531 skills found · Page 1 of 18
loco-3d / CrocoddylCrocoddyl is an optimal control library for robot control under contact sequence. Its solver is based on various efficient Differential Dynamic Programming (DDP)-like algorithms
VictorTaelin / Interaction CalculusA programming language and model of computation that matches the optimal λ-calculus reduction algorithm perfectly.
acado / AcadoACADO Toolkit is a software environment and algorithm collection for automatic control and dynamic optimization. It provides a general framework for using a great variety of algorithms for direct optimal control, including model predictive control, state and parameter estimation and robust optimization.
haris989 / NSGA IIThis is a python implementation of NSGA-II algorithm. NSGA is a popular non-domination based genetic algorithm for multi-objective optimization. It is a very effective algorithm but has been generally criticized for its computational complexity, lack of elitism and for choosing the optimal parameter value for sharing parameter σshare. A modified version, NSGA II was developed, which has a better sorting algorithm , incorporates elitism and no sharing parameter needs to be chosen a priori.
yangjiaolong / Go ICPImplementation of the Go-ICP algorithm for globally optimal 3D pointset registration
YuePanEdward / GH ICPGH-ICP: Iterative Closest Point algorithm with global optimal matching and hybrid metric [3DV' 18]
gpeyre / SinkhornAutoDiffToolbox to integrate optimal transport loss functions using automatic differentiation and Sinkhorn's algorithm
sayantann11 / All Classification Templetes For MLClassification - Machine Learning This is ‘Classification’ tutorial which is a part of the Machine Learning course offered by Simplilearn. We will learn Classification algorithms, types of classification algorithms, support vector machines(SVM), Naive Bayes, Decision Tree and Random Forest Classifier in this tutorial. Objectives Let us look at some of the objectives covered under this section of Machine Learning tutorial. Define Classification and list its algorithms Describe Logistic Regression and Sigmoid Probability Explain K-Nearest Neighbors and KNN classification Understand Support Vector Machines, Polynomial Kernel, and Kernel Trick Analyze Kernel Support Vector Machines with an example Implement the Naïve Bayes Classifier Demonstrate Decision Tree Classifier Describe Random Forest Classifier Classification: Meaning Classification is a type of supervised learning. It specifies the class to which data elements belong to and is best used when the output has finite and discrete values. It predicts a class for an input variable as well. There are 2 types of Classification: Binomial Multi-Class Classification: Use Cases Some of the key areas where classification cases are being used: To find whether an email received is a spam or ham To identify customer segments To find if a bank loan is granted To identify if a kid will pass or fail in an examination Classification: Example Social media sentiment analysis has two potential outcomes, positive or negative, as displayed by the chart given below. https://www.simplilearn.com/ice9/free_resources_article_thumb/classification-example-machine-learning.JPG This chart shows the classification of the Iris flower dataset into its three sub-species indicated by codes 0, 1, and 2. https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-flower-dataset-graph.JPG The test set dots represent the assignment of new test data points to one class or the other based on the trained classifier model. Types of Classification Algorithms Let’s have a quick look into the types of Classification Algorithm below. Linear Models Logistic Regression Support Vector Machines Nonlinear models K-nearest Neighbors (KNN) Kernel Support Vector Machines (SVM) Naïve Bayes Decision Tree Classification Random Forest Classification Logistic Regression: Meaning Let us understand the Logistic Regression model below. This refers to a regression model that is used for classification. This method is widely used for binary classification problems. It can also be extended to multi-class classification problems. Here, the dependent variable is categorical: y ϵ {0, 1} A binary dependent variable can have only two values, like 0 or 1, win or lose, pass or fail, healthy or sick, etc In this case, you model the probability distribution of output y as 1 or 0. This is called the sigmoid probability (σ). If σ(θ Tx) > 0.5, set y = 1, else set y = 0 Unlike Linear Regression (and its Normal Equation solution), there is no closed form solution for finding optimal weights of Logistic Regression. Instead, you must solve this with maximum likelihood estimation (a probability model to detect the maximum likelihood of something happening). It can be used to calculate the probability of a given outcome in a binary model, like the probability of being classified as sick or passing an exam. https://www.simplilearn.com/ice9/free_resources_article_thumb/logistic-regression-example-graph.JPG Sigmoid Probability The probability in the logistic regression is often represented by the Sigmoid function (also called the logistic function or the S-curve): https://www.simplilearn.com/ice9/free_resources_article_thumb/sigmoid-function-machine-learning.JPG In this equation, t represents data values * the number of hours studied and S(t) represents the probability of passing the exam. Assume sigmoid function: https://www.simplilearn.com/ice9/free_resources_article_thumb/sigmoid-probability-machine-learning.JPG g(z) tends toward 1 as z -> infinity , and g(z) tends toward 0 as z -> infinity K-nearest Neighbors (KNN) K-nearest Neighbors algorithm is used to assign a data point to clusters based on similarity measurement. It uses a supervised method for classification. The steps to writing a k-means algorithm are as given below: https://www.simplilearn.com/ice9/free_resources_article_thumb/knn-distribution-graph-machine-learning.JPG Choose the number of k and a distance metric. (k = 5 is common) Find k-nearest neighbors of the sample that you want to classify Assign the class label by majority vote. KNN Classification A new input point is classified in the category such that it has the most number of neighbors from that category. For example: https://www.simplilearn.com/ice9/free_resources_article_thumb/knn-classification-machine-learning.JPG Classify a patient as high risk or low risk. Mark email as spam or ham. Keen on learning about Classification Algorithms in Machine Learning? Click here! Support Vector Machine (SVM) Let us understand Support Vector Machine (SVM) in detail below. SVMs are classification algorithms used to assign data to various classes. They involve detecting hyperplanes which segregate data into classes. SVMs are very versatile and are also capable of performing linear or nonlinear classification, regression, and outlier detection. Once ideal hyperplanes are discovered, new data points can be easily classified. https://www.simplilearn.com/ice9/free_resources_article_thumb/support-vector-machines-graph-machine-learning.JPG The optimization objective is to find “maximum margin hyperplane” that is farthest from the closest points in the two classes (these points are called support vectors). In the given figure, the middle line represents the hyperplane. SVM Example Let’s look at this image below and have an idea about SVM in general. Hyperplanes with larger margins have lower generalization error. The positive and negative hyperplanes are represented by: https://www.simplilearn.com/ice9/free_resources_article_thumb/positive-negative-hyperplanes-machine-learning.JPG Classification of any new input sample xtest : If w0 + wTxtest > 1, the sample xtest is said to be in the class toward the right of the positive hyperplane. If w0 + wTxtest < -1, the sample xtest is said to be in the class toward the left of the negative hyperplane. When you subtract the two equations, you get: https://www.simplilearn.com/ice9/free_resources_article_thumb/equation-subtraction-machine-learning.JPG Length of vector w is (L2 norm length): https://www.simplilearn.com/ice9/free_resources_article_thumb/length-of-vector-machine-learning.JPG You normalize with the length of w to arrive at: https://www.simplilearn.com/ice9/free_resources_article_thumb/normalize-equation-machine-learning.JPG SVM: Hard Margin Classification Given below are some points to understand Hard Margin Classification. The left side of equation SVM-1 given above can be interpreted as the distance between the positive (+ve) and negative (-ve) hyperplanes; in other words, it is the margin that can be maximized. Hence the objective of the function is to maximize with the constraint that the samples are classified correctly, which is represented as : https://www.simplilearn.com/ice9/free_resources_article_thumb/hard-margin-classification-machine-learning.JPG This means that you are minimizing ‖w‖. This also means that all positive samples are on one side of the positive hyperplane and all negative samples are on the other side of the negative hyperplane. This can be written concisely as : https://www.simplilearn.com/ice9/free_resources_article_thumb/hard-margin-classification-formula.JPG Minimizing ‖w‖ is the same as minimizing. This figure is better as it is differentiable even at w = 0. The approach listed above is called “hard margin linear SVM classifier.” SVM: Soft Margin Classification Given below are some points to understand Soft Margin Classification. To allow for linear constraints to be relaxed for nonlinearly separable data, a slack variable is introduced. (i) measures how much ith instance is allowed to violate the margin. The slack variable is simply added to the linear constraints. https://www.simplilearn.com/ice9/free_resources_article_thumb/soft-margin-calculation-machine-learning.JPG Subject to the above constraints, the new objective to be minimized becomes: https://www.simplilearn.com/ice9/free_resources_article_thumb/soft-margin-calculation-formula.JPG You have two conflicting objectives now—minimizing slack variable to reduce margin violations and minimizing to increase the margin. The hyperparameter C allows us to define this trade-off. Large values of C correspond to larger error penalties (so smaller margins), whereas smaller values of C allow for higher misclassification errors and larger margins. https://www.simplilearn.com/ice9/free_resources_article_thumb/machine-learning-certification-video-preview.jpg SVM: Regularization The concept of C is the reverse of regularization. Higher C means lower regularization, which increases bias and lowers the variance (causing overfitting). https://www.simplilearn.com/ice9/free_resources_article_thumb/concept-of-c-graph-machine-learning.JPG IRIS Data Set The Iris dataset contains measurements of 150 IRIS flowers from three different species: Setosa Versicolor Viriginica Each row represents one sample. Flower measurements in centimeters are stored as columns. These are called features. IRIS Data Set: SVM Let’s train an SVM model using sci-kit-learn for the Iris dataset: https://www.simplilearn.com/ice9/free_resources_article_thumb/svm-model-graph-machine-learning.JPG Nonlinear SVM Classification There are two ways to solve nonlinear SVMs: by adding polynomial features by adding similarity features Polynomial features can be added to datasets; in some cases, this can create a linearly separable dataset. https://www.simplilearn.com/ice9/free_resources_article_thumb/nonlinear-classification-svm-machine-learning.JPG In the figure on the left, there is only 1 feature x1. This dataset is not linearly separable. If you add x2 = (x1)2 (figure on the right), the data becomes linearly separable. Polynomial Kernel In sci-kit-learn, one can use a Pipeline class for creating polynomial features. Classification results for the Moons dataset are shown in the figure. https://www.simplilearn.com/ice9/free_resources_article_thumb/polynomial-kernel-machine-learning.JPG Polynomial Kernel with Kernel Trick Let us look at the image below and understand Kernel Trick in detail. https://www.simplilearn.com/ice9/free_resources_article_thumb/polynomial-kernel-with-kernel-trick.JPG For large dimensional datasets, adding too many polynomial features can slow down the model. You can apply a kernel trick with the effect of polynomial features without actually adding them. The code is shown (SVC class) below trains an SVM classifier using a 3rd-degree polynomial kernel but with a kernel trick. https://www.simplilearn.com/ice9/free_resources_article_thumb/polynomial-kernel-equation-machine-learning.JPG The hyperparameter coefθ controls the influence of high-degree polynomials. Kernel SVM Let us understand in detail about Kernel SVM. Kernel SVMs are used for classification of nonlinear data. In the chart, nonlinear data is projected into a higher dimensional space via a mapping function where it becomes linearly separable. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-machine-learning.JPG In the higher dimension, a linear separating hyperplane can be derived and used for classification. A reverse projection of the higher dimension back to original feature space takes it back to nonlinear shape. As mentioned previously, SVMs can be kernelized to solve nonlinear classification problems. You can create a sample dataset for XOR gate (nonlinear problem) from NumPy. 100 samples will be assigned the class sample 1, and 100 samples will be assigned the class label -1. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-graph-machine-learning.JPG As you can see, this data is not linearly separable. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-non-separable.JPG You now use the kernel trick to classify XOR dataset created earlier. https://www.simplilearn.com/ice9/free_resources_article_thumb/kernel-svm-xor-machine-learning.JPG Naïve Bayes Classifier What is Naive Bayes Classifier? Have you ever wondered how your mail provider implements spam filtering or how online news channels perform news text classification or even how companies perform sentiment analysis of their audience on social media? All of this and more are done through a machine learning algorithm called Naive Bayes Classifier. Naive Bayes Named after Thomas Bayes from the 1700s who first coined this in the Western literature. Naive Bayes classifier works on the principle of conditional probability as given by the Bayes theorem. Advantages of Naive Bayes Classifier Listed below are six benefits of Naive Bayes Classifier. Very simple and easy to implement Needs less training data Handles both continuous and discrete data Highly scalable with the number of predictors and data points As it is fast, it can be used in real-time predictions Not sensitive to irrelevant features Bayes Theorem We will understand Bayes Theorem in detail from the points mentioned below. According to the Bayes model, the conditional probability P(Y|X) can be calculated as: P(Y|X) = P(X|Y)P(Y) / P(X) This means you have to estimate a very large number of P(X|Y) probabilities for a relatively small vector space X. For example, for a Boolean Y and 30 possible Boolean attributes in the X vector, you will have to estimate 3 billion probabilities P(X|Y). To make it practical, a Naïve Bayes classifier is used, which assumes conditional independence of P(X) to each other, with a given value of Y. This reduces the number of probability estimates to 2*30=60 in the above example. Naïve Bayes Classifier for SMS Spam Detection Consider a labeled SMS database having 5574 messages. It has messages as given below: https://www.simplilearn.com/ice9/free_resources_article_thumb/naive-bayes-spam-machine-learning.JPG Each message is marked as spam or ham in the data set. Let’s train a model with Naïve Bayes algorithm to detect spam from ham. The message lengths and their frequency (in the training dataset) are as shown below: https://www.simplilearn.com/ice9/free_resources_article_thumb/naive-bayes-spam-spam-detection.JPG Analyze the logic you use to train an algorithm to detect spam: Split each message into individual words/tokens (bag of words). Lemmatize the data (each word takes its base form, like “walking” or “walked” is replaced with “walk”). Convert data to vectors using scikit-learn module CountVectorizer. Run TFIDF to remove common words like “is,” “are,” “and.” Now apply scikit-learn module for Naïve Bayes MultinomialNB to get the Spam Detector. This spam detector can then be used to classify a random new message as spam or ham. Next, the accuracy of the spam detector is checked using the Confusion Matrix. For the SMS spam example above, the confusion matrix is shown on the right. Accuracy Rate = Correct / Total = (4827 + 592)/5574 = 97.21% Error Rate = Wrong / Total = (155 + 0)/5574 = 2.78% https://www.simplilearn.com/ice9/free_resources_article_thumb/confusion-matrix-machine-learning.JPG Although confusion Matrix is useful, some more precise metrics are provided by Precision and Recall. https://www.simplilearn.com/ice9/free_resources_article_thumb/precision-recall-matrix-machine-learning.JPG Precision refers to the accuracy of positive predictions. https://www.simplilearn.com/ice9/free_resources_article_thumb/precision-formula-machine-learning.JPG Recall refers to the ratio of positive instances that are correctly detected by the classifier (also known as True positive rate or TPR). https://www.simplilearn.com/ice9/free_resources_article_thumb/recall-formula-machine-learning.JPG Precision/Recall Trade-off To detect age-appropriate videos for kids, you need high precision (low recall) to ensure that only safe videos make the cut (even though a few safe videos may be left out). The high recall is needed (low precision is acceptable) in-store surveillance to catch shoplifters; a few false alarms are acceptable, but all shoplifters must be caught. Learn about Naive Bayes in detail. Click here! Decision Tree Classifier Some aspects of the Decision Tree Classifier mentioned below are. Decision Trees (DT) can be used both for classification and regression. The advantage of decision trees is that they require very little data preparation. They do not require feature scaling or centering at all. They are also the fundamental components of Random Forests, one of the most powerful ML algorithms. Unlike Random Forests and Neural Networks (which do black-box modeling), Decision Trees are white box models, which means that inner workings of these models are clearly understood. In the case of classification, the data is segregated based on a series of questions. Any new data point is assigned to the selected leaf node. https://www.simplilearn.com/ice9/free_resources_article_thumb/decision-tree-classifier-machine-learning.JPG Start at the tree root and split the data on the feature using the decision algorithm, resulting in the largest information gain (IG). This splitting procedure is then repeated in an iterative process at each child node until the leaves are pure. This means that the samples at each node belonging to the same class. In practice, you can set a limit on the depth of the tree to prevent overfitting. The purity is compromised here as the final leaves may still have some impurity. The figure shows the classification of the Iris dataset. https://www.simplilearn.com/ice9/free_resources_article_thumb/decision-tree-classifier-graph.JPG IRIS Decision Tree Let’s build a Decision Tree using scikit-learn for the Iris flower dataset and also visualize it using export_graphviz API. https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-decision-tree-machine-learning.JPG The output of export_graphviz can be converted into png format: https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-decision-tree-output.JPG Sample attribute stands for the number of training instances the node applies to. Value attribute stands for the number of training instances of each class the node applies to. Gini impurity measures the node’s impurity. A node is “pure” (gini=0) if all training instances it applies to belong to the same class. https://www.simplilearn.com/ice9/free_resources_article_thumb/impurity-formula-machine-learning.JPG For example, for Versicolor (green color node), the Gini is 1-(0/54)2 -(49/54)2 -(5/54) 2 ≈ 0.168 https://www.simplilearn.com/ice9/free_resources_article_thumb/iris-decision-tree-sample.JPG Decision Boundaries Let us learn to create decision boundaries below. For the first node (depth 0), the solid line splits the data (Iris-Setosa on left). Gini is 0 for Setosa node, so no further split is possible. The second node (depth 1) splits the data into Versicolor and Virginica. If max_depth were set as 3, a third split would happen (vertical dotted line). https://www.simplilearn.com/ice9/free_resources_article_thumb/decision-tree-boundaries.JPG For a sample with petal length 5 cm and petal width 1.5 cm, the tree traverses to depth 2 left node, so the probability predictions for this sample are 0% for Iris-Setosa (0/54), 90.7% for Iris-Versicolor (49/54), and 9.3% for Iris-Virginica (5/54) CART Training Algorithm Scikit-learn uses Classification and Regression Trees (CART) algorithm to train Decision Trees. CART algorithm: Split the data into two subsets using a single feature k and threshold tk (example, petal length < “2.45 cm”). This is done recursively for each node. k and tk are chosen such that they produce the purest subsets (weighted by their size). The objective is to minimize the cost function as given below: https://www.simplilearn.com/ice9/free_resources_article_thumb/cart-training-algorithm-machine-learning.JPG The algorithm stops executing if one of the following situations occurs: max_depth is reached No further splits are found for each node Other hyperparameters may be used to stop the tree: min_samples_split min_samples_leaf min_weight_fraction_leaf max_leaf_nodes Gini Impurity or Entropy Entropy is one more measure of impurity and can be used in place of Gini. https://www.simplilearn.com/ice9/free_resources_article_thumb/gini-impurity-entrophy.JPG It is a degree of uncertainty, and Information Gain is the reduction that occurs in entropy as one traverses down the tree. Entropy is zero for a DT node when the node contains instances of only one class. Entropy for depth 2 left node in the example given above is: https://www.simplilearn.com/ice9/free_resources_article_thumb/entrophy-for-depth-2.JPG Gini and Entropy both lead to similar trees. DT: Regularization The following figure shows two decision trees on the moons dataset. https://www.simplilearn.com/ice9/free_resources_article_thumb/dt-regularization-machine-learning.JPG The decision tree on the right is restricted by min_samples_leaf = 4. The model on the left is overfitting, while the model on the right generalizes better. Random Forest Classifier Let us have an understanding of Random Forest Classifier below. A random forest can be considered an ensemble of decision trees (Ensemble learning). Random Forest algorithm: Draw a random bootstrap sample of size n (randomly choose n samples from the training set). Grow a decision tree from the bootstrap sample. At each node, randomly select d features. Split the node using the feature that provides the best split according to the objective function, for instance by maximizing the information gain. Repeat the steps 1 to 2 k times. (k is the number of trees you want to create, using a subset of samples) Aggregate the prediction by each tree for a new data point to assign the class label by majority vote (pick the group selected by the most number of trees and assign new data point to that group). Random Forests are opaque, which means it is difficult to visualize their inner workings. https://www.simplilearn.com/ice9/free_resources_article_thumb/random-forest-classifier-graph.JPG However, the advantages outweigh their limitations since you do not have to worry about hyperparameters except k, which stands for the number of decision trees to be created from a subset of samples. RF is quite robust to noise from the individual decision trees. Hence, you need not prune individual decision trees. The larger the number of decision trees, the more accurate the Random Forest prediction is. (This, however, comes with higher computation cost). Key Takeaways Let us quickly run through what we have learned so far in this Classification tutorial. Classification algorithms are supervised learning methods to split data into classes. They can work on Linear Data as well as Nonlinear Data. Logistic Regression can classify data based on weighted parameters and sigmoid conversion to calculate the probability of classes. K-nearest Neighbors (KNN) algorithm uses similar features to classify data. Support Vector Machines (SVMs) classify data by detecting the maximum margin hyperplane between data classes. Naïve Bayes, a simplified Bayes Model, can help classify data using conditional probability models. Decision Trees are powerful classifiers and use tree splitting logic until pure or somewhat pure leaf node classes are attained. Random Forests apply Ensemble Learning to Decision Trees for more accurate classification predictions. Conclusion This completes ‘Classification’ tutorial. In the next tutorial, we will learn 'Unsupervised Learning with Clustering.'
tahanakabi / DRL For Microgrid Energy ManagementWe study the performance of various deep reinforcement learning algorithms for the problem of microgrid’s energy management system. We propose a novel microgrid model that consists of a wind turbine generator, an energy storage system, a population of thermostatically controlled loads, a population of price-responsive loads, and a connection to the main grid. The proposed energy management system is designed to coordinate between the different sources of flexibility by defining the priority resources, the direct demand control signals and the electricity prices. Seven deep reinforcement learning algorithms are implemented and empirically compared in this paper. The numerical results show a significant difference between the different deep reinforcement learning algorithms in their ability to converge to optimal policies. By adding an experience replay and a second semi-deterministic training phase to the well-known Asynchronous advantage actor critic algorithm, we achieved considerably better performance and converged to superior policies in terms of energy efficiency and economic value.
Root-lee / Put Flavors SA2018 Huawei Software Elite Challenge, using simulated annealing algorithm + first-fit algorithm to find the optimal method for placing virtual machines.
eth-cscs / COSMADistributed Communication-Optimal Matrix-Matrix Multiplication Algorithm
albumentations-team / AutoalbumentAutoML for image augmentation. AutoAlbument uses the Faster AutoAugment algorithm to find optimal augmentation policies. Documentation - https://albumentations.ai/docs/autoalbument/
Aastha2104 / Parkinson Disease PredictionIntroduction Parkinson’s Disease is the second most prevalent neurodegenerative disorder after Alzheimer’s, affecting more than 10 million people worldwide. Parkinson’s is characterized primarily by the deterioration of motor and cognitive ability. There is no single test which can be administered for diagnosis. Instead, doctors must perform a careful clinical analysis of the patient’s medical history. Unfortunately, this method of diagnosis is highly inaccurate. A study from the National Institute of Neurological Disorders finds that early diagnosis (having symptoms for 5 years or less) is only 53% accurate. This is not much better than random guessing, but an early diagnosis is critical to effective treatment. Because of these difficulties, I investigate a machine learning approach to accurately diagnose Parkinson’s, using a dataset of various speech features (a non-invasive yet characteristic tool) from the University of Oxford. Why speech features? Speech is very predictive and characteristic of Parkinson’s disease; almost every Parkinson’s patient experiences severe vocal degradation (inability to produce sustained phonations, tremor, hoarseness), so it makes sense to use voice to diagnose the disease. Voice analysis gives the added benefit of being non-invasive, inexpensive, and very easy to extract clinically. Background Parkinson's Disease Parkinson’s is a progressive neurodegenerative condition resulting from the death of the dopamine containing cells of the substantia nigra (which plays an important role in movement). Symptoms include: “frozen” facial features, bradykinesia (slowness of movement), akinesia (impairment of voluntary movement), tremor, and voice impairment. Typically, by the time the disease is diagnosed, 60% of nigrostriatal neurons have degenerated, and 80% of striatal dopamine have been depleted. Performance Metrics TP = true positive, FP = false positive, TN = true negative, FN = false negative Accuracy: (TP+TN)/(P+N) Matthews Correlation Coefficient: 1=perfect, 0=random, -1=completely inaccurate Algorithms Employed Logistic Regression (LR): Uses the sigmoid logistic equation with weights (coefficient values) and biases (constants) to model the probability of a certain class for binary classification. An output of 1 represents one class, and an output of 0 represents the other. Training the model will learn the optimal weights and biases. Linear Discriminant Analysis (LDA): Assumes that the data is Gaussian and each feature has the same variance. LDA estimates the mean and variance for each class from the training data, and then uses properties of statistics (Bayes theorem , Gaussian distribution, etc) to compute the probability of a particular instance belonging to a given class. The class with the largest probability is the prediction. k Nearest Neighbors (KNN): Makes predictions about the validation set using the entire training set. KNN makes a prediction about a new instance by searching through the entire set to find the k “closest” instances. “Closeness” is determined using a proximity measurement (Euclidean) across all features. The class that the majority of the k closest instances belong to is the class that the model predicts the new instance to be. Decision Tree (DT): Represented by a binary tree, where each root node represents an input variable and a split point, and each leaf node contains an output used to make a prediction. Neural Network (NN): Models the way the human brain makes decisions. Each neuron takes in 1+ inputs, and then uses an activation function to process the input with weights and biases to produce an output. Neurons can be arranged into layers, and multiple layers can form a network to model complex decisions. Training the network involves using the training instances to optimize the weights and biases. Naive Bayes (NB): Simplifies the calculation of probabilities by assuming that all features are independent of one another (a strong but effective assumption). Employs Bayes Theorem to calculate the probabilities that the instance to be predicted is in each class, then finds the class with the highest probability. Gradient Boost (GB): Generally used when seeking a model with very high predictive performance. Used to reduce bias and variance (“error”) by combining multiple “weak learners” (not very good models) to create a “strong learner” (high performance model). Involves 3 elements: a loss function (error function) to be optimized, a weak learner (decision tree) to make predictions, and an additive model to add trees to minimize the loss function. Gradient descent is used to minimize error after adding each tree (one by one). Engineering Goal Produce a machine learning model to diagnose Parkinson’s disease given various features of a patient’s speech with at least 90% accuracy and/or a Matthews Correlation Coefficient of at least 0.9. Compare various algorithms and parameters to determine the best model for predicting Parkinson’s. Dataset Description Source: the University of Oxford 195 instances (147 subjects with Parkinson’s, 48 without Parkinson’s) 22 features (elements that are possibly characteristic of Parkinson’s, such as frequency, pitch, amplitude / period of the sound wave) 1 label (1 for Parkinson’s, 0 for no Parkinson’s) Project Pipeline pipeline Summary of Procedure Split the Oxford Parkinson’s Dataset into two parts: one for training, one for validation (evaluate how well the model performs) Train each of the following algorithms with the training set: Logistic Regression, Linear Discriminant Analysis, k Nearest Neighbors, Decision Tree, Neural Network, Naive Bayes, Gradient Boost Evaluate results using the validation set Repeat for the following training set to validation set splits: 80% training / 20% validation, 75% / 25%, and 70% / 30% Repeat for a rescaled version of the dataset (scale all the numbers in the dataset to a range from 0 to 1: this helps to reduce the effect of outliers) Conduct 5 trials and average the results Data a_o a_r m_o m_r Data Analysis In general, the models tended to perform the best (both in terms of accuracy and Matthews Correlation Coefficient) on the rescaled dataset with a 75-25 train-test split. The two highest performing algorithms, k Nearest Neighbors and the Neural Network, both achieved an accuracy of 98%. The NN achieved a MCC of 0.96, while KNN achieved a MCC of 0.94. These figures outperform most existing literature and significantly outperform current methods of diagnosis. Conclusion and Significance These robust results suggest that a machine learning approach can indeed be implemented to significantly improve diagnosis methods of Parkinson’s disease. Given the necessity of early diagnosis for effective treatment, my machine learning models provide a very promising alternative to the current, rather ineffective method of diagnosis. Current methods of early diagnosis are only 53% accurate, while my machine learning model produces 98% accuracy. This 45% increase is critical because an accurate, early diagnosis is needed to effectively treat the disease. Typically, by the time the disease is diagnosed, 60% of nigrostriatal neurons have degenerated, and 80% of striatal dopamine have been depleted. With an earlier diagnosis, much of this degradation could have been slowed or treated. My results are very significant because Parkinson’s affects over 10 million people worldwide who could benefit greatly from an early, accurate diagnosis. Not only is my machine learning approach more accurate in terms of diagnostic accuracy, it is also more scalable, less expensive, and therefore more accessible to people who might not have access to established medical facilities and professionals. The diagnosis is also much simpler, requiring only a 10-15 second voice recording and producing an immediate diagnosis. Future Research Given more time and resources, I would investigate the following: Create a mobile application which would allow the user to record his/her voice, extract the necessary vocal features, and feed it into my machine learning model to diagnose Parkinson’s. Use larger datasets in conjunction with the University of Oxford dataset. Tune and improve my models even further to achieve even better results. Investigate different structures and types of neural networks. Construct a novel algorithm specifically suited for the prediction of Parkinson’s. Generalize my findings and algorithms for all types of dementia disorders, such as Alzheimer’s. References Bind, Shubham. "A Survey of Machine Learning Based Approaches for Parkinson Disease Prediction." International Journal of Computer Science and Information Technologies 6 (2015): n. pag. International Journal of Computer Science and Information Technologies. 2015. Web. 8 Mar. 2017. Brooks, Megan. "Diagnosing Parkinson's Disease Still Challenging." Medscape Medical News. National Institute of Neurological Disorders, 31 July 2014. Web. 20 Mar. 2017. Exploiting Nonlinear Recurrence and Fractal Scaling Properties for Voice Disorder Detection', Little MA, McSharry PE, Roberts SJ, Costello DAE, Moroz IM. BioMedical Engineering OnLine 2007, 6:23 (26 June 2007) Hashmi, Sumaiya F. "A Machine Learning Approach to Diagnosis of Parkinson’s Disease."Claremont Colleges Scholarship. Claremont College, 2013. Web. 10 Mar. 2017. Karplus, Abraham. "Machine Learning Algorithms for Cancer Diagnosis." Machine Learning Algorithms for Cancer Diagnosis (n.d.): n. pag. Mar. 2012. Web. 20 Mar. 2017. Little, Max. "Parkinsons Data Set." UCI Machine Learning Repository. University of Oxford, 26 June 2008. Web. 20 Feb. 2017. Ozcift, Akin, and Arif Gulten. "Classifier Ensemble Construction with Rotation Forest to Improve Medical Diagnosis Performance of Machine Learning Algorithms." Computer Methods and Programs in Biomedicine 104.3 (2011): 443-51. Semantic Scholar. 2011. Web. 15 Mar. 2017. "Parkinson’s Disease Dementia." UCI MIND. N.p., 19 Oct. 2015. Web. 17 Feb. 2017. Salvatore, C., A. Cerasa, I. Castiglioni, F. Gallivanone, A. Augimeri, M. Lopez, G. Arabia, M. Morelli, M.c. Gilardi, and A. Quattrone. "Machine Learning on Brain MRI Data for Differential Diagnosis of Parkinson's Disease and Progressive Supranuclear Palsy."Journal of Neuroscience Methods 222 (2014): 230-37. 2014. Web. 18 Mar. 2017. Shahbakhi, Mohammad, Danial Taheri Far, and Ehsan Tahami. "Speech Analysis for Diagnosis of Parkinson’s Disease Using Genetic Algorithm and Support Vector Machine."Journal of Biomedical Science and Engineering 07.04 (2014): 147-56. Scientific Research. July 2014. Web. 2 Mar. 2017. "Speech and Communication." Speech and Communication. Parkinson's Disease Foundation, n.d. Web. 22 Mar. 2017. Sriram, Tarigoppula V. S., M. Venkateswara Rao, G. V. Satya Narayana, and D. S. V. G. K. Kaladhar. "Diagnosis of Parkinson Disease Using Machine Learning and Data Mining Systems from Voice Dataset." SpringerLink. Springer, Cham, 01 Jan. 1970. Web. 17 Mar. 2017.
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