In classification problem, we can adjust soft margin to make things easier. However, in some cases, especially in real-world data collections, the classification problem can be extremely hard because of the noise introduced. In 2D space, the following graph can be obtained:
We can easily conclude that these two classes of data can not be classified. However, usually the features of data can be huge, which can not be plot in 2D or 3D space. I also tried TSNE to visualize the classified data. But since TSNE uses KL to train, while SVM uses loss function, I can not get anything from the following picture.
where the green ones are true positive, blue ones are false negative, yellow ones are false positive, black ones are true negative.
So my question is: is there a scientific method that can be used to analyse whether a problem can be classified or not?
Related
I'm going through CS231n to understand the basics of neural networks.
Attached is the slide in which Justin (the tutor) gives the reasoning for why data preprocessing is required and I don't completely understand. The explanation given is similar to the one given on the slide and I don't get it. The slide is below.
The second question I have is: is it actually normalisation or standardisation? This link implies that it is standardisation, whereas the course material says it is normalisation.
Any help will be appreciated.
A) The meaning of "less sensitive to small changes in weights" can easily be visualized. Imagine to operate a little change in the weights of the drawn hyperplane, i.e. rotate it a bit. If the samples are located around the origin, you'll notice that they can still be correctly classified. If they're far away from the origin, the same little change in weights will lead to bigger misclassifications.
B) Sometimes standardization and normalization are used interchangeably.
Standardization: I quote from Machine Learning and Pattern Recognition by Bishop : "For the purposes of this example, we have made a linear re-scaling of the data, known as standardizing, such that each of the variables has zero mean and unit standard deviation."
Normalization could be e.g. min-max normalization when you scale all feature values to the [0,1] range, or feature vector normalization when you divide the feature vector by its modulus.
I'm interested in taking advantage of some partially labeled data that I have in a deep learning task. I'm using a fully convolutional approach, not sampling patches from the labeled regions.
I have masks that outline regions of definite positive examples in an image, but the unmasked regions in the images are not necessarily negative - they may be positive. Does anyone know of a way to incorporate this type of class in a deep learning setting?
Triplet/contrastive loss seems like it may be the way to go, but I'm not sure how to accommodate the "fuzzy" or ambiguous negative/positive space.
Try label smoothing as described in section 7.5.1 of Deep Learning book:
We can assume that for some small constant eps, the training set label y is correct with probability 1 - eps, and otherwise any of the other possible labels might be correct.
Label smoothing regularizes a model based on a softmax with k output values by replacing the hard 0 and 1 classification targets with targets of eps / k and 1 - (k - 1) / k * eps, respectively.
See my question about implementing label smoothing in Pandas.
Otherwise if you know for sure, that some areas are negative, other are positive while some are uncertain, then you can introduce a third uncertain class. I have worked with data sets that contained uncertain class, which corresponded to samples that could belong to any of the available classes.
I'm assuming that you are struggling with a data segmantation task with a problem of a ill-definied background (e.g. you are not sure if all examples are correctly labeled). Recently I came across the similiar problem and this is what I came across during my research:
In old days before deep learning and at the begining of deep learning era - the common way to deal with that is to smooth your output with some kind of a probability model which would take into account the possibility of a noisy labels (you could read about this in a Learning to Label from Noisy Data chapter from this book. It's important to discriminate this probabilistic models from models used to smooth your labels w.r.t. to image or label structure like classical CRFs for bilateral smoothing.
What we finally used (and worked really well) is the Channel Inhibited Softmax idea from this paper. In terms of a mathematical properties - it makes your network much more robust to some objects not labeled - because it makes your network to output much higher positive valued logits at correctly labeled objects.
You could treat this as a semi-supervised problem. Use the full dataset without labels to train a bottleneck autoencoder structure (or a GAN approach). This pretrained model can then be adjusted (e.g. removing the last layers, adding a better layer structure at the end on top of the bottleneck features) and finetuned on the labeled data.
I have features with 18 dimensions after doing feature selection and will be used to train classifier, RNN, HMM, etc.
The features contain stddev, mean and derivative of accelerometer and gyroscope.
These features have different units and normalization/standardization will lose the true meaning of features.
For example, the unit of one feature vector is rotational velocity (degree/sec), the value in that feature is between -120 and 120.
Another is stddev of acceleration of x-axis, the value is mainly between 0 and 2.
If I want to do standardization, all the feature vectors will be centered near 0, with negative/positive values spread around zero. --> Even the stddev will have negative values! It totally loses actual meaning?
Am I on the wrong track? Any information is appreciated! Thanks!
It is always strongly recomendated to perform feature scaling and normalization as preprocessing step, and it will even benefit gradient descent(the most common learning algorithm),even in your case it would be useful but if you are in doubt you can perform cross validation. For example when using images and neural networks, sometimes after normalization the features(pixels) get negative values, that doesnt make the training data to lose meaning.
I have been doing reading about Self Organizing Maps, and I understand the Algorithm(I think), however something still eludes me.
How do you interpret the trained network?
How would you then actually use it for say, a classification task(once you have done the clustering with your training data)?
All of the material I seem to find(printed and digital) focuses on the training of the Algorithm. I believe I may be missing something crucial.
Regards
SOMs are mainly a dimensionality reduction algorithm, not a classification tool. They are used for the dimensionality reduction just like PCA and similar methods (as once trained, you can check which neuron is activated by your input and use this neuron's position as the value), the only actual difference is their ability to preserve a given topology of output representation.
So what is SOM actually producing is a mapping from your input space X to the reduced space Y (the most common is a 2d lattice, making Y a 2 dimensional space). To perform actual classification you should transform your data through this mapping, and run some other, classificational model (SVM, Neural Network, Decision Tree, etc.).
In other words - SOMs are used for finding other representation of the data. Representation, which is easy for further analyzis by humans (as it is mostly 2dimensional and can be plotted), and very easy for any further classification models. This is a great method of visualizing highly dimensional data, analyzing "what is going on", how are some classes grouped geometricaly, etc.. But they should not be confused with other neural models like artificial neural networks or even growing neural gas (which is a very similar concept, yet giving a direct data clustering) as they serve a different purpose.
Of course one can use SOMs directly for the classification, but this is a modification of the original idea, which requires other data representation, and in general, it does not work that well as using some other classifier on top of it.
EDIT
There are at least few ways of visualizing the trained SOM:
one can render the SOM's neurons as points in the input space, with edges connecting the topologicaly close ones (this is possible only if the input space has small number of dimensions, like 2-3)
display data classes on the SOM's topology - if your data is labeled with some numbers {1,..k}, we can bind some k colors to them, for binary case let us consider blue and red. Next, for each data point we calculate its corresponding neuron in the SOM and add this label's color to the neuron. Once all data have been processed, we plot the SOM's neurons, each with its original position in the topology, with the color being some agregate (eg. mean) of colors assigned to it. This approach, if we use some simple topology like 2d grid, gives us a nice low-dimensional representation of data. In the following image, subimages from the third one to the end are the results of such visualization, where red color means label 1("yes" answer) andbluemeans label2` ("no" answer)
onc can also visualize the inter-neuron distances by calculating how far away are each connected neurons and plotting it on the SOM's map (second subimage in the above visualization)
one can cluster the neuron's positions with some clustering algorithm (like K-means) and visualize the clusters ids as colors (first subimage)
How exactly is an U-matrix constructed in order to visualise a self-organizing-map? More specifically, suppose that I have an output grid of 3x3 nodes (that have already been trained), how do I construct a U-matrix from this? You can e.g. assume that the neurons (and inputs) have dimension 4.
I have found several resources on the web, but they are not clear or they are contradictory. For example, the original paper is full of typos.
A U-matrix is a visual representation of the distances between neurons in the input data dimension space. Namely you calculate the distance between adjacent neurons, using their trained vector. If your input dimension was 4, then each neuron in the trained map also corresponds to a 4-dimensional vector. Let's say you have a 3x3 hexagonal map.
The U-matrix will be a 5x5 matrix with interpolated elements for each connection between two neurons like this
The {x,y} elements are the distance between neuron x and y, and the values in {x} elements are the mean of the surrounding values. For example, {4,5} = distance(4,5) and {4} = mean({1,4}, {2,4}, {4,5}, {4,7}). For the calculation of the distance you use the trained 4-dimensional vector of each neuron and the distance formula that you used for the training of the map (usually Euclidian distance). So, the values of the U-matrix are only numbers (not vectors). Then you can assign a light gray colour to the largest of these values and a dark gray to the smallest and the other values to corresponding shades of gray. You can use these colours to paint the cells of the U-matrix and have a visualized representation of the distances between neurons.
Have also a look at this web article.
The original paper cited in the question states:
A naive application of Kohonen's algorithm, although preserving the topology of the input data is not able to show clusters inherent in the input data.
Firstly, that's true, secondly, it is a deep mis-understanding of the SOM, thirdly it is also a mis-understanding of the purpose of calculating the SOM.
Just take the RGB color space as an example: are there 3 colors (RGB), or 6 (RGBCMY), or 8 (+BW), or more? How would you define that independent of the purpose, ie inherent in the data itself?
My recommendation would be not to use maximum likelihood estimators of cluster boundaries at all - not even such primitive ones as the U-Matrix -, because the underlying argument is already flawed. No matter which method you then use to determine the cluster, you would inherit that flaw. More precisely, the determination of cluster boundaries is not interesting at all, and it is loosing information regarding the true intention of building a SOM. So, why do we build SOM's from data?
Let us start with some basics:
Any SOM is a representative model of a data space, for it reduces the dimensionality of the latter. For it is a model it can be used as a diagnostic as well as a predictive tool. Yet, both cases are not justified by some universal objectivity. Instead, models are deeply dependent on the purpose and the accepted associated risk for errors.
Let us assume for a moment the U-Matrix (or similar) would be reasonable. So we determine some clusters on the map. It is not only an issue how to justify the criterion for it (outside of the purpose itself), it is also problematic because any further calculation destroys some information (it is a model about a model).
The only interesting thing on a SOM is the accuracy itself viz the classification error, not some estimation of it. Thus, the estimation of the model in terms of validation and robustness is the only thing that is interesting.
Any prediction has a purpose and the acceptance of the prediction is a function of the accuracy, which in turn can be expressed by the classification error. Note that the classification error can be determined for 2-class models as well as for multi-class models. If you don't have a purpose, you should not do anything with your data.
Inversely, the concept of "number of clusters" is completely dependent on the criterion "allowed divergence within clusters", so it is masking the most important thing of the structure of the data. It is also dependent on the risk and the risk structure (in terms of type I/II errors) you are willing to take.
So, how could we determine the number classes on a SOM? If there is no exterior apriori reasoning available, the only feasible way would be an a-posteriori check of the goodness-of-fit. On a given SOM, impose different numbers of classes and measure the deviations in terms of mis-classification cost, then choose (subjectively) the most pleasing one (using some fancy heuristics, like Occam's razor)
Taken together, the U-matrix is pretending objectivity where no objectivity can be. It is a serious misunderstanding of modeling altogether.
IMHO it is one of the greatest advantages of the SOM that all the parameters implied by it are accessible and open for being parameterized. Approaches like the U-matrix destroy just that, by disregarding this transparency and closing it again with opaque statistical reasoning.