A Two Dimensional Visualization Right So I Took V1 and V2 and I Showed You a Two Dimensional Visualization in Christopher Allah's Blog Right So While PCA Is PC Has Its Own Applications There Lots Of Techniques So You Might Say Why Are We Learning Piece Lean Right What About Other Techniques PCA You're Calling It Very Simple And You're Saying This Knee Is One Of The State-of-the-Art One Of The Best Are There Other Techniques In Between Yes There Are Techniques Like Multi-Dimensional Scaling Salmon Mapping And There Are Also Graph Based Techniques Which

These techniques graph based techniques all these techniques have been developed over the last 20 or so years almost the last 20 years while these techniques are very important we said it's important because in this course we are trying to cover the techniques which are most used in the industry right so that's why we chose to cover pca and disney by the way Disney's is a very very young technique it was the actual paper 40 steam was published in 2008 by by a phenomenal group of researchers called Lawrence and Geoffrey Hinton Geoffrey Hinton is by the way the Godfather of modern deep learning a phenomenal researcher anyway we'll learn more about Geoffrey intense contributions when we learn deep deep networks and when we learn about neural networks and deep learning okay so this is this is this is like today we are in 2017 so this is slightly under 10 years old technique and it's it's really really state-of-the-art the mathematics behind it are also fairly advanced now as far as TC is concerned this is state of the art so we are not covering MDA Simon mapping graph based techniques etcetera because we believe that TCE can do better than most of these techniques in most cases I'm not saying these techniques do not have applications but this Lee will do a pretty good job or very very comparable job to other techniques and hence we are covering PC and testing in a dimensional reduction sections now you might ask okay what is the what is so special about Disney by the way Disney works very well for visualization which means if you are given D dimensional data I can map this to 2d or 3d data okay using teach knee and the visualization that I get from the visualization that I get after tea-stained 2d are terrific they're really really beautiful really really clean and very easy to understand what's happening now you might ask how is the Slee very different at a very very intuitive level what is what is the fundamental difference between TV and pc of course we'll understand it much better when we learn the internals of T of piece T but let me give you a one one key point here imagine if if I have a data set like this right we saw this data set when we realized that when we read this is one type of data set where okay suppose if I have a data set like this okay it says you might have a data set like this this is feature 1 and feature two what what is my my my key my V one we'll be in this direction if I'm trying to project data from two d-21b right this is a cluster of points this is a cluster of points right so what happened so we saw this as one of the limitations of PCA right so what happens when I try to when I try to project all the data to v1 these two sets of points will now get projected onto a small on the same area and we lose the information that they will well separated clusters of points or groups of points right

So in a nutshell PC is trying to preserve the global shape of data okay deeper so PCA tries to preserve tries to preserve the global shape of data the global shape or structure of data so you might say okay your colleague at global structure because this is this is it's trying to preserve all the it's because variance maximization is a form of global shape or structure but there is also local structure here right what is the local structure mean local structure means that okay this point is closer to this point and this point is closer to this point so all these points are close to each other right TC sorry PCA doesn't doesn't care about distances between points it cares about the direction which maximizes variance okay we'll understand more about global structure preservation and local structure preservation when we learn the internals of TCE in the next few videos but just at high level just just keep in mind that PCA preserves global structure verity Snee can choose to preserve no construction I can also make tasty preserve global structure by just changing one parameter okay so in a nutshell tea still preserves the local structure said okay these points are close to each other and hence we will see that we will see that just bear with me this is a high level point that I'm making here I'll explain these details of global structure preservation and local structure preservation with detailed examples in the next few videos

"WEBVTTKind: captionsLanguage: enso one of the most powerful and state of the art techniques for dimensionality reduction is called TC I've used this term multiple times and I told you that will cover this technique so T stands for the T in T distributed s in stochastic in a neighborhood in ham building so this is the T s and E okay this saw this name might sound like like like like very very crazy and very technical don't worry we'll understand what this is very very easy it's a very very intuitively geometrically elegant solution for dimensional reduction and this is literally one of the state of the art or one of one of the best state of the art or one of the best dimensional reduction techniques that we have especially for visualization so especially for visualization of data this is probably one of the best techniques we have so we did learn PCA right a while ago in the previous videos PC is a very very basic fairly old technique right we saw we saw in the case of feminists that PCA was not doing really good job except for zero so we saw in the case of M nest data that it was not doing a very very good job in in separating out all the digits when when I was trying to do a two dimensional visualization right so I took I took v1 and v2 and I showed you a two dimensional visualization in in Christopher Allah's blog right so while PCA is PC has its own applications there lots of techniques so you might say why are we learning piece lean right what about other techniques PCA you're calling it very simple and you're saying this knee is one of the state-of-the-art one of the best are there other techniques in between yes there are techniques like multi-dimensional scaling salmon mapping and there are also graph based techniques which which all these techniques graph based techniques all these techniques have been developed over the last 20 or so years almost the last 20 years while these techniques are very important we said it's important because in this course we are trying to cover the techniques which are most used in the industry right so that's why we chose to cover pca and disney by the way Disney's is a very very young technique it was the actual paper 40 steam was published in 2008 by by a phenomenal group of researchers called Lawrence and Geoffrey Hinton Geoffrey Hinton is by the way the Godfather of modern deep learning a phenomenal researcher anyway we'll learn more about Geoffrey intense contributions when we learn deep deep networks and when we learn about neural networks and deep learning okay so this is this is this is like today we are in 2017 so this is slightly under 10 years old technique and it's it's really really state-of-the-art the mathematics behind it are also fairly advanced now as far as TC is concerned this is state of the art so we are not covering MDA Simon mapping graph based techniques etcetera because we believe that TCE can do better than most of these techniques in most cases I'm not saying these techniques do not have applications but this Lee will do a pretty good job or very very comparable job to other techniques and hence we are covering PC and testing in a dimensional reduction sections now you might ask okay what is the what is so special about Disney by the way Disney works very well for visualization which means if you are given D dimensional data I can map this to 2d or 3d data okay using teach knee and the visualization that I get from the visualization that I get after tea-stained 2d are terrific they're really really beautiful really really clean and very easy to understand what's happening now you might ask how is the Slee very different at a very very intuitive level what is what is the fundamental difference between TV and pc of course we'll understand it much better when we learn the internals of T of piece T but let me give you a one one key point here imagine if if I have a data set like this right we saw this data set when we realized that when we read this is one type of data set where okay suppose if I have a data set like this okay it says you might have a data set like this this is feature 1 and feature two what what is my my my key my V one we'll be in this direction if I'm trying to project data from two d-21b right this is a cluster of points this is a cluster of points right so what happened so we saw this as one of the limitations of PCA right so what happens when I try to when I try to project all the data to v1 these two sets of points will now get projected onto a small on the same area and we lose the information that they will well separated clusters of points or groups of points right so in a nutshell PC is trying to preserve the global shape of data okay deeper so PCA tries to preserve tries to preserve the global shape of data the global shape or structure of data so you might say okay your colleague at global structure because this is this is it's trying to preserve all the it's because variance maximization is a form of global shape or structure but there is also local structure here right what is the local structure mean local structure means that okay this point is closer to this point and this point is closer to this point so all these points are close to each other right TC sorry PCA doesn't doesn't care about distances between points it cares about the direction which maximizes variance okay we'll understand more about global structure preservation and local structure preservation when we learn the internals of TC in the next few videos but just at high level just just keep in mind that PCA preserves global structure Verity Snee can choose to preserve no construction I can also make tasty preserve global structure by just changing one parameter okay so in a nutshell tea still preserves the local structure said okay these points are close to each other and hence we will see that we will see that just bear with me this is a high level point that I'm making here I'll explain these details of global structure preservation and local structure preservation with detailed examples in the next few videosso one of the most powerful and state of the art techniques for dimensionality reduction is called TC I've used this term multiple times and I told you that will cover this technique so T stands for the T in T distributed s in stochastic in a neighborhood in ham building so this is the T s and E okay this saw this name might sound like like like like very very crazy and very technical don't worry we'll understand what this is very very easy it's a very very intuitively geometrically elegant solution for dimensional reduction and this is literally one of the state of the art or one of one of the best state of the art or one of the best dimensional reduction techniques that we have especially for visualization so especially for visualization of data this is probably one of the best techniques we have so we did learn PCA right a while ago in the previous videos PC is a very very basic fairly old technique right we saw we saw in the case of feminists that PCA was not doing really good job except for zero so we saw in the case of M nest data that it was not doing a very very good job in in separating out all the digits when when I was trying to do a two dimensional visualization right so I took I took v1 and v2 and I showed you a two dimensional visualization in in Christopher Allah's blog right so while PCA is PC has its own applications there lots of techniques so you might say why are we learning piece lean right what about other techniques PCA you're calling it very simple and you're saying this knee is one of the state-of-the-art one of the best are there other techniques in between yes there are techniques like multi-dimensional scaling salmon mapping and there are also graph based techniques which which all these techniques graph based techniques all these techniques have been developed over the last 20 or so years almost the last 20 years while these techniques are very important we said it's important because in this course we are trying to cover the techniques which are most used in the industry right so that's why we chose to cover pca and disney by the way Disney's is a very very young technique it was the actual paper 40 steam was published in 2008 by by a phenomenal group of researchers called Lawrence and Geoffrey Hinton Geoffrey Hinton is by the way the Godfather of modern deep learning a phenomenal researcher anyway we'll learn more about Geoffrey intense contributions when we learn deep deep networks and when we learn about neural networks and deep learning okay so this is this is this is like today we are in 2017 so this is slightly under 10 years old technique and it's it's really really state-of-the-art the mathematics behind it are also fairly advanced now as far as TC is concerned this is state of the art so we are not covering MDA Simon mapping graph based techniques etcetera because we believe that TCE can do better than most of these techniques in most cases I'm not saying these techniques do not have applications but this Lee will do a pretty good job or very very comparable job to other techniques and hence we are covering PC and testing in a dimensional reduction sections now you might ask okay what is the what is so special about Disney by the way Disney works very well for visualization which means if you are given D dimensional data I can map this to 2d or 3d data okay using teach knee and the visualization that I get from the visualization that I get after tea-stained 2d are terrific they're really really beautiful really really clean and very easy to understand what's happening now you might ask how is the Slee very different at a very very intuitive level what is what is the fundamental difference between TV and pc of course we'll understand it much better when we learn the internals of T of piece T but let me give you a one one key point here imagine if if I have a data set like this right we saw this data set when we realized that when we read this is one type of data set where okay suppose if I have a data set like this okay it says you might have a data set like this this is feature 1 and feature two what what is my my my key my V one we'll be in this direction if I'm trying to project data from two d-21b right this is a cluster of points this is a cluster of points right so what happened so we saw this as one of the limitations of PCA right so what happens when I try to when I try to project all the data to v1 these two sets of points will now get projected onto a small on the same area and we lose the information that they will well separated clusters of points or groups of points right so in a nutshell PC is trying to preserve the global shape of data okay deeper so PCA tries to preserve tries to preserve the global shape of data the global shape or structure of data so you might say okay your colleague at global structure because this is this is it's trying to preserve all the it's because variance maximization is a form of global shape or structure but there is also local structure here right what is the local structure mean local structure means that okay this point is closer to this point and this point is closer to this point so all these points are close to each other right TC sorry PCA doesn't doesn't care about distances between points it cares about the direction which maximizes variance okay we'll understand more about global structure preservation and local structure preservation when we learn the internals of TC in the next few videos but just at high level just just keep in mind that PCA preserves global structure Verity Snee can choose to preserve no construction I can also make tasty preserve global structure by just changing one parameter okay so in a nutshell tea still preserves the local structure said okay these points are close to each other and hence we will see that we will see that just bear with me this is a high level point that I'm making here I'll explain these details of global structure preservation and local structure preservation with detailed examples in the next few videos\n"