Equation for Logistic regression while using One Hot Encoding - machine-learning

When the features are numeric, like these:
The feature matrix X in the hypothesis sigmoid(transpose(theta).X)) will be:
However, when we have 1 more feature here - color, which can be red or blue or green, on doing One Hot Encoding each will be a vector like: [1 0 0] [0 1 0] and [0 0 1].
I'm unable to figure out how to merge these One Hot Encoding vectors to already existing feature matrix and then use it in the equation for hypothesis

Yes, you should remove all not encoded categorical features from dataset, encode them and add their encoded values from one hot encoding, also you have to add corresponding weights into theta of course. Then you can fit your new model on this new dataset

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Dimensions of LSTM variant in Deep Mind's Differentiable Neural Computer (DNC)

I'm trying to implement Deep Mind's DNC - Nature paper- with PyTorch 0.4.0.
When implementing the variant of LSTM they used I encountered some troubles with dimensions.
To simplify suppose BATCH=1.
The equations they list in the paper are these:
where [x;h] means a concatenation of x and h into one single vector, and i, f and o are column vectors.
My question is about how the state s_t is computed.
The second addendum is obtained by multiplying i with a column vector and so the result is either a scalar (transpose i first, then do scalar product) or wrong (two column vectors multiplied).
So the state results in a single scalar...
With the same reasoning the hidden state h_t is a scalar too, but it has to be a column vector.
Obviously I'm wrong somewhere, but I can't figure out where.
By looking at Wikipedia LSTM Article I think I figured it out.
This is the formal implementation of standard LSTM found in the article:
The circle represents element-by-element product.
By using this product in the corresponding parts of DNC equations (s_t and o_t) the dimensions work.

Normalization of data before activation function

I am Altering this tutorial to matlab where I am trying to classify to 1/0 class. each of my data points x is of dimension 30, that is it has 30 features. This is my first NN.
My problem is, when I try to calculate a1=np.tanh(z1) or in matlab a1 = tanh(z1); I am getting either 1 or -1 values since |z1|>2.
Should I Normalize the values?
Is there any promises I missed in the tutorial to stay within the -2 < z1 < 2 range?
Am I correct in assuming it is a problem step out of boundaries?
Input values should always be normalized, usually to the [0, 1] range. The network might not train otherwise.
Another thing that is worth noting is that you are using tanh as activation, and this function saturates at the extremes, which means zero gradient. Other activation functions like the ReLU (max(0, x)) don't have this problem. It is worth a try.

How to classify text with scikit's SVM?

I have a text classification task. By now i only tagged a corpus and extracted some features in a bigram format (i.e bigram = [('word', 'word'),...,('word', 'word')]. I would like to classify some text, as i understand SVM algorithm only can receive vectors in orther to classify, so i use some vectorizer in scikit as follows:
bigram = [ [('load', 'superior')
('point', 'medium'), ('color', 'white'),
('the load', 'tower')]]
fh = FeatureHasher(input_type='string')
X = fh.transform(((' '.join(x) for x in sample)
for sample in bigram))
print X
the output is a sparse matrix:
(0, 226456) -1.0
(0, 607603) -1.0
(0, 668514) 1.0
(0, 715910) -1.0
How can i use the previous sparse matrix X to classify with SVC?, assuming that i have 2 classes and a train and test sets.
As others have pointed out, your matrix is just a list of feature vectors for the documents in your corpus. Use these vectors as features for classification. You just need classification labels y and then you can use SVC().fit(X, y).
But... the way that you have asked this makes me think that maybe you don't have any classification labels. In this case, I think you want to be doing clustering rather than classification. You could use one of the clustering algorithms to do this. I suggest sklearn.cluster.MiniBatchKMeans to start. You can then output the top 5-10 words for each cluster and form labels from those.

Normalizing feature values for SVM

I've been playing with some SVM implementations and I am wondering - what is the best way to normalize feature values to fit into one range? (from 0 to 1)
Let's suppose I have 3 features with values in ranges of:
3 - 5.
0.02 - 0.05
10-15.
How do I convert all of those values into range of [0,1]?
What If, during training, the highest value of feature number 1 that I will encounter is 5 and after I begin to use my model on much bigger datasets, I will stumble upon values as high as 7? Then in the converted range, it would exceed 1...
How do I normalize values during training to account for the possibility of "values in the wild" exceeding the highest(or lowest) values the model "seen" during training? How will the model react to that and how I make it work properly when that happens?
Besides scaling to unit length method provided by Tim, standardization is most often used in machine learning field. Please note that when your test data comes, it makes more sense to use the mean value and standard deviation from your training samples to do this scaling. If you have a very large amount of training data, it is safe to assume they obey the normal distribution, so the possibility that new test data is out-of-range won't be that high. Refer to this post for more details.
You normalise a vector by converting it to a unit vector. This trains the SVM on the relative values of the features, not the magnitudes. The normalisation algorithm will work on vectors with any values.
To convert to a unit vector, divide each value by the length of the vector. For example, a vector of [4 0.02 12] has a length of 12.6491. The normalised vector is then [4/12.6491 0.02/12.6491 12/12.6491] = [0.316 0.0016 0.949].
If "in the wild" we encounter a vector of [400 2 1200] it will normalise to the same unit vector as above. The magnitudes of the features is "cancelled out" by the normalisation and we are left with relative values between 0 and 1.

OpenCV + HOG +SVM: help needed with SVM single feature vector

I try to implement a people detecting system based on SVM and HOG using OpenCV2.3. But I got stucked.
I came this far:
I can compute HOG values from an image database and then I calculate with LIBSVM the SVM vectors, so I get e.g. 1419 SVM vectors with 3780 values each.
OpenCV just wants one feature vector in the method hog.setSVMDetector(). Therefore I have to calculate one feature vector from my 1419 SVM vectors, that LIBSVM has calculated.
I found one hint, how to calculate this single feature vector: link
“The detecting feature vector at component i (where i is in the range e.g. 0-3779) is built out of the sum of the support vectors at i * the alpha value of that support vector, e.g.
det[i] = sum_j (sv_j[i] * alpha[j]) , where j is the number of the support vector, i
is the number of the components of the support vector.”
According to this, my routine works this way:
I take the first element of my first SVM vector, multiply it with the alpha value and add it with the first element of the second SVM vector that has been multiplied with alpha value, …
But after summing up all 1419 elements I get quite high values:
16.0657, -0.351117, 2.73681, 17.5677, -8.10134,
11.0206, -13.4837, -2.84614, 16.796, 15.0564,
8.19778, -0.7101, 5.25691, -9.53694, 23.9357,
If you compare them, to the default vector in the OpenCV sample peopledetect.cpp (and hog.cpp in the OpenCV source)
0.05359386f, -0.14721455f, -0.05532170f, 0.05077307f,
0.11547081f, -0.04268804f, 0.04635834f, -0.05468199f, 0.08232084f,
0.10424068f, -0.02294518f, 0.01108519f, 0.01378693f, 0.11193510f,
0.01268418f, 0.08528346f, -0.06309239f, 0.13054633f, 0.08100729f,
-0.05209739f, -0.04315529f, 0.09341384f, 0.11035026f, -0.07596218f,
-0.05517511f, -0.04465296f, 0.02947334f, 0.04555536f,
you see, that the default vector values are in the boundaries between –1 and +1, but my values exceed them far.
I think, my single feature vector routine needs some adjustment, any ideas?
Regards,
Christoph
The aggregated vector's values do look high.
I used the loadSVMfromModelFile() located in http://lnx.mangaitalia.net/trainer/main.cpp
I had to remove svinstr.sync(); from the code since it caused losing parts of the lines and getting wrong results.
I don't know much about the rest of the file, I only used this function.

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