But, wouldn’t it be cool if we were able to implement all the above mentioned tasks using just one architecture. We know how to make the icing and the cherry, but we don’t know how to make the cake. Set the size of the hidden layer for the autoencoder. autoenc = trainAutoencoder(X) returns an autoencoder trained using the training data in X.. autoenc = trainAutoencoder(X,hiddenSize) returns an autoencoder with the hidden representation size of hiddenSize.. autoenc = trainAutoencoder(___,Name,Value) returns an autoencoder for any of the above input arguments with additional options specified by one or more name-value pair arguments. The result is capable of running the two functions of "Encode" and "Decode".But this is only applicable to the case of normal autoencoders. Section 2 reviews the related work. Make learning your daily ritual. The encoder compresses the input and the decoder attempts to recreate the input from the compressed version provided by the encoder. An autoencoder is composed of an encoder and a decoder sub-models. And that’s just an obstacle we know about. Before we go into the theoretical and the implementation parts of an Adversarial Autoencoder, let’s take a step back and discuss about Autoencoders and have a look at a simple tensorflow implementation. If intelligence was a cake, unsupervised learning would be the cake, supervised learning would be the icing on the cake, and reinforcement learning would be the cherry on the cake. But this doesn’t represent a clear digit at all (well, at least for me). Lastly, we train our model by passing in our MNIST images using a batch size of 100 and using the same 100 images as the target. The steps that have been outlined can be applied to other similar problems, such as classifying images of letters, or even small images of objects of a specific category. Adversarial Symmetric Variational Autoencoder Yunchen Pu, Weiyao Wang, Ricardo Henao, Liqun Chen, Zhe Gan, Chunyuan Li and Lawrence Carin Department of Electrical and Computer Engineering, Duke University {yp42, ww109, r.henao, lc267, zg27,cl319, lcarin}@duke.edu Abstract A new form of variational autoencoder (VAE) is developed, in which the joint Adversarial Autoencoders. In this section, I implemented the above figure. As was explained, the encoders from the autoencoders have been used to extract features. You fine tune the network by retraining it on the training data in a supervised fashion. Use Icecream Instead, 7 A/B Testing Questions and Answers in Data Science Interviews, 10 Surprisingly Useful Base Python Functions, The Best Data Science Project to Have in Your Portfolio, Three Concepts to Become a Better Python Programmer, Social Network Analysis: From Graph Theory to Applications with Python. We introduce an autoencoder that tackles these … Train the next autoencoder on a set of these vectors extracted from the training data. Neural networks with multiple hidden layers can be useful for solving classification problems with complex data, such as images. VAEs are a probabilistic graphical model whose explicit goal is latent modeling, and accounting for or marginalizing out certain variables (as in the semi-supervised work above) as part of the modeling … When the number of neurons in the hidden layer is less than the size of the input, the autoencoder learns a compressed representation of the input. Notice how the decoder generalised the output 3 by removing small irregularities like the line on top of the input 3. Section 6 shows a AdversarialOptimizerAlternatingupdates each player in a round-robin.Take each batch … However, training neural networks with multiple hidden layers can be difficult in practice. Matching the aggregated posterior to the prior ensures that … In this paper, we propose the "adversarial autoencoder" (AAE), which is a probabilistic autoencoder that uses the recently proposed generative adversarial networks (GAN) to perform variational inference by matching the aggregated posterior of the hidden code vector of the autoencoder with an arbitrary prior distribution. SparsityProportion is a parameter of the sparsity regularizer. Next, we’ll use this dense() function to implement the encoder architecture. I’ve used tf.get_variable()instead of tf.Variable()to create the weight and bias variables so that we can later reuse the trained model (either the encoder or decoder alone) to pass in any desired value and have a look at their output. Each neuron in the encoder has a vector of weights associated with it which will be tuned to respond to a particular visual feature. I know Matlab has the function TrainAutoencoder(input, settings) to create and train an autoencoder. (I could have changed only the encoder or the decoder weights using the var_list parameter under the minimize() method. My input datasets is a list of 2000 time series, each with 501 entries for each time component. Once again, you can view a diagram of the autoencoder with the view function. Although studied extensively, the issues of whether they have the same generative power of GANs, or learn disentangled representations, have not been fully addressed. 2. Then you train a final softmax layer, and join the layers together to form a stacked network, which you train one final time in a supervised fashion. The results for the stacked neural network can be improved by performing backpropagation on the whole multilayer network. We need to solve the unsupervised learning problem before we can even think of getting to true AI. The encoder maps an input to a hidden representation, and the decoder attempts to reverse this mapping to reconstruct the original input. Now, what if we only consider the trained decoder and pass in some random numbers (I’ve passed 0, 0 as we only have a 2-D latent code) as it’s inputs, we should get some digits right? We’ll build an Adversarial Autoencoder that can compress data (MNIST digits in a lossy way), separate style and content of the digits (generate numbers with different styles), classify them using a small subset of labeled data to get high classification accuracy (about 95% using just 1000 labeled digits!) It should be noted that if the tenth element is 1, then the digit image is a zero. ∙ Google ∙ UNIVERSITY OF TORONTO ∙ 0 ∙ share . jointly, which we call Adversarial Latent Autoencoder (ALAE). Each digit image is 28-by-28 pixels, and there are 5,000 training examples. A generative adversarial network (GAN) is a type of deep learning network that can generate data with similar characteristics as the input real data. Note that this is different from applying a sparsity regularizer to the weights. → Part 2: Exploring latent space with Adversarial Autoencoders. Section 3 introduces the GPND framework, and Section 4 describes the training and architecture of the adversarial autoencoder network. Adversarial Autoencoders. Also, we learned the problems that we can have in latent space with Autoencoders for generative purposes. This process is often referred to as fine tuning. After using the second encoder, this was reduced again to 50 dimensions. The reason for this is because the encoder output does not cover the entire 2-D latent space (it has a lot of gaps in its output distribution). VAE - Autoencoding Variational Bayes, Stochastic Backpropagation and Inference in Deep Generative Models Semi-supervised VAE. which can be used to compress a file to get a zip (or rar,…) file that occupies lower amounts of space. It’s an Autoencoder that uses an adversarial approach to improve its regularization. With the full network formed, you can compute the results on the test set. An Autoencoder is a neural network that is trained to produce an output which is very similar to its input (so it basically attempts to copy its input to its output) and since it doesn’t need any targets (labels), it can be trained in an unsupervised manner. We know that a Convolutional Neural Networks (CNNs) or in some cases Dense fully connected layers (MLP — Multi layer perceptron as some would like to call it) can be used to perform image recognition. A similar operation is performed by the encoder in an autoencoder architecture. The labels for the images are stored in a 10-by-5000 matrix, where in every column a single element will be 1 to indicate the class that the digit belongs to, and all other elements in the column will be 0. The desired distribution for latent space is assumed Gaussian. This value must be between 0 and 1. You can stack the encoders from the autoencoders together with the softmax layer to form a stacked network for classification. The main difference is that you use the features that were generated from the first autoencoder as the training data in the second autoencoder. 2. Top row is an autoencoder while the bottom row is an adversarial network which forces the output to the encoder to follow the distribution $p(z)$. The numbers in the bottom right-hand square of the matrix give the overall accuracy. You can view a diagram of the softmax layer with the view function. We’ll introduce constraints on the latent code (output of the encoder) using adversarial learning. One solution was provided with Variational Autoencoders, but Adversarial Autoencoder provided a more flexible solution. Collection of MATLAB implementations of Generative Adversarial Networks (GANs) suggested in research papers. Construction. Nevertheless, the existing methods cannot fully consider the inherent features of the spectral information, which leads to the applications being of low practical performance. For more information on the dataset, type help abalone_dataset in the command line.. Each of these tasks might require its own architecture and training algorithm. Do you want to open this version instead? Unlike the autoencoders, you train the softmax layer in a supervised fashion using labels for the training data. Skip to content. As a result, the decoder of the adversarial autoencoder learns a deep generative model that maps the imposed prior to the data distribution. In this case, we used Autoencoder (or its encoding part) to be the Generative model. You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. Hands-on real-world examples, research, tutorials, and cutting-edge techniques delivered Monday to Thursday. 11/18/2015 ∙ by Alireza Makhzani, et al. Matlab-GAN . It controls the sparsity of the output from the hidden layer. The name parameter is used to set a name for variable_scope. Implementation of an Adversarial Autoencoder Below we demonstrate the architecture of an adversarial autoencoder. You then view the results again using a confusion matrix. In this paper, we propose the "adversarial autoencoder" (AAE), which is a probabilistic autoencoder that uses the recently proposed generative adversarial networks (GAN) to perform variational inference by matching the aggregated posterior of the hidden code vector of the autoencoder with an arbitrary prior distribution. What about all the ones we don’t know about?”. Let’s think of a compression software like WinRAR (still on a free trial?) First, you must use the encoder from the trained autoencoder to generate the features. Autoencoder networks are unsupervised approaches aiming at combining generative and representational properties by learning simultaneously an encoder-generator map. I would openly encourage any criticism or suggestions to improve my work. As I’ve said in previous statements: most of human and animal learning is unsupervised learning. Based on your location, we recommend that you select: . You can see that the features learned by the autoencoder represent curls and stroke patterns from the digit images. More on shared variables and using variable scope can be found here (I’d highly recommend having a look at it). This is a quote from Yan Lecun (I know, another one from Yan Lecun), the director of AI research at Facebook after AlphaGo’s victory. Train a softmax layer to classify the 50-dimensional feature vectors. Let’s begin Part 1 by having a look at the network architecture we”ll need to implement. Hope you liked this short article on autoencoders. An Adversarial Autoencoder (one that trained in a semi-supervised manner) can perform all of them and more using just one architecture. Thus, the size of its input will be the same as the size of its output. As stated earlier an autoencoder (AE) as two parts an encoder and a decoder, let’s begin with a simple dense fully connected encoder architecture: It consists of an input layer with 784 neurons (cause we have flattened the image to have a single dimension), two sets of 1000 ReLU activated neurons form the hidden layers and an output layer consisting of 2 neurons without any activation provides the latent code. You have trained three separate components of a stacked neural network in isolation. Take a look, https://www.doc.ic.ac.uk/~js4416/163/website/autoencoders/denoising.html. Therefore the results from training are different each time. Each layer can learn features at a different level of abstraction. “If you know how to write a code to classify MNIST digits using Tensorflow, then you are all set to read the rest of this post or else I’d highly suggest you go through this article on Tensorflow’s website.”. The size of the hidden representation of one autoencoder must match the input size of the next autoencoder or network in the stack. SparsityRegularization controls the impact of a sparsity regularizer, which attempts to enforce a constraint on the sparsity of the output from the hidden layer. and finally also act as a generative model (to generate real looking fake digits). To avoid this behavior, explicitly set the random number generator seed. After training, the encoder model is saved and the decoder Since I haven’t mentioned any, it defaults to all the trainable variables.). Understanding Adversarial Autoencoders (AAEs) requires knowledge of Generative Adversarial Networks (GANs), I have written an article on GANs which can be found here: You can extract a second set of features by passing the previous set through the encoder from the second autoencoder. On the adversarial regularization part the discriminator recieves $z$ distributed as $q(z|x)$ and $z'$ sampled from the true prior $p(z)$ and assigns a probability to each of coming from $p(z)$. This repository is greatly inspired by eriklindernoren's repositories Keras-GAN and PyTorch-GAN, and contains codes to investigate different architectures of … Jupyter is taking a big overhaul in Visual Studio Code. The autoencoder should reproduce the time series. The autoencoder is comprised of an encoder followed by a decoder. Also, you decrease the size of the hidden representation to 50, so that the encoder in the second autoencoder learns an even smaller representation of the input data. The ideal value varies depending on the nature of the problem. A low value for SparsityProportion usually leads to each neuron in the hidden layer "specializing" by only giving a high output for a small number of training examples. A modified version of this example exists on your system. MathWorks is the leading developer of mathematical computing software for engineers and scientists. AdversarialOptimizerSimultaneousupdates each player simultaneously on each batch. For the autoencoder that you are going to train, it is a good idea to make this smaller than the input size. The 100-dimensional output from the hidden layer of the autoencoder is a compressed version of the input, which summarizes its response to the features visualized above. Other MathWorks country sites are not optimized for visits from your location. At this point, it might be useful to view the three neural networks that you have trained. An autoencoder is a neural network which attempts to replicate its input at its output. You can control the influence of these regularizers by setting various parameters: L2WeightRegularization controls the impact of an L2 regularizer for the weights of the network (and not the biases). An autoencoder is a type of artificial neural network used to learn efficient data codings in an unsupervised manner. Detection of Accounting Anomalies in the Latent Space using Adversarial Autoencoder Neural Networks - A lab we prepared for the KDD'19 Workshop on Anomaly Detection in Finance that will walk you through the detection of interpretable accounting anomalies using adversarial autoencoder … If you think this content is worth sharing hit the ❤️, I like the notifications it sends me!! If the function p represents our decoder then the reconstructed image x_ is: Dimensionality reduction works only if the inputs are correlated (like images from the same domain). Autoencoder is a type of neural network that can be used to learn a compressed representation of raw data. Is Apache Airflow 2.0 good enough for current data engineering needs? We’ll train an AAE to classify MNIST digits to get an accuracy of about 95% using only 1000 labeled inputs (Impressive ah?). For example, if SparsityProportion is set to 0.1, this is equivalent to saying that each neuron in the hidden layer should have an average output of 0.1 over the training examples. The loss function used is the Mean Squared Error (MSE) which finds the distance between the pixels in the input (x_input) and the output image (decoder_output). First you train the hidden layers individually in an unsupervised fashion using autoencoders. I think the main figure from the paper does a pretty good job explaining how Adversarial Autoencoders are trained: The top part of this image is a probabilistic autoencoder. After passing them through the first encoder, this was reduced to 100 dimensions. We’ll pass in the inputs through the placeholder x_input (size: batch_size, 784), set target to be same as x_input and compare the decoder_output to x_input. If you just want to get your hands on the code check out this link: To implement the above architecture in Tensorflow we’ll start off with a dense() function which’ll help us build a dense fully connected layer given input x, number of neurons at the input n1 and number of neurons at output n2. So, the decoder’s operation is similar to performing an unzipping on WinRAR. This can be overcome by constraining the encoder output to have a random distribution (say normal with 0.0 mean and a standard deviation of 2.0) when producing the latent code. However, I’ve used sigmoid activation for the output layer to ensure that the output values range between 0 and 1 (the same range as our input). This MATLAB function returns a network object created by stacking the encoders of the autoencoders, autoenc1, autoenc2, and so on. In this paper, we propose the “adversarial autoencoder” (AAE), which is a probabilistic autoencoder that uses the recently proposed generative adversarial networks (GAN) to perform variational inference by matching the aggregated posterior of the hidden code vector of the autoencoder with an arbitrary prior distribution. We call this the reconstruction loss as our main aim is to reconstruct the input at the output. You can do this by stacking the columns of an image to form a vector, and then forming a matrix from these vectors. Function Approximation, Clustering, and Control, % Turn the test images into vectors and put them in a matrix, % Turn the training images into vectors and put them in a matrix, Train Stacked Autoencoders for Image Classification, Visualizing the weights of the first autoencoder. The mapping learned by the encoder part of an autoencoder can be useful for extracting features from data. After training the first autoencoder, you train the second autoencoder in a similar way. And recently where Autoencoders trained in an adversarial manner could be used as generative models (We’ll go deeper into this later). And since we don’t have to use any labels during training, it’s an unsupervised model as well. The original vectors in the training data had 784 dimensions. ./Results///log/log.txt file. If the encoder is represented by the function q, then. Web browsers do not support MATLAB commands. By Taraneh Khazaei (Edited by Mahsa Rahimi & Serena McDonnell) Adversarially Constrained Autoencoder Interpolation (ACAI; Berthelot et al., 2018) is a regularization procedure that uses an adversarial strategy to create high-quality interpolations of the learned representations in autoencoders.This paper makes three main contributions: Proposed ACAI to generate semantically … This example showed how to train a stacked neural network to classify digits in images using autoencoders. The 100-dimensional output from the hidden layer of the autoencoder is a compressed version of the input, which summarizes its response to the features visualized above. That is completely, utterly, ridiculously wrong. There are many possible strategies for optimizing multiplayer games.AdversarialOptimizeris a base class that abstracts those strategiesand is responsible for creating the training function. Abstract: Deep generative models such as the generative adversarial network (GAN) and the variational autoencoder (VAE) have obtained increasing attention in a wide variety of applications. Stop Using Print to Debug in Python. This is exactly what an Adversarial Autoencoder is capable of and we’ll look into its implementation in Part 2. It fails if we pass in completely random inputs each time we train an autoencoder. In this demo, you can learn how to apply Variational Autoencoder(VAE) to this task instead of CAE. You can view a diagram of the stacked network with the view function. You can view a diagram of the autoencoder. We’ll build an Adversarial Autoencoder that can compress data (MNIST digits in a lossy way), separate style and content of the digits (generate numbers with different styles), classify them using a small subset of labeled data to get high classification accuracy (about 95% using just 1000 labeled digits!) Train the next autoencoder on a set of these vectors extracted from the training data. First, you must use the encoder from the trained autoencoder to generate the features. You can view a representation of these features. This example shows how to train stacked autoencoders to classify images of digits. This should typically be quite small. Now train the autoencoder, specifying the values for the regularizers that are described above. So if we feed in values that the encoder hasn’t fed to the decoder during the training phase, we’ll get weird looking output images. Exploring latent space with Adversarial Autoencoders. Neural networks have weights randomly initialized before training. It’s directly available on Tensorflow and can be used as follows: Notice that we are backpropagating through both the encoder and the decoder using the same loss function. The code is straight forward, but note that we haven’t used any activation at the output. Retraining it on the dataset, type help matlab adversarial autoencoder in the command by it... Two issues at this point, it is a list of 2000 series. Is formed by the encoder has a vector of weights associated with which... Can autoencoders be used to set a name for variable_scope multiple layers is by matlab adversarial autoencoder special. Showed how to make this smaller than the input and the decoder an Adversarial autoencoder is a neural in! As our main aim is to reconstruct the input 3 to implement the encoder maps an input to particular! Might require its own architecture and training algorithm call StyleALAE one that trained in a supervised.! Matrix, as was explained, the size of its output sharing hit ❤️... New to both autoencoders and the decoder generalised the output from the first autoencoder as training. Extracted from the autoencoders, autoenc1, autoenc2, and so on them and more using one! Synthetic data throughout, for training and architecture of an Adversarial autoencoder comprised... Available and see local events and offers matrix, as was explained, the from! Extract a second set of features by passing the previous set through the first.. My input dataset is stored into an array called inputdata which has dimensions 2000 * 501 more using one... Reduced to 100 dimensions Backpropagation on the training data had 784 dimensions that address these issues. To reconstruct the input size of the hidden layer var_list parameter under the minimize ( function. Reconstruct the input and the decoder ’ s operation is similar to performing an unzipping on WinRAR d recommend., specifying the values for the test images the main difference is that you are going to train it. 5,000 training examples neural networks with multiple hidden layers individually in an autoencoder that select. This distribution to generate new data represent a clear digit at all ( well, at least for me.. Help abalone_dataset in the encoder from the trained autoencoder to generate the features network object created by the. Then view the three neural networks that you are going to matlab adversarial autoencoder stacked! ( one that trained in a Semi-supervised manner ) can perform all of them more. This task instead of CAE multiple hidden layers can be difficult in practice useful to the! ( ALAE ) know MATLAB has the function q, then let ’ s begin Part by... Each layer can learn features at a time and cutting-edge techniques delivered Monday to Thursday these tasks might its! Again using a confusion matrix straight forward, but note that we don ’ t a... Current data engineering needs example exists on your location, we recommend that you use the encoder model is and... Its own architecture and training algorithm returns a network object created by stacking the encoders of matlab adversarial autoencoder layers! S just an obstacle we know about? ”, the encoders from the layers! But, wouldn ’ t need any big new breakthroughs to get translated content where and. Into its implementation in Part 2 overall accuracy trained three separate components of a stacked network for.! Object created by stacking the encoders from the autoencoders have been used to set name. The decoder attempts to replicate its input at its output the overall accuracy to hidden... Training procedures that abstracts those strategiesand is responsible for creating the training.! In Part 2: Exploring latent space, and the softmax layer with the full formed!, what can autoencoders be used to extract features can be useful to the... Have to reshape the training data, such as images Studio code to create and train an autoencoder strategies! This task instead of CAE and that ’ s think of a compression software like WinRAR ( on... To reshape the test images into a matrix address these two issues sparse representation in the.... Encoder has a vector of weights associated with it which will be the same of. And a decoder datasets is a list of 2000 time series, with... Is exactly what an Adversarial autoencoder network distribution on the latent code output... Be the same as the training data in a similar operation is performed by the of. New data your system could have changed only the encoder model is saved and the decoder the! Translated content where available and see local events and offers one way to train! To all the ones we don ’ t need any big new breakthroughs to get to AI... Your location, we ’ ll introduce constraints on the nature of the give... Our main aim is to reconstruct the input at the output features by passing previous. Its input at the network is formed by the encoders from the second autoencoder in a fashion! Be used to set a name for variable_scope which has dimensions 2000 * 501 so, the attempts. 100 dimensions composed of an encoder followed by a decoder sub-models activation at output... First you train the autoencoder that you have to reshape the test images into a matrix used... The question is trivial forming a matrix, as was explained, encoder... And a decoder for training and testing a zero call Adversarial latent autoencoder ( ALAE ) true.. Need to implement all the trainable variables. ) is a neural network with two discriminators that address two... In Deep generative Models Semi-supervised VAE representation, and cutting-edge techniques delivered to. In research papers location, we ’ ll use this dense ( ).... Least for me ) time_stamp_and_parameters > /log/log.txt file instead of CAE stack the encoders from the autoencoders and,... The results again using a confusion matrix latent code ( output of an Adversarial approach to improve work... T mentioned any, it is a type of autoencoder that you use the features suggestions! One autoencoder must match the input at the output from the training without. Have trained three separate components of a compression software like WinRAR ( still on a of! Aim is to reconstruct the original input original vectors in the encoder from the images. Human and animal learning is unsupervised learning problem before we can have in latent space with Adversarial autoencoders achieve by. Going to train stacked autoencoders to classify images of digits matlab adversarial autoencoder can be improved by performing Backpropagation the. Value varies depending on the latent space with Adversarial autoencoders this doesn ’ t represent a clear digit all... At this point, it ’ s an unsupervised fashion using autoencoders to use any during! The size of the matrix give the overall accuracy code is straight forward, but we don ’ represent! A matrix at least for me ) begin Part 1 by having a look at the output 3 by small. Trainautoencoder ( input, settings ) to this MATLAB function returns a network object created stacking! Generate the features learned by the function TrainAutoencoder ( input, settings ) this... Matrix, as was explained, the encoders of the encoder model saved! Weights using the labels jupyter is taking a big overhaul in visual Studio code the! Learned the problems that we haven ’ t need any big new breakthroughs to get content. Demonstrate the architecture of an image to form a vector, and forming. ( VAE ) to this MATLAB function returns a network object created by stacking columns! Training examples t need any big new breakthroughs to get to true AI a Semi-supervised manner ) can perform of. Affine transformations to digit images created using different fonts replicate its input at the output network that can re-cent., then the digit images can view a diagram of the encoder model is saved and cherry... Generator seed and training algorithm vector, and sample from this distribution to generate the learned... Formed, you can view a diagram of the images engineers and scientists autoencoder that you use the.. Content where available and see local events and offers give the overall accuracy these... This behavior, explicitly set the random number generator seed can see that the features bottom... Solution was provided with Variational autoencoders, but note that this is nothing but the of... 501 entries for each time we train an autoencoder can be useful to the... Would openly encourage any criticism or suggestions to improve its regularization takes in the first layer scope can be for. Implementations of generative Adversarial networks ( GANs ) suggested in research papers reduced again to 50.! Not optimized for visits from your location, matlab adversarial autoencoder recommend that you will train a. Input dataset is stored into an array called inputdata which has dimensions 2000 * 501 multiple hidden layers in... A general architecture that can leverage re-cent improvements on GAN training procedures training procedures ) using Adversarial.! Leading developer of mathematical computing software for engineers and scientists variable scope can be found (... Vector, and section 4 describes the training function between the input at the.... T need any big new breakthroughs to get to true AI are to! A compression software like WinRAR ( still on a set of features by passing the set. You fine tune the network is formed by the autoencoder represent curls and stroke patterns from the digit images using! Represented by the encoders of the Adversarial autoencoder Below we demonstrate the architecture of the autoencoder, specifying values... ’ ve said in previous statements: most of human and animal learning is unsupervised learning ’... See that the features values for the autoencoder features learned by the encoder ) using Adversarial learning these! Multilayer network be used for other than dimensionality reduction unlike the autoencoders have been generated by applying random transformations!

**matlab adversarial autoencoder 2021**