Maxpooling is a technique I read about it here https://computersciencewiki.org/index.php/Max-pooling_/_Pooling. I understand, that it is used to approximate the input. Which is to reduce the time a neural network may spend working on it. What I can't pinpoint is, why should it select the max values? is that effective? if so why?. Other options could be like selecting mean, or min, or maybe the top left values(for instance).
We select max of window to take the pixel which is most activated (more activation of a pixel means more information).
There are variations like avg-pooling to take the mean of all pixels of a window, but in practice there is not a lot of difference in the results.
Max-Pooling is effective and fast. Another reason to use max-pool over avg-pool is computing the gradient (in the backprop) will be fast for max-pooling.
Related
I am trying to implement a binary classifier using logistic regression for data drawn from 2 point sets (classes y (-1, 1)). As seen below, we can use the parameter a to prevent overfitting.
Now I am not sure, how to choose the "good" value for a.
Another thing I am not sure about is how to choose a "good" convergence criterion for this sort of problem.
Value of 'a'
Choosing "good" things is a sort of meta-regression: pick any value for a that seems reasonable. Run the regression. Try again with a values larger and smaller by a factor of 3. If either works better than the original, try another factor of 3 in that direction -- but round it from 9x to 10x for readability.
You get the idea ... play with it until you get in the right range. Unless you're really trying to optimize the result, you probably won't need to narrow it down much closer than that factor of 3.
Data Set Partition
ML folks have spent a lot of words analysing the best split. The optimal split depends very much on your data space. As a global heuristic, use half or a bit more for training; of the rest, no more than half should be used for testing, the rest for validation. For instance, 50:20:30 is a viable approximation for train:test:validate.
Again, you get to play with this somewhat ... except that any true test of the error rate would be entirely new data.
Convergence
This depends very much on the characteristics of your empirical error space near the best solution, as well as near local regions of low gradient.
The first consideration is to choose an error function that is likely to be convex and have no flattish regions. The second is to get some feeling for the magnitude of the gradient in the region of a desired solution (normalizing your data will help with this); use this to help choose the convergence radius; you might want to play with that 3x scaling here, too. The final one is to play with the learning rate, so that it's scaled to the normalized data.
Does any of this help?
Is there anything faster than sliding window? I tried sort of binary search with overlapping rectangles - it kinda works but sometimes cuts off part of the blob (expected, right) - see the video in http://juick.com/lurker/2142051
Binary search makes no sense, because it is an algorithm for searching for specific values in a sorted structure.
Unless you have some apriori knowledge about the image, you need to check all possible locations, which is the sliding window method you suggested.
Chris is correct, unless you can say something about the statistics of the surrounding regions, e.g., "certain arrangements of pixels around the spot I'm looking for are unlikely". Note, this is different from saying "will never happen", and any algorithm based on statistical approaches will have an associated probability of (wrong box found).
If you think the statistics of the larger regions around your desired location might be informative, you might be able to do some block-processing on larger blocks before doing the fine-level sliding window. For example, if you can say with high probability that a certain 64 x 64 region doesn't contain the max, then, you can throw out a lot of [64 x 64] pixel regions, with 32 pixel overlap using (maybe) only a few features.
You can train something like AdaBoost to do this. See the classic Viola-Jones work which does this for face-detection http://en.wikipedia.org/wiki/Viola%E2%80%93Jones_object_detection_framework
If you absolutely need the maxima location, then like Chris said, you need to search everywhere.
Im using GPUImage in my project and I need an efficient way of taking the column sums. Naive way would obviously be retrieving the raw data and adding values of every column. Can anybody suggest a faster way for that?
One way to do this would be to use the approach I take with the GPUImageAverageColor class (as described in this answer), only instead of reducing the total size of each frame at each step, only do this for one dimension of the image.
The average color filter determines the average color of the overall image by stepping down in a factor of four in both X and Y, averaging 16 pixels into one at each step. If operating in a single direction, you should be able to use hardware interpolation to get an 18X reduction in a single direction per step with good performance. Your final step might either require a quick CPU-based iteration on the much smaller image or a tweaked version of this shader that pulls the last few pixels in a column together into the final result pixel for that column.
You notice that I've been talking about averaging here, because the output values for any OpenGL ES operation will need to be in terms of colors, which only have a 0-255 range per channel. A sum will easily overflow this, but you could use an average as an approximation of your sum, with a more limited dynamic range.
If you only care about one color channel, you could possibly encode a larger value into the RGBA channels and maintain a 32-bit sum that way.
Beyond what I describe above, you could look at performing this sum with the help of the Accelerate framework. While probably not quite as fast as doing a shader-based reduction, it might be good enough for your needs.
I'm trying to read through PCA and saw that the objective was to maximize the variance. I don't quite understand why. Any explanation of other related topics would be helpful
Variance is a measure of the "variability" of the data you have. Potentially the number of components is infinite (actually, after numerization it is at most equal to the rank of the matrix, as #jazibjamil pointed out), so you want to "squeeze" the most information in each component of the finite set you build.
If, to exaggerate, you were to select a single principal component, you would want it to account for the most variability possible: hence the search for maximum variance, so that the one component collects the most "uniqueness" from the data set.
Note that PCA does not actually increase the variance of your data. Rather, it rotates the data set in such a way as to align the directions in which it is spread out the most with the principal axes. This enables you to remove those dimensions along which the data is almost flat. This decreases the dimensionality of the data while keeping the variance (or spread) among the points as close to the original as possible.
Maximizing the component vector variances is the same as maximizing the 'uniqueness' of those vectors. Thus you're vectors are as distant from each other as possible. That way if you only use the first N component vectors you're going to capture more space with highly varying vectors than with like vectors. Think about what Principal Component actually means.
Take for example a situation where you have 2 lines that are orthogonal in a 3D space. You can capture the environment much more completely with those orthogonal lines than 2 lines that are parallel (or nearly parallel). When applied to very high dimensional states using very few vectors, this becomes a much more important relationship among the vectors to maintain. In a linear algebra sense you want independent rows to be produced by PCA, otherwise some of those rows will be redundant.
See this PDF from Princeton's CS Department for a basic explanation.
max variance is basically setting these axis that occupy the maximum spread of the datapoints, why? because the direction of this axis is what really matters as it kinda explains correlations and later on we will compress/project the points along those axis to get rid of some dimensions
Trying to write some code that deals with this task:
As an starting point, I have around 20 "profiles" (imagine a landscape profile), i.e. one-dimensional arrays of around 1000 real values.
Each profile has a real-valued desired outcome, the "effective height".
The effective height is some sort of average but height, width and position of peaks play a particular role.
My aim is to generalize from the input data so as to calculate the effective height for further profiles.
Is there a machine learning algorithm or principle that could help?
Principle 1: Extract the most import features, instead of feeding it everything
As you said, "The effective height is some sort of average but height, width and position of peaks play a particular role." So that you have a strong priori assumption that these measures are the most important for learning. If I were you, I would calculate these measures at first, and use them as the input for learning, instead of the raw data.
Principle 2: While choosing a learning algorithm, the first thing to care about would be the the linear separability
Suppose the height is a function of those measures, then you have to think about that to what extent the function is linear. For example if the function is almost linear, then a very simple Perceptron would be perfect. Otherwise if it's far from linear, you might want to pick up a multiple-layer neural network. If it's far far far from linear....please turn to principle 1, and check out if you are extracting the right features.
Principle 3: More data help
As you said, you have around 20 "profiles" for training. In general speaking, that's not enough. Almost all of the machine learning algorithms were designed for somehow big data. Even they claimed that their algorithm is good at learning small sample, but usually not as small as 20. Get more data!
Maybe multivariate linear regression suffices?
I would probably use a combination of what you said about which features play the most important role, and then train a regression on that. Basically, you need at least one coefficient corresponding to each feature, and you need substantially more data points than coefficients. So, I would pick something like the heights and width of the two biggest peaks. You've now reduced every profile to just 4 numbers. Now do this trick: divide the data into 5 groups of 4. Pick the first 4 groups. Reduce all those profiles to 4 numbers, and then use the desired outcomes to come up with a regression. Once you have trained the regression, try your technique on the last 4 points and see how well it works. Repeat this procedure 5 times, each time leaving out a different set of data. This is called cross-validation, and it's very handy.
Obviously getting more data would help.