Deep Research and Development

Introduction A high-performance SVM classifier will likely need thousands of support vectors, and the resulting high complexity of classification prevents their use in many practical applications, with large numbers of training samples or large numbers of features in the input space. To handle this, several approximations to the RBF kernel (and similar kernels) have been devised. Typically, these take the form of a function z that maps a single vector to a vector of higher dimensionality, approximating the kernel. where Phi is the implicit mapping embedded in the RBF kernel. Implementation Scikit-learn has already implemented Fourier transform and Nystroem approximation techniques using RBFSampler and Nystroem classes accordingly. import matplotlib.pyplot as plt import numpy as np from sklearn import datasets, svm, pipeline from sklearn.kernel_approximation import (RBFSampler, Nystroem) # The digits dataset digits = datasets.load_digits(n_class=9) # To apply an clas...

Introduction The goal of anomaly detection is to identify cases that are unusual within data that is seemingly homogeneous. Anomaly detection is an important tool for detecting fraud, network intrusion, and other rare events that may have great significance but are hard to find. Outliers are cases that are unusual because they fall outside the distribution that is considered normal for the data. The distance from the center of a normal distribution indicates how typical a given point is with respect to the distribution of the data. Each case can be ranked according to the probability that it is either typical or atypical. Anomaly detection is a form of classification and is implemented as one-class classification, because only one class is represented in the training data. An anomaly detection model predicts whether a data point is typical for a given distribution or not. An atypical data point can be either an outlier or an example of a previously unseen class. Normally, a...

Introduction Remember we've talked about random forest and how it was used to improve the performance of a single Decision Tree classifier . The idea of fitting a number of decision tree classifiers on various sub-samples of the dataset and using averaging to improve the predictive accuracy can be used to other algorithms as well and it's called boosting. There are several boosting techniques, which can be used to improve our algorithm, we'll cover the most used ones: AdaBoost and Bagging boost. AdaBoost An AdaBoost classifier begins by fitting a classifier on the original dataset and then fits additional copies of the classifier on the same dataset, but where the weights of incorrectly classified instances are adjusted such that subsequent classifiers focus more on difficult cases. Bagging boost A Bagging classifier fits base classifiers each on random subsets of the original dataset and then aggregate their individual predictions to form a final prediction. I...

Introduction Having learnt different optimization and classification methods, you must feel quit confident to start exploring the datasets of interest. However you might very quickly run into a dataset, which no matter how hyper-parameters are set , is just not linearly separable. Surely there is no place for despair, especially since we have just a classifier to deal with these situation, called Support Vector Machine. How it works Support Vector Machine, or SVM, are a set of supervised learning methods used for classification and with a slight change for regression. The core idea of it is to linearly separate the hyper-space of features. The prefix hyper is not occasional, as SVM increases the dimension of feature space to achieve it's goal. The power of the method comes from using kernel functions , which enable it to operate in a high-dimensional, implicit feature space without ever computing the coordinates of the data in that space, but rather by simply computing...