I recently implemented a simple Perceptron. This type of perceptron (composed of only one neuron giving binary information in output) can only solve problems where classes can be linearly separable.
I would like to implement a simple shape recognition in images of 8 by 8 pixels. I would like for example my neural network to be able to tell me if what I drawn is a circle, or not.
How to know if this problem has classes being linearly separable ? Because there is 64 inputs, can it still be linearly separable ? Can a simple perceptron solve this kind of problem ? If not, what kind of perceptron can ? I am a bit confused about that.
Thank you !
This problem, in a general sense, can not be solved by a single layer perception. In general other network structures such as convolutional neural networks are best for solving image classification problems, however given the small size of your images a multilayer perception may be sufficient.
Most problems are linearly separable, but not necessarily in 2 dimensions. Adding extra layers to a network allows it to transform data in higher dimensions so that it is linearly separable.
Look into multilayer perceptrons or convolutional neural networks. Examples of classification on the MNIST dataset might be helpful as well.
Related
I'm working on a (high energy physics related) problem using CNNs.
For understanding the problem, let's consider these examples here.
The left-hand side is the input to the CNN, the right-hand side the desired output. So the network is supposed to cluster the input. The actual algorithm behind this clustering (i.e. how we got the desired output for training) is really complex and we want the CNN to learn this.
I've tried different CNN architectures, for example one similar to the U-net architecture (https://arxiv.org/abs/1505.04597) but also various concatenations of convolutional layers, etc.
The outputs are always really similar (for all architectures).
Here you can see some CNN predictions.
In principle the network is performing quite well, but as you can see, in most cases the CNN output consists of several filled pixels that are directly next to each other, which will never (!) happen in the true cases.
I've been using mean squared error as the loss function in all of the networks.
Do you have any suggestions how one could avoid this problem and improve the networks performance?
Or is this a general limitation to CNNs and in practice it is not possible to solve such a problem using CNNs?
Thank you very much!
My suggestion would be to split up the work. First use a U-Shaped NN to find the activations in a binary segmentation task (like in your paper) and then regress on the found activations to find their final values. In my experience this works way better than doing regression on large images, because the MSE will result in blurry outputs, as you have observed.
The CNN does not know that you wanted a sharp result. As mentioned by #Thomas, MSE tends to give you blurry result as it is the nature of that loss function. Giving a blurry result does not introduce large loss in MSE.
An easy modification would be to use L1 Loss (absolute difference instead of squared error). It has a constant gradient unlike MSE whose gradient decreases with error.
If you really wanted a sharp result, it would be easier to add a manual step -- non maximum suppression (NMS). In practice, a 3x3 box-max filter might do.
Thank you for viewing my question. I'm trying to do image classification based on some pre-trained models, the images should be classified to 40 classes. I want to use VGG and Xception pre-trained model to convert each image to two 1000-dimensions vectors and stack them to a 1*2000 dimensions vector as the input of my network and the network has an 40 dimensions output. The network has 2 hidden layers, one with 1024 neurons and the other one has 512 neurons.
Structure:
image-> vgg(1*1000 dimensions), xception(1*1000 dimensions)->(1*2000 dimensions) as input -> 1024 neurons -> 512 neurons -> 40 dimension output -> softmax
However, using this structure I can only achieve about 30% accuracy. So my question is that how could I optimize the structure of my networks to achieve higher accuracy? I'm new to deep learning so I'm not quiet sure my current design is 'correct'. I'm really looking forward to your advice
I'm not entirely sure I understand your network architecture, but some pieces don't look right to me.
There are two major transfer learning scenarios:
ConvNet as fixed feature extractor. Take a pretrained network (any of VGG and Xception will do, do not need both), remove the last fully-connected layer (this layer’s outputs are the 1000 class scores for a different task like ImageNet), then treat the rest of the ConvNet as a fixed feature extractor for the new dataset. For example, in an AlexNet, this would compute a 4096-D vector for every image that contains the activations of the hidden layer immediately before the classifier. Once you extract the 4096-D codes for all images, train a linear classifier (e.g. Linear SVM or Softmax classifier) for the new dataset.
Tip #1: take only one pretrained network.
Tip #2: no need for multiple hidden layers for your own classifier.
Fine-tuning the ConvNet. The second strategy is to not only replace and retrain the classifier on top of the ConvNet on the new dataset, but to also fine-tune the weights of the pretrained network by continuing the backpropagation. It is possible to fine-tune all the layers of the ConvNet, or it’s possible to keep some of the earlier layers fixed (due to overfitting concerns) and only fine-tune some higher-level portion of the network. This is motivated by the observation that the earlier features of a ConvNet contain more generic features (e.g. edge detectors or color blob detectors) that should be useful to many tasks, but later layers of the ConvNet becomes progressively more specific to the details of the classes contained in the original dataset.
Tip #3: keep the early pretrained layers fixed.
Tip #4: use a small learning rate for fine-tuning because you don't want to distort other pretrained layers too quickly and too much.
This architecture much more resembled the ones I saw that solve the same problem and has higher chances to hit high accuracy.
There are couple of steps you may try when the model is not fitting well:
Increase training time and decrease learning rate. It may be stopping at very bad local optima.
Add additional layers that can extract specific features for the large number of classes.
Create multiple two-class deep networks for each class ('yes' or 'no' output class). This will let each network be more specialized for each class, rather than training one single network to learn all 40 classes.
Increase training samples.
In a convolutional net (CNN), someone answered to me than filters are initialized randomly.
I'm ok for this, but, when there is the gradient descent, who is learning? The features maps, or the filters ?
My intuition is the filters are learning, because they need to recognize complex things.
But I would like to be sure about this.
In the context of convolutional neural networks, kernel = filter = feature detector.
Here is a great illustration from Stanford's deep learning tutorial (also nicely explained by Denny Britz).
The filter is the yellow sliding window, and its value is:
The feature map is the pink matrix. Its value depends on both the filter and the image: as a result, it doesn't make sense to learn the feature map. Only the filter is learnt when the network is trained. The network may have other weights to be trained as well.
As aleju said, filters weights are learned. Feature maps are outputs of the convolutional layers. Besides convolutional filter weights, there are also weights of fully connected (and other types) layers.
I think I read somewhere that convolutional neural networks do not suffer from the vanishing gradient problem as much as standard sigmoid neural networks with increasing number of layers. But I have not been able to find a 'why'.
Does it truly not suffer from the problem or am I wrong and it depends on the activation function?
[I have been using Rectified Linear Units, so I have never tested the Sigmoid Units for Convolutional Neural Networks]
Convolutional neural networks (like standard sigmoid neural networks) do suffer from the vanishing gradient problem. The most recommended approaches to overcome the vanishing gradient problem are:
Layerwise pre-training
Choice of the activation function
You may see that the state-of-the-art deep neural network for computer vision problem (like the ImageNet winners) have used convolutional layers as the first few layers of the their network, but it is not the key for solving the vanishing gradient. The key is usually training the network greedily layer by layer. Using convolutional layers have several other important benefits of course. Especially in vision problems when the input size is large (the pixels of an image), using convolutional layers for the first layers are recommended because they have fewer parameters than fully-connected layers and you don't end up with billions of parameters for the first layer (which will make your network prone to overfitting).
However, it has been shown (like this paper) for several tasks that using Rectified linear units alleviates the problem of vanishing gradients (as oppose to conventional sigmoid functions).
Recent advances had alleviate the effects of vanishing gradients in deep neural networks. Among contributing advances include:
Usage of GPU for training deep neural networks
Usage of better activation functions. (At this point rectified linear units (ReLU) seems to work the best.)
With these advances, deep neural networks can be trained even without layerwise pretraining.
Source:
http://devblogs.nvidia.com/parallelforall/deep-learning-nutshell-history-training/
we do not use Sigmoid and Tanh as Activation functions which causes vanishing Gradient Problems. Mostly nowadays we use RELU based activation functions in training a Deep Neural Network Model to avoid such complications and improve the accuracy.
It’s because the gradient or slope of RELU activation if it’s over 0, is 1. Sigmoid derivative has a maximum slope of .25, which means that during the backward pass, you are multiplying gradients with values less than 1, and if you have more and more layers, you are multiplying it with values less than 1, making gradients smaller and smaller. RELU activation solves this by having a gradient slope of 1, so during backpropagation, there isn’t gradients passed back that are progressively getting smaller and smaller. but instead they are staying the same, which is how RELU solves the vanishing gradient problem.
One thing to note about RELU however is that if you have a value less than 0, that neuron is dead, and the gradient passed back is 0, meaning that during backpropagation, you will have 0 gradient being passed back if you had a value less than 0.
An alternative is Leaky RELU, which gives some gradient for values less than 0.
The first answer is from 2015 and a bit of age.
Today, CNNs typically also use batchnorm - while there is some debate why this helps: the inventors mention covariate shift: https://arxiv.org/abs/1502.03167
There are other theories like smoothing the loss landscape: https://arxiv.org/abs/1805.11604
Either way, it is a method that helps to deal significantly with vanishing/exploding gradient problem that is also relevant for CNNs. In CNNs you also apply the chain rule to get gradients. That is the update of the first layer is proportional to the product of N numbers, where N is the number of inputs. It is very likely that this number is either relatively big or small compared to the update of the last layer. This might be seen by looking at the variance of a product of random variables that quickly grows the more variables are being multiplied: https://stats.stackexchange.com/questions/52646/variance-of-product-of-multiple-random-variables
For recurrent networks that have long sequences of inputs, ie. of length L, the situation is often worse than for CNN, since there the product consists of L numbers. Often the sequence length L in a RNN is much larger than the number of layers N in a CNN.
I would like to implement a Picture Classification using Neural Network. I want to know the way to select the Features from the Picture and the number of Hidden units or Layers to go with.
For now i have an idea of changing the size of image to some 50x50 or smaller so that the number of Features are less and that all inputs have constant size.The features would be RGB value of each of the pixels.Will it be fine or there is some other better way?
Also i decided to go with 1 Hidden Layer with half the number of units as in Inputs. I can change the number to get better results. Or would i require more layers ?
There are numerous image data sets that are successfully learned by neural networks, like
MNIST (here you will find many links to papers)
NORB
and CIFAR-10/100.
Not that you need many training examples. Usually one hidden layer is sufficient. But it can be hard to determine the "right" number of neurons. Sometimes the number of hidden neurons should even be greater than the number of inputs. When you use 2 or more hidden layer you will usually need less hidden nodes and the training will be faster. But when you have to many hidden layers it can be difficult to train the weights in the first layer.
A kind of neural network that is designed especially for images are convolutional neural networks. They usually work much better than multilayer perceptrons and are much faster.
50x50 image features matrix is 2500 features with RGB values. Your neural network may memorize this but most probably will perform poorly on other images.
Therefore this type of problem is more about image-processing , feature extraction. Your features will change according to your requirements. See this similar question about image processing and neural networks
1 layer network will only be suitable for linear problems, are you sure your problem is linear? Otherwise you will need multi layer neural network