Develop Reference

Using neural network in data analysis

I am trying to build an application which would take in
an array of [time pressure]. Say about 200 of them to be filled.
And i have several more constants such as
- Viscosity
- density
- volume
- area
Outputs would be about 3 of them.
Would it be possible to use neural network (Either encog/accord.net) to feed in
the time-pressure data and the constants with the expected outputs,
so that the program would be able to estimate the outputs based
on a different time-pressure data and different constant values?

Every application in data mining is different, but a great place to start is with weka. it has a Java and C# API and its dead easy to apply different machine learning algorithms. Many researchers in my old research team have used this really sucessfully in the past.
Defining your features, using only discrimative features and cleaning any noise your feature set is the first place to start as the algorithms will only work with a good feature set. The first step to good data mining is preprocessing of the data.

Need an audio analysis library to create real time feedback from audio file?

Real-time is not necessarily required, however I am creating a game for my final year project and I wish to use the power of audio to create dynamic levels based solely on a music track that is playing. I aim to create this game for the PS Vita using playstation mobile and C#, but if i want i can switch to C++ and PSP.
I can use a WAV file, and hopefully extract the amplitude of the waveform, as well as calculating other characteristics like average frequency and approximate BPM from this data to create a level.
I have no qualms about trying to work with this raw data, I just want to know a way I can actually GET that information first. If i can extract the samples and assertain different characteristics of these samples, I can store them and work out changes in loudness, pitch and more to create notes etc.
I am using C#, but if at all possible i can either use p/invoke or switch my project to another device that uses C++ instead of C#.
I'm panicking a bit here, cos I really am a bit stumped.
Many thanks guys.

Unfortunately i don't think you'll be able to use C# to do this - AFAIK, there is no JIT compiler for it. I remember reading about something for Mono, which would make it available to use with C#, but i'm not sure right now.
That said - i would go with c++. If you go that way, you can make use of a vast amount of audio analysis libraries, like CLAM (http://clam-project.org/).
Don't panic (imagine big, friendly letters.) Envision the necessary parts for the project step by step, tackle one by one, and you'll be done in no time. =)

The problem you describe here is one of music/audio feature extraction and a substantial body of academic work exists that you can draw on. Another useful term of art with which to search is Music Information Retrieval (MIR).
The list of 'features' that researchers have attempted to retrieve from recordings is large and varied, from deterministic things such as pitch and key through emotional characteristics, such as 'energy'.
Most of these turn out to be more difficult than you might imagine, and typically only about 60-70% accurate - although for your requirements, this is probably adequate.
A good entry point might be download Sonic Visualiser, for which a large number of feature extraction plug-ins exist, and are open-source. You'll at least get a feel for what's possible.
Update: Another useful term of art is Onset detection - this is typically used to describe beat detection algorithms.

Aubio is a C/C++ library that does pitch tracking, onset detection and bpm tracking, among other things.
As for "extracting the amplitude of the waveform", the waveform is amplitude, i.e., you could just pick the audio sample with the greatest absolute value every n samples and use that value to do the "amplitude" part of the visualization.
Here's some code that might help you get started reading WAVE data in C#.
Here's some information about writing a C# wrapper for the FFTW library.

Accord.NET to estimate Muliple Regression HMM model

The Accord.NET Project Home (http://code.google.com/p/accord/) contains examples of creating, training, and evaluating Hidden Markov Models based on sequences of one-variable observations. I'd like to do the same, but with sequences of many variables. I'm envisioning a multiple regression structure with a dependent variable and multiple independent variables. I want to be able estimate an HMM where the output includes estimated intercepts and coefficients for each state, along with a transition probability matrix. An example is time-varying betas for stock returns. e.g. ret(IBM) = intercept + b1*ret(Index) + b2*ret(SectorETF) + error, but where intercept, b1, and b2 are state-dependent.
Marcelo Perlin offers exactly this functionality in his MS_Regress package for Matlab. However, I want this functionality in C#. So, any help would be greatly appreciated on either (1) using Accord.NET libraries to estimate a multiple regression HMM model, (2) translating Marcelo Perlin's package into C#, or (3) other ideas on how to achieve my goal.
Thank you!

The Accord.NET Framework supports multidimensional features as well. You can specify any probability distribution to use in the states by using generics, and there is also an example available in the documentation.
If you have, for example, two-dimensional observation vectors, and choose to assume multidimensional model assuming Gaussian emission densities, you could use:
// Assume a Normal distribution for two-dimensional samples.
var density = new MultivariateNormalDistribution(dimension: 2);
// Create a continuous hidden Markov Model with two states organized in a forward
// topology and an underlying multivariate Normal distribution as emission density.
var model = new HiddenMarkovModel<MultivariateNormalDistribution>(new Forward(2), density);
and then you can learn the model using the generic versions of the usual Baum-Welch, Viterbi or Maximum Likelihood learners.
However, what the framework unfortunately still doesn't support is the exact regression form you mentioned. But it looks very interesting. Perhaps it could be added to the framework somewhere in the future. If you wish, please leave it as a suggestion together with some references and papers in the Issue Tracker of the project. It would seems like a very useful addition.

Creating a DSP system from scratch

I love electronic music and I am interested in how it all ticks.
I've found lots of helpful questions on Stack Overflow on libraries that can be used to play with audio, filters etc. But what I am really curious about is what is actually hapening: how is the data being passed between effects and oscillators? I have done research into the mathematical side of dsp and I've got that end of the problem sussed but I am unsure what buffering system to use etc. The final goal is to have a simple object heirarchy of effects and oscillators that pass the data between each other (maybe using multithreading if I don't end up pulling out all my hair trying to implement it). It's not going to be the next Propellerhead Reason but I am interested in how it all works and this is more of an exercise than something that will yeild an end product.
At the moment I use .net and C# and I have recently learnt F# (which may or may not lead to some interesting ways of handling the data) but if these are not suitable for the job I can learn another system if necessary.
The question is: what is the best way to get the large amounts of signal data through the program using buffers? For instance would I be better off using a Queue, Array,Linked List etc? Should I make the samples immutable and create a new set of data each time I apply an effect to the system or just edit the values in the buffer? Shoud I have a dispatcher/thread pool style object that organises passing data or should the effect functions pass data directly between each other?
Thanks.
EDIT: another related question is how would I then use the windows API to play this array? I don't really want to use DirectShow because Microsoft has pretty much left it to die now
EDIT2: thanks for all the answers. After looking at all the technologies I will either use XNA 4(I spent a while trawling the internet and found this site which explains how to do it) or NAudio to output the music... not sure which one yet, depends on how advanced the system ends up being. When C# 5.0 comes out I will use its async capabilities to create an effects architecture on top of that. I've pretty much used everybody's answer equally so now I have a conundrum of who to give the bounty to...

Have you looked at VST.NET (http://vstnet.codeplex.com/)? It's a library to write VST using C# and it has some examples. You can also consider writing a VST, so that your code can be used from any host application (but even if you don't want, looking at their code can be useful).
Signal data is usually big and requires a lot of processing. Do not use a linked list! Most libraries I know simply use an array to put all the audio data (after all, that's what the sound card expect).
From a VST.NET sample:
public override void Process(VstAudioBuffer[] inChannels, VstAudioBuffer[] outChannels)
{
VstAudioBuffer audioChannel = outChannels[0];
for (int n = 0; n < audioChannel.SampleCount; n++)
{
audioChannel[n] = Delay.ProcessSample(inChannels[0][n]);
}
}
The audioChannel is a wrapper around an unmanaged float* buffer.
You probably store your samples in an immutable array. Then, when you want to play them, you copy the data in the output buffer (change the frequency if you want) and perform effects in this buffer. Note you can use several output buffers (or channels) and sum them at the end.
Edit
I know two low-level ways to play your array: DirectSound and WaveOut from Windows API. C# Example using DirectSound. C# example with WaveOut. However, you might prefer use an external higher-level library, like NAudio. NAudio is convenient for .NET audio manipulation - see this blog post for sending a sine wave to the audio card. You can see they are also using an array of float, which is what I recommend (if you do your computations using bytes, you'll end up with a lot of aliasing in the sound).

F# is probably a good choice here, as it's well fitted to manipulate functions. Functions are probably good building blocks for signal creation and processing.
F# is also good at manipulating collections in general, and arrays in particular, thanks to the higher-order functions in the Array module.
These qualities make F# popular in the finance sector and are also useful for signal processing, I would guess.
Visual F# 2010 for Technical Computing has a section dedicated to Fourier Transform, which could be relevant to what you want to do. I guess there is plenty of free information about the transform on the net, though.
Finally, to play samples, you can use XNA. I think the latest version of the API (4.0) also allows recording, but I have never used that. There is a famous music editing app for the Xbox called ezmuse+ Hamst3r Edition that uses XNA, so it's definitely possible.

With respect to buffering and asynchrony/threading/synchronization issues I suggest you to take a look at the new TPL Data Flow library. With its block primitives, concurrent data structures, data flow networks, async message prcessing, and TPL's Task based abstraction (that can be used with the async/await C# 5 features), it's a very good fit for this type of applications.

I don't know if this is really what you're looking for, but this was one of my personal projects while in college. I didn't truly understand how sound and DSP worked until I implemented it myself. I was trying to get as close to the speaker as possible, so I did it using only libsndfile, to handle the file format intricacies for me.
Basically, my first project was to create a large array of doubles, fill it with a sine wave, then use sf_writef_double() to write that array to a file to create something that I could play, and see the result in a waveform editor.
Next, I added another function in between the sine call, and the write call, to add an effect.
This way you start playing with very low-level oscillators and effects, and you can see the results immediately. Plus, it's very little code to get something like this working.
Personally, I would start with the simplest possible solution you can, then slowly add on. Try just writing out to a file and using your audio player to play it, so you don't have to deal with the audio apis. Just use a single array to start, and modify-in-place. Definitely start off single-threaded. As your project grows, you can start moving to other solutions, like pipes instead of the array, multi-threading it, or working with the audio API.
If you're wanting to create a project you can ship, depending on exactly what it is, you'll probably have to move to more complex libraries, like some real-time audio processing. But the basics you learn by doing the simple way above will definitely help when you get to this point.
Good luck!

I've done quite a bit of real-time DSP, although not with audio. While either of your ideas (immutable buffer) vs (mutable buffer modified in place) could work, what I prefer to do is create a single permanent buffer for each link in the signal path. Most effects don't lend themselves well to modification in place, since each input sample affects multiple output samples. The buffer-for-each-link technique works especially well when you have resampling stages.
Here, when samples arrive, the first buffer is overwritten. Then the first filter reads the new data from its input buffer (the first buffer) and writes to its output (the second buffer). Then it invokes the second stage to read from the second buffer and write into the third.
This pattern completely eliminates dynamic allocation, allows each stage to keep a variable amount of history (since effects need some memory), and is very flexible as far as enabling rearranging the filters in the path.

Alright, I'll have a stab at the bounty as well then :)
I'm actually in a very similar situation. I've been making electronic music for ages, but only over the past couple of years I've started exploring actual audio processing.
You mention that you have researched the maths. I think that's crucial. I'm currently fighting my way through Ken Steiglitz' A Digital Signal Processing Primer - With Applications to Digital Audio and Computer Music. If you don't know your complex numbers and phasors it's going to be very difficult.
I'm a Linux guy so I've started writing LADSPA plugins in C. I think it's good to start at that basic level, to really understand what's going on. If I was on Windows I'd download the VST SDK from Steinberg and write a quick proof of concept plugin that just adds noise or whatever.
Another benefit of choosing a framework like VST or LADSPA is that you can immediately use your plugins in your normal audio suite. The satisfaction of applying your first home-built plugin to an audio track is unbeatable. Plus, you will be able to share your plugins with other musicians.
There are probably ways to do this in C#/F#, but I would recommend C++ if you plan to write VST plugins, just to avoid any unnecessary overhead. That seems to be the industry standard.
In terms of buffering, I've been using circular buffers (a good article here: http://www.dspguide.com/ch28/2.htm). A good exercise is to implement a finite response filter (what Steiglitz refers to as a feedforward filter) - these rely on buffering and are quite fun to play around with.
I've got a repo on Github with a few very basic LADSPA plugins. The architectural difference aside, they could potentially be useful for someone writing VST plugins as well. https://github.com/andreasjansson/my_ladspa_plugins
Another good source of example code is the CSound project. There's tonnes of DSP code in there, and the software is aimed primarily at musicians.

Start with reading this and this.
This will give you idea on WHAT you have to do.
Then, learn DirectShow architecture - and learn HOW not to do it, but try to create your simplified version of it.

You could have a look at BYOND. It is an environment for programmatic audio / midi instrument and effect creation in C#. It is available as standalone and as VST instru and effect.
FULL DISCLOSURE I am the developer of BYOND.

.NET Neural Network or AI for Future Predictions

I am looking for some kind of intelligent (I was thinking AI or Neural network) library that I can feed a list of historical data and this will predict the next sequence of outputs.
As an example I would like to feed the library the following figures 1,2,3,4,5
and based on this, it should predict the next sequence is 6,7,8,9,10 etc.
The inputs will be a lot more complex and contain much more information.
This will be used in a C# application.
If you have any recommendations or warning that will be great.
Thanks
EDIT
What I am trying to do i using historical sales data, predict what amount a specific client is most likely going to spend in the next period.
I do understand that there are dozens of external factors that can influence a clients purchases but for now I need to merely base it on the sales history and then plot a graph showing past sales and predicted sales.

If you're looking for a .NET API, then I would recommend you try AForge.NET http://code.google.com/p/aforge/
If you just want to try various machine learning algorithms on a data set that you have at your disposal, then I would recommend that you play around with Weka; it's (relatively) easy to use and it implements a lot of ML/AI algorithms. Run multiple runs with different settings for each algorithm and try as many algorithms as you can. Most of them will have some predictive power and if you combine the right ones, then you might really get something useful.

If I understand your question correctly, you want to approximate and extrapolate an unknown function. In your example, you know the function values
f(0) = 1
f(1) = 2
f(2) = 3
f(3) = 4
f(4) = 5
A good approximation for these points would be f(x) = x+1, and that would yield f(5) = 6... as expected. The problem is, you can't solve this without knowledge about the function you want to extrapolate: Is it linear? Is it a polynomial? Is it smooth? Is it (approximately or exactly) cyclic? What is the range and domain of the function? The more you know about the function you want to extrapolate, the better your predictions will be.

I just have a warning, sorry. =)
Mathematically, there is no reason for your sequence above to be followed by a "6". I can easily give you a simple function, whose next value is any value you like. Its just that humans like simple rules, and therefore tend to see a connection in these sequences, that in reality is not there. Therefore, this is a impossible task for a computer, if you do not want to feed it with additional information.
Edit:
In the case that you suspect your data to have a known functional dependence, and there are uncontrollable outside factors, maybe regression analysis will have good results. To start easy, look at linear regression first.
If you cannot assume linear dependence, there is a nice application that looks for functions fitting your historical data... I'll update this post with its name as soon as I remember. =)