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Comparisons of two unsupervised machine learning applications using PCA, ICA, and NMF.

We used these three algorithms for two interesting applications: Blind Source Separation (Cocktail Party Problem) and Hand-written Digit Recognition.

Blind source separation (cocktail party problem)

Imagine yourself at a cocktail party, and Haley is telling a boring story. You are much more interested in the gossip that Alex is telling Sam, so you tune out Alex and focus on Sam’s words. Congratulations: you have just demonstrated the human ability to solve the “cocktail party problem” — to pick out one thread of speech from the babble of two or more people. Here, we use machine learning techniques to achieve this goal. In this example, we have four different mixtures of four different sounds (CNN new material, Bach’s Symphony, Finnish Song and Pop Song Breakeven), mimicking the effect of having four microphones at four different places in a room (The number of mixtures should be equal to or greater than the number of sound sources for these algorithms to work). We feed this mixed data matrix (8 components in total, two channels for each audio file) into ICA, and the four components with the largest singular values corresponds to the four components we are looking for. The waveforms are plotted below. There’s little noise in the background, but it’s still very identifiable. PCA and NMF, however, only pick out one component.

Source waveforms

sources

Recovered waveforms using fastica

_ICA

Another extended interesting feature: If we have two different mixtures of the two channels in a song, ICA will be able to extract the background music from a song (think karaoke).

Hand-written digit recognition

Have you ever thought about how USPS handles millions of mails each day? Obviously it will be great pain and tremendous work if postmen have to identify the postcodes people scribble manually and sort them into different bins. Their solution is to scan the handwritten addresses and utilize machine learning techniques to achieve automatic sorting. Here we ask our algorithms to learn the most significant features of digit 8. The dataset contains 542 samples. Here's some example digits in the dataset: dataset1

and the first eight components given by PCA, ICA and NMF: comp_8

The interpretation for these components is as follows: the first component captures the most significant feature of digit 8, meaning that most of the 8 in the dataset have this feature (looks like this), while the succeeding ones gives the second most significant feature etc. We see that NMF picks out the most significant features of 8 in its first component, compared to ICA and NMF. It is a little hard to characterize the result besides just looking at it. If we do have labels (supervised learning), and turn this into a classification problem in which we may have more than one digits, the result can be more accurately characterized in terms of training error/test error.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
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cm
tijani
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A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
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Can you compute that for me. Ty
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what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Adjanou
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A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
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you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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Maurice Reply
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answer
Magreth
progressive wave
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
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Who can show me the full solution in this problem?
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Source:  OpenStax, Elec 301 projects fall 2013. OpenStax CNX. Sep 14, 2014 Download for free at http://legacy.cnx.org/content/col11709/1.1
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