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lo-th / Fullikjavascript fast iterative solver for Inverse Kinematics
JuliaLinearAlgebra / IterativeSolvers.jlIterative algorithms for solving linear systems, eigensystems, and singular value problems
abess-team / Skscopeskscope: Sparse-Constrained OPtimization via itErative-solvers
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.'
molyswu / Hand Detectionusing Neural Networks (SSD) on Tensorflow. This repo documents steps and scripts used to train a hand detector using Tensorflow (Object Detection API). As with any DNN based task, the most expensive (and riskiest) part of the process has to do with finding or creating the right (annotated) dataset. I was interested mainly in detecting hands on a table (egocentric view point). I experimented first with the [Oxford Hands Dataset](http://www.robots.ox.ac.uk/~vgg/data/hands/) (the results were not good). I then tried the [Egohands Dataset](http://vision.soic.indiana.edu/projects/egohands/) which was a much better fit to my requirements. The goal of this repo/post is to demonstrate how neural networks can be applied to the (hard) problem of tracking hands (egocentric and other views). Better still, provide code that can be adapted to other uses cases. If you use this tutorial or models in your research or project, please cite [this](#citing-this-tutorial). Here is the detector in action. <img src="images/hand1.gif" width="33.3%"><img src="images/hand2.gif" width="33.3%"><img src="images/hand3.gif" width="33.3%"> Realtime detection on video stream from a webcam . <img src="images/chess1.gif" width="33.3%"><img src="images/chess2.gif" width="33.3%"><img src="images/chess3.gif" width="33.3%"> Detection on a Youtube video. Both examples above were run on a macbook pro **CPU** (i7, 2.5GHz, 16GB). Some fps numbers are: | FPS | Image Size | Device| Comments| | ------------- | ------------- | ------------- | ------------- | | 21 | 320 * 240 | Macbook pro (i7, 2.5GHz, 16GB) | Run without visualizing results| | 16 | 320 * 240 | Macbook pro (i7, 2.5GHz, 16GB) | Run while visualizing results (image above) | | 11 | 640 * 480 | Macbook pro (i7, 2.5GHz, 16GB) | Run while visualizing results (image above) | > Note: The code in this repo is written and tested with Tensorflow `1.4.0-rc0`. Using a different version may result in [some errors](https://github.com/tensorflow/models/issues/1581). You may need to [generate your own frozen model](https://pythonprogramming.net/testing-custom-object-detector-tensorflow-object-detection-api-tutorial/?completed=/training-custom-objects-tensorflow-object-detection-api-tutorial/) graph using the [model checkpoints](model-checkpoint) in the repo to fit your TF version. **Content of this document** - Motivation - Why Track/Detect hands with Neural Networks - Data preparation and network training in Tensorflow (Dataset, Import, Training) - Training the hand detection Model - Using the Detector to Detect/Track hands - Thoughts on Optimizations. > P.S if you are using or have used the models provided here, feel free to reach out on twitter ([@vykthur](https://twitter.com/vykthur)) and share your work! ## Motivation - Why Track/Detect hands with Neural Networks? There are several existing approaches to tracking hands in the computer vision domain. Incidentally, many of these approaches are rule based (e.g extracting background based on texture and boundary features, distinguishing between hands and background using color histograms and HOG classifiers,) making them not very robust. For example, these algorithms might get confused if the background is unusual or in situations where sharp changes in lighting conditions cause sharp changes in skin color or the tracked object becomes occluded.(see [here for a review](https://www.cse.unr.edu/~bebis/handposerev.pdf) paper on hand pose estimation from the HCI perspective) With sufficiently large datasets, neural networks provide opportunity to train models that perform well and address challenges of existing object tracking/detection algorithms - varied/poor lighting, noisy environments, diverse viewpoints and even occlusion. The main drawbacks to usage for real-time tracking/detection is that they can be complex, are relatively slow compared to tracking-only algorithms and it can be quite expensive to assemble a good dataset. But things are changing with advances in fast neural networks. Furthermore, this entire area of work has been made more approachable by deep learning frameworks (such as the tensorflow object detection api) that simplify the process of training a model for custom object detection. More importantly, the advent of fast neural network models like ssd, faster r-cnn, rfcn (see [here](https://github.com/tensorflow/models/blob/master/research/object_detection/g3doc/detection_model_zoo.md#coco-trained-models-coco-models) ) etc make neural networks an attractive candidate for real-time detection (and tracking) applications. Hopefully, this repo demonstrates this. > If you are not interested in the process of training the detector, you can skip straight to applying the [pretrained model I provide in detecting hands](#detecting-hands). Training a model is a multi-stage process (assembling dataset, cleaning, splitting into training/test partitions and generating an inference graph). While I lightly touch on the details of these parts, there are a few other tutorials cover training a custom object detector using the tensorflow object detection api in more detail[ see [here](https://pythonprogramming.net/training-custom-objects-tensorflow-object-detection-api-tutorial/) and [here](https://towardsdatascience.com/how-to-train-your-own-object-detector-with-tensorflows-object-detector-api-bec72ecfe1d9) ]. I recommend you walk through those if interested in training a custom object detector from scratch. ## Data preparation and network training in Tensorflow (Dataset, Import, Training) **The Egohands Dataset** The hand detector model is built using data from the [Egohands Dataset](http://vision.soic.indiana.edu/projects/egohands/) dataset. This dataset works well for several reasons. It contains high quality, pixel level annotations (>15000 ground truth labels) where hands are located across 4800 images. All images are captured from an egocentric view (Google glass) across 48 different environments (indoor, outdoor) and activities (playing cards, chess, jenga, solving puzzles etc). <img src="images/egohandstrain.jpg" width="100%"> If you will be using the Egohands dataset, you can cite them as follows: > Bambach, Sven, et al. "Lending a hand: Detecting hands and recognizing activities in complex egocentric interactions." Proceedings of the IEEE International Conference on Computer Vision. 2015. The Egohands dataset (zip file with labelled data) contains 48 folders of locations where video data was collected (100 images per folder). ``` -- LOCATION_X -- frame_1.jpg -- frame_2.jpg ... -- frame_100.jpg -- polygons.mat // contains annotations for all 100 images in current folder -- LOCATION_Y -- frame_1.jpg -- frame_2.jpg ... -- frame_100.jpg -- polygons.mat // contains annotations for all 100 images in current folder ``` **Converting data to Tensorflow Format** Some initial work needs to be done to the Egohands dataset to transform it into the format (`tfrecord`) which Tensorflow needs to train a model. This repo contains `egohands_dataset_clean.py` a script that will help you generate these csv files. - Downloads the egohands datasets - Renames all files to include their directory names to ensure each filename is unique - Splits the dataset into train (80%), test (10%) and eval (10%) folders. - Reads in `polygons.mat` for each folder, generates bounding boxes and visualizes them to ensure correctness (see image above). - Once the script is done running, you should have an images folder containing three folders - train, test and eval. Each of these folders should also contain a csv label document each - `train_labels.csv`, `test_labels.csv` that can be used to generate `tfrecords` Note: While the egohands dataset provides four separate labels for hands (own left, own right, other left, and other right), for my purpose, I am only interested in the general `hand` class and label all training data as `hand`. You can modify the data prep script to generate `tfrecords` that support 4 labels. Next: convert your dataset + csv files to tfrecords. A helpful guide on this can be found [here](https://pythonprogramming.net/creating-tfrecord-files-tensorflow-object-detection-api-tutorial/).For each folder, you should be able to generate `train.record`, `test.record` required in the training process. ## Training the hand detection Model Now that the dataset has been assembled (and your tfrecords), the next task is to train a model based on this. With neural networks, it is possible to use a process called [transfer learning](https://www.tensorflow.org/tutorials/image_retraining) to shorten the amount of time needed to train the entire model. This means we can take an existing model (that has been trained well on a related domain (here image classification) and retrain its final layer(s) to detect hands for us. Sweet!. Given that neural networks sometimes have thousands or millions of parameters that can take weeks or months to train, transfer learning helps shorten training time to possibly hours. Tensorflow does offer a few models (in the tensorflow [model zoo](https://github.com/tensorflow/models/blob/master/research/object_detection/g3doc/detection_model_zoo.md#coco-trained-models-coco-models)) and I chose to use the `ssd_mobilenet_v1_coco` model as my start point given it is currently (one of) the fastest models (read the SSD research [paper here](https://arxiv.org/pdf/1512.02325.pdf)). The training process can be done locally on your CPU machine which may take a while or better on a (cloud) GPU machine (which is what I did). For reference, training on my macbook pro (tensorflow compiled from source to take advantage of the mac's cpu architecture) the maximum speed I got was 5 seconds per step as opposed to the ~0.5 seconds per step I got with a GPU. For reference it would take about 12 days to run 200k steps on my mac (i7, 2.5GHz, 16GB) compared to ~5hrs on a GPU. > **Training on your own images**: Please use the [guide provided by Harrison from pythonprogramming](https://pythonprogramming.net/training-custom-objects-tensorflow-object-detection-api-tutorial/) on how to generate tfrecords given your label csv files and your images. The guide also covers how to start the training process if training locally. [see [here] (https://pythonprogramming.net/training-custom-objects-tensorflow-object-detection-api-tutorial/)]. If training in the cloud using a service like GCP, see the [guide here](https://github.com/tensorflow/models/blob/master/research/object_detection/g3doc/running_on_cloud.md). As the training process progresses, the expectation is that total loss (errors) gets reduced to its possible minimum (about a value of 1 or thereabout). By observing the tensorboard graphs for total loss(see image below), it should be possible to get an idea of when the training process is complete (total loss does not decrease with further iterations/steps). I ran my training job for 200k steps (took about 5 hours) and stopped at a total Loss (errors) value of 2.575.(In retrospect, I could have stopped the training at about 50k steps and gotten a similar total loss value). With tensorflow, you can also run an evaluation concurrently that assesses your model to see how well it performs on the test data. A commonly used metric for performance is mean average precision (mAP) which is single number used to summarize the area under the precision-recall curve. mAP is a measure of how well the model generates a bounding box that has at least a 50% overlap with the ground truth bounding box in our test dataset. For the hand detector trained here, the mAP value was **0.9686@0.5IOU**. mAP values range from 0-1, the higher the better. <img src="images/accuracy.jpg" width="100%"> Once training is completed, the trained inference graph (`frozen_inference_graph.pb`) is then exported (see the earlier referenced guides for how to do this) and saved in the `hand_inference_graph` folder. Now its time to do some interesting detection. ## Using the Detector to Detect/Track hands If you have not done this yet, please following the guide on installing [Tensorflow and the Tensorflow object detection api](https://github.com/tensorflow/models/blob/master/research/object_detection/g3doc/installation.md). This will walk you through setting up the tensorflow framework, cloning the tensorflow github repo and a guide on - Load the `frozen_inference_graph.pb` trained on the hands dataset as well as the corresponding label map. In this repo, this is done in the `utils/detector_utils.py` script by the `load_inference_graph` method. ```python detection_graph = tf.Graph() with detection_graph.as_default(): od_graph_def = tf.GraphDef() with tf.gfile.GFile(PATH_TO_CKPT, 'rb') as fid: serialized_graph = fid.read() od_graph_def.ParseFromString(serialized_graph) tf.import_graph_def(od_graph_def, name='') sess = tf.Session(graph=detection_graph) print("> ====== Hand Inference graph loaded.") ``` - Detect hands. In this repo, this is done in the `utils/detector_utils.py` script by the `detect_objects` method. ```python (boxes, scores, classes, num) = sess.run( [detection_boxes, detection_scores, detection_classes, num_detections], feed_dict={image_tensor: image_np_expanded}) ``` - Visualize detected bounding detection_boxes. In this repo, this is done in the `utils/detector_utils.py` script by the `draw_box_on_image` method. This repo contains two scripts that tie all these steps together. - detect_multi_threaded.py : A threaded implementation for reading camera video input detection and detecting. Takes a set of command line flags to set parameters such as `--display` (visualize detections), image parameters `--width` and `--height`, videe `--source` (0 for camera) etc. - detect_single_threaded.py : Same as above, but single threaded. This script works for video files by setting the video source parameter videe `--source` (path to a video file). ```cmd # load and run detection on video at path "videos/chess.mov" python detect_single_threaded.py --source videos/chess.mov ``` > Update: If you do have errors loading the frozen inference graph in this repo, feel free to generate a new graph that fits your TF version from the model-checkpoint in this repo. Use the [export_inference_graph.py](https://github.com/tensorflow/models/blob/master/research/object_detection/export_inference_graph.py) script provided in the tensorflow object detection api repo. More guidance on this [here](https://pythonprogramming.net/testing-custom-object-detector-tensorflow-object-detection-api-tutorial/?completed=/training-custom-objects-tensorflow-object-detection-api-tutorial/). ## Thoughts on Optimization. A few things that led to noticeable performance increases. - Threading: Turns out that reading images from a webcam is a heavy I/O event and if run on the main application thread can slow down the program. I implemented some good ideas from [Adrian Rosebuck](https://www.pyimagesearch.com/2017/02/06/faster-video-file-fps-with-cv2-videocapture-and-opencv/) on parrallelizing image capture across multiple worker threads. This mostly led to an FPS increase of about 5 points. - For those new to Opencv, images from the `cv2.read()` method return images in [BGR format](https://www.learnopencv.com/why-does-opencv-use-bgr-color-format/). Ensure you convert to RGB before detection (accuracy will be much reduced if you dont). ```python cv2.cvtColor(image_np, cv2.COLOR_BGR2RGB) ``` - Keeping your input image small will increase fps without any significant accuracy drop.(I used about 320 x 240 compared to the 1280 x 720 which my webcam provides). - Model Quantization. Moving from the current 32 bit to 8 bit can achieve up to 4x reduction in memory required to load and store models. One way to further speed up this model is to explore the use of [8-bit fixed point quantization](https://heartbeat.fritz.ai/8-bit-quantization-and-tensorflow-lite-speeding-up-mobile-inference-with-low-precision-a882dfcafbbd). Performance can also be increased by a clever combination of tracking algorithms with the already decent detection and this is something I am still experimenting with. Have ideas for optimizing better, please share! <img src="images/general.jpg" width="100%"> Note: The detector does reflect some limitations associated with the training set. This includes non-egocentric viewpoints, very noisy backgrounds (e.g in a sea of hands) and sometimes skin tone. There is opportunity to improve these with additional data. ## Integrating Multiple DNNs. One way to make things more interesting is to integrate our new knowledge of where "hands" are with other detectors trained to recognize other objects. Unfortunately, while our hand detector can in fact detect hands, it cannot detect other objects (a factor or how it is trained). To create a detector that classifies multiple different objects would mean a long involved process of assembling datasets for each class and a lengthy training process. > Given the above, a potential strategy is to explore structures that allow us **efficiently** interleave output form multiple pretrained models for various object classes and have them detect multiple objects on a single image. An example of this is with my primary use case where I am interested in understanding the position of objects on a table with respect to hands on same table. I am currently doing some work on a threaded application that loads multiple detectors and outputs bounding boxes on a single image. More on this soon.
tum-pbs / Solver In The LoopSolver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers
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primme / PrimmePReconditioned Iterative MultiMethod Eigensolver for solving symmetric/Hermitian eigenvalue problems and singular value problems
ctkelley / SIAMFANLEquations.jlThis is a Julia package of nonlinear solvers. These codes are used in my book, Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia.
sahands / Simple SatSimple recursive and iterative SAT solver written in Python.
yining043 / VRP DACTThis repo implements our paper, "Learning to Iteratively Solve Routing Problems with Dual-Aspect Collaborative Transformer", which has been accepted at NeurIPS 2021.
anishida / LisLis (Library of Iterative Solvers for linear systems, pronounced [lis]) is a parallel software library to solve discretized linear equations and eigenvalue problems that arise from the numerical solution of partial differential equations using iterative methods.
adler-j / Learned Gradient TomographySolving ill-posed inverse problems using iterative deep neural networks
lusixing / Energy Efficiency Optimization For MIMO Interference NetworksSolving energy efficiency optimization problem for MIMO interference wireless network using iterative semi-definite programming with WMMSE (SDP-WMMSE) algorithm and successive convex approximation (SCA) algorithm
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SS-YS / MDP With Value Iteration And Policy IterationAn introduction to Markov decision process (MDP) and two algorithms that solve MDPs (value iteration & policy iteration) along with their Python implementations.
ruvnet / Sublinear Time SolverRust + WASM sublinear-time solver for asymmetric diagonally dominant systems. Exposes Neumann series, push, and hybrid random-walk algorithms with npm/npx CLI and Flow-Nexus HTTP streaming for swarm cost propagation and verification.
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The terminal or concrete expressions provide specific conversions on different types of data. (MeasurementConversion) The Mediator design pattern is used to handle communication between related objects (Colleagues). All communication is handled by a Mediator Object and the Colleagues don't need to know anything about each other to work together. (TestStockMediator) The Memento design pattern provides a way to store previous states of an Object easily. It has 3 main classes: 1) Memento: The basic object that is stored in different states. 2) Originator: Sets and Gets values from the currently targeted Memento. Creates new Mementos and assigns current values to them. 3) Caretaker: Holds an ArrayList that contains all previous versions of the Memento. It can store and retrieve stored Mementos. (TestMemento) The Visitor design pattern allows you to add methods to classes of different types without much altering to those classes. You can make completely different methods depending on the class used with this pattern. (VisitorTest)
