. Hence, as the name suggests, this regressor implements learning based on the k nearest neighbors. The choice of the value of k is dependent on data. Lets understand it more with the help of an implementation example.
The Radius in the name of this regressor represents the nearest neighbors within a specified radius r, where r is a floating-point value specified by the user. Hence as the name suggests, this regressor implements learning based on the number neighbors within a fixed radius r of each training point. Lets understand it more with the help if an implementation example
I would like to give full credits to the respective authors as these are my personal python notebooks taken from deep learning courses from Andrew Ng, Data School and Udemy :) This is a simple python notebook hosted generously through Github Pages that is on my main personal notes repository on https://github.com/ritchieng/ritchieng.github.io. They are meant for my personal review but I have open-source my repository of personal notes as a lot of people found it useful.
I am currently trying to implement an ROC Curve for my kNN classification algorithm. I am aware that an ROC Curve is a plot of True Positive Rate vs False Positive Rate, I am just struggling with finding those values from my dataset. I import 'autoimmune.csv' into my python script and run the kNN algorithm on it to output an accuracy value. Scikit-learn.org documentation shows that to generate the TPR and FPR I need to pass in values of y_test and y_scores as shown below:
y_score : array, shape = [n_samples] Target scores, can either be probability estimates of the positive class, confidence values, or non-thresholded measure of decisions (as returned by decision_function on some classifiers).
You can get probability estimates using the predict_proba() method of the KNeighborsClassifier in sklearn. This returns a numpy array with two columns for a binary classification, one each for the negative and positive class. For the roc_curve() function you want to use probability estimates of the positive class, so you can replace your:
Notice how you need to take all the rows of the second column with [:, 1] to only select the probability estimates of the positive class. Here's a minimal reproducible example using the Wisconsin breast cancer dataset, since I don't have your autoimmune.csv: