跟读练习: Introduction to Diminsionality Reduction (a.k.a. Manifold Learning) - 通过YouTube学习英语口语
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Hi everyone, my name is Bing Breton and I'm a professor at the University of Washington in Seattle.
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Hi everyone, my name is Bing Breton and I'm a professor at the University of Washington in Seattle.
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In this next series of lectures we're going to be talking about one of my favorite topics, nonlinear dimensionality reduction, sometimes also known as manifold learning.
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So what is this field about?
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What is actually a manifold?
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We're going to be breaking it down and going through some of the most popular ways of performing nonlinear dimensionality reduction.
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We're also going to be giving some examples
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and talking about different ways in which you can
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and also cannot use manifold learning as a tool in your work
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so the basic tenant of manifold learning and non-linear dimensionality reduction is
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that even if you have really really big
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and complicated data patterns do in fact exist in the data we believe this to be true
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because you know after all
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if the patterns don't exist why are we bothering to collect this data in the first place
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so we believe um as a as a starting point
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that patterns exist in complicated data so we have to to believe this.
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Now, when we're talking about dimensionality reduction, part of the problem is that we have to be able to visualize the data.
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Now, I and hopefully most of you are humans who are constrained to walk around in this three-dimensional world.
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And a lot of what my visual intuition is in two dimensions, so things that can be done on a piece of paper
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or at least on a computer screen and so
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if i have data that is higher than two or three dimensional
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and that's most data sets we have a the next video is going to be all about examples
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and intuition about high dimensional data sets what we have a problem
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which is that the data is there
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and the patterns do exist the data we believe to be true i can't actually see it
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and for me because i'm a really visual person i like seeing the data
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so a lot of the challenge in manifold learning is figuring out what the the patterns actually are
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so that we can actually see it and gain some intuition for data.
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So I found these rare earth magnets in my office and it's one of my favorite office toys to play with.
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So I brought them as a prop to show you what kind of high dimensional data might look like.
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So let's say your data is like this little ball of little magnets here.
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It's roughly a smash into a little ball.
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And so in order to describe all of the data sets on this little ball, you kind of need all three dimensions because we exist in a three dimensional world.
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Now on the other hand, let's say your data looked more like something that I smashed up into this little ribbon here.
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Okay, now if your data looks more like this, okay, where it's a little ribbon, what you can see here is that even though this toy,
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just like the other toy, exists in three-dimensional world, it is in in fact, lying on a surface.
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Okay?
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Now, the surface could be a flat surface, like you can describe it by a plane.
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All right, so we call this in linear algebra subspace because it's planar and it's flat.
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And that's great because you can use linear dimensionality reduction techniques to describe this plane.
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So I can rotate it however I want in three-dimensional space.
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It's still kind of on a plane, and I can describe that plane.
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This is a simpler way of describing my data.
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The problem becomes if the plane becomes warped of some kind.
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So let's say I can make a little bracelet out of it, and now it's a little ring, okay?
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Or maybe it's not connected, and it's just kind of curvy like this, okay?
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This does not fundamentally change the fact
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that all of the data points on my little toy are still on a flat-ish surface.
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I can flatten it, it's locally flat, just like the surface of the Earth is locally flat, this Earth that we all walk on.
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But if you zoom out and look at it, you can see that you actually do need three-dimensional to describe the data set,
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but locally, it's lying on this flat-ish curved surface.
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That's kind of roughly speaking, if I'm waving my hands around, what a manifold is.
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It's a description of something that is approximately flat, if you look closely enough, but globally, it might be curved.
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And so if I can learn what this curved surface is, then I'm able to describe my data much more simply
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by describing the curve and then figuring out where my data points are on this curve
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without having to use all three dimensions.
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Now, the idea here is that we need to be able to reduce and visualize the data.
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So here's like a physical prop of visualizing my data set.
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Most data sets are not something that you can play with as a desk toy.
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And so the goal of Manifold Learning is to reduce the data.
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We need to reduce and visualize the data.
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We want to reduce it because we suspect that patterns do in fact exist, so we can describe it more simply.
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And we want to visualize it because humans are really intuitive visual creatures.
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And so when we can see something, we believe in it and we can actually see patterns in it that wouldn't have been obvious otherwise.
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And the reason we want to do this is because we want to gain intuition.
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And we want to communicate to ourselves
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and to each other about what we've actually got is one
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of the most compact ways of communicating your data is being able to make a really compelling visualization.
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Now, the trick here with dimensionality reduction and manifold learning is how do we do this, right?
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How do we actually pick out patterns that exist in the data set and reduce and visualize them?
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So it turns out that, hopefully I can demonstrate again with this little toy here, it has to do with this notion of what's actually close, like what's similar to each other.
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Like, am I similar to my cousin more than some random person on the street?
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Probably.
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But, like, how do you define that?
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So let's say that we have this curved surface here, okay, my little toy.
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And you can see that it's lying on this flattish surface, this curved surface.
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And so two neighboring points are on the surface, are close to each other because they're actually touching each other.
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They're close to each other, right?
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So we kind of want to say that if we're going to reduce the dimensionality of my data set here, my little ring, my little bracelet I've made,
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I want the points that are closer in the original data set to also end up closer in my reduced learned manifold,
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in my reduced dimensionality space.
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And points that are farther apart should also end up farther apart in my reduced space, so that I haven't lost information.
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So things that used to be similar should actually be similar should end up closer together in my reduced space.
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And things that are farther apart, less similar, should also end up less similar and less farther apart in my reduced space.
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The problem then becomes, how do I actually define that?
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So how do you actually compute distances in high dimensional spaces?
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And what is the most compact way of doing it?
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What's the most convenient way of doing it?
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These are decisions we have to make.
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So part of what we're going to be learning in the
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next couple of lectures are common ways to defining distances and similarity.
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So the punchline here is that there's no one right way of doing it.
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This is a decision that one makes, and I'm gonna tell you about some of the most common ways of doing it
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that seems to work well for different types of datasets, and how do you make these kinds of decisions.
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And then also, what do we mean by more similar?
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Like all similarities, are they all equally important?
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So for example here, I can compute kind of like, grid size distances between any of these two points on my dataset here, okay?
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But you can kind of see that the data sets over here are close in physical 3D space, in this studio space, to the points over here, right?
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Because they're actually really close to each other.
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Is that the same?
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Does that matter as much as the fact that you actually have to go?
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They're not actually connected.
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They're not actually touching each other as little magnets.
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Does that matter?
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Because you had to count connected magnets, you'd have to go all the way up here to get to the other side.
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And is that notion of distance more important than the fact that as the fly flies, you can get right over there.
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These are all valid notions of similarity and distance, but are they all equally important in the context of manifold learning?
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That's something that we're going to be talking about.
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And then this idea of points that start out closer together should end up close together.
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Well, what does ending up close together mean?
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How do we interpret the fact that we end up with some kind of visualization of a beautiful manifold?
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And can we actually interpret two points
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that are closer together in the manifold space as being actually more similar in an interpretable, meaningful, engineering relevant way.
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This is something that we'll discuss as well
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because it is variously different depending on the algorithm you use and also on your notion of distance.
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So we're going to dig right into it in the next lecture.
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But I'm going to leave you with the idea that manifolds are everywhere.
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We're going to do some manifold explaining right now.
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But there's no one right way of doing manifold learning.
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We're going to start by looking at some linear methods first
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and trying to draw connections between our notions of similarity
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and distance with some linear algebra and some linear dimensionality reductions
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that you've already heard about earlier in the series
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and then we're going to generalize these concepts to talk about non-linear dimensionality reduction with some examples and to build some intuitions.
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为什么与此视频练习口语？
通过与这段视频进行口语练习，学习者不仅能够提升自己的语言表达能力，还可以在非线性维度缩减这一复杂主题上，培养自己的理解和思维能力。视频中的讲解者以清晰的示范和实例，深入浅出地介绍了数据可视化和模式识别的概念，因此观看并跟读视频内容，有助于提高英语听力与口语的流利度。在这样的情境下练习，学习者能够潜移默化地提高语言应用能力，特别是涉及到专业词汇和表达时。使用“英语影子跟读”的技巧，重复讲者的语句，可以帮助增强记忆，同时也能提升语音语调的准确性。
语法与表达在语境中的运用
- 非线性维度缩减 (nonlinear dimensionality reduction)：这一术语表达了数据处理中的关键概念，学习者可以通过反复练习这种专业名词，提高在数据科学领域的英语水平。
- 描述所有的数据集 (describe all of the data sets)：这个句子结构强调了讲者如何清晰阐述复杂概念的方法，对提高英语表达能力十分重要。
- 数据的模式确实存在 (patterns do exist in the data)：这一表达强化了讲者传递信息的逻辑性，学习者可以模仿这种结构，提升自身的逻辑表达能力。
常见发音陷阱
在这段视频中，某些英语单词可能会对刚学习者造成发音上的困难。例如，“dimensionality”这个词对于非母语者来说尤为复杂，建议反复听取讲者的发音并尝试模仿。此外，词汇“manifold”在不同口音中可能有所不同，熟悉其发音可以帮助学习者在不同语境中更自如地使用。通过“看YouTube学英语”和进行“shadow speak”练习，学习者可以克服这些发音的挑战，提高发音的准确性和自信心。
什么是跟读法？
跟读法 (Shadowing) 是一种有科学依据的语言学习技巧，最初开发用于专业口译员的培训，并由多语言者Alexander Arguelles博士普及。这个方法简单而强大：您在听英语母语原声的同时立即大声重复——就像是一个延迟1-2秒紧跟说话者的影子。与被动听力或语法练习不同，跟读法强迫您的大脑和口腔肌肉同时处理并模仿真实的讲话模式。研究表明它能显着提高发音准确性，语调，节奏，连读，听力理解和口语流利度——使其成为雅思口语备考和真实英语交流最有效的方法之一。