WEBVTT 00:00:00.000 --> 00:00:03.799 Imagine holding an apple in your hand, like right 00:00:03.799 --> 00:00:06.919 now. You can instantly see its height, its width, 00:00:07.280 --> 00:00:09.800 its depth. Great. You can rotate it. Exactly. 00:00:09.880 --> 00:00:12.220 You just turn it around, judge its weight, and 00:00:12.220 --> 00:00:14.519 understand its physical shape in the real world. 00:00:14.900 --> 00:00:18.399 And your brain, it evolved to do this flawlessly. 00:00:18.640 --> 00:00:20.260 Yeah, it's highly specialized for three -dimensional 00:00:20.260 --> 00:00:23.620 space. But what if I asked you to visualize an 00:00:23.620 --> 00:00:28.160 apple that exists in, like, a thousand dimensions 00:00:28.160 --> 00:00:30.699 at the exact same time. You, I mean, you physically 00:00:30.699 --> 00:00:32.960 cannot do it. Right. The human brain just hits 00:00:32.960 --> 00:00:35.799 a biological brick wall there. We're completely 00:00:35.799 --> 00:00:38.380 trapped in our default operating system of, you 00:00:38.380 --> 00:00:40.759 know, up, down, left, right, forward, and backward. 00:00:40.820 --> 00:00:43.119 And that is a massive problem when you step into 00:00:43.119 --> 00:00:46.479 the world of modern data. Because today, we're 00:00:46.479 --> 00:00:49.780 generating datasets where a single object doesn't 00:00:49.780 --> 00:00:53.950 just have three properties. It has hundreds or 00:00:53.950 --> 00:00:56.270 even thousands of variables attached to it all 00:00:56.270 --> 00:00:58.570 at once. It really is the ultimate cognitive 00:00:58.570 --> 00:01:00.369 bottleneck of our era because we've built these 00:01:00.369 --> 00:01:02.250 machines that can easily collect and process 00:01:02.250 --> 00:01:04.909 thousands of dimensions of information, but we 00:01:04.909 --> 00:01:07.769 can't see it. Exactly. If human beings cannot 00:01:07.769 --> 00:01:10.129 actually see those relationships, we can't intuitively 00:01:10.129 --> 00:01:13.030 understand them. So we're just left staring at 00:01:13.030 --> 00:01:15.840 these giant spreadsheets of numbers. completely 00:01:15.840 --> 00:01:19.500 blind to the hidden structures inside, we desperately 00:01:19.500 --> 00:01:22.120 need a bridge between that mathematical complexity 00:01:22.120 --> 00:01:24.760 of the data and, well, the visual limitations 00:01:24.760 --> 00:01:27.219 of our own minds. Which brings us to the mission 00:01:27.219 --> 00:01:30.219 of our deep dive today. We are looking at a really 00:01:30.219 --> 00:01:32.879 dense, highly technical set of source materials 00:01:32.879 --> 00:01:35.599 detailing a statistical method with, frankly, 00:01:36.439 --> 00:01:38.959 a very intimidating name. Oh, yeah. It's called 00:01:38.959 --> 00:01:41.900 t -distributed stochastic neighbor embedding. 00:01:42.170 --> 00:01:45.030 Or, thankfully, T -S -N -E for short. Much better. 00:01:45.170 --> 00:01:47.909 Yeah, way better. So our goal for you, the listener, 00:01:48.310 --> 00:01:50.390 is to decode this complex math. We're going to 00:01:50.390 --> 00:01:53.349 figure out how it acts as this massive dimensional 00:01:53.349 --> 00:01:55.650 translator, taking those impossible layers of 00:01:55.650 --> 00:01:57.909 data and just crushing them down into two or 00:01:57.909 --> 00:02:00.109 three dimensional maps that you and I can actually 00:02:00.109 --> 00:02:03.349 look at and comprehend. OK, let's unpack this. 00:02:03.590 --> 00:02:05.930 To truly understand how T -S -N -E pulls off 00:02:05.930 --> 00:02:07.810 this translation, we should probably look at 00:02:07.810 --> 00:02:10.590 its foundation. The algorithm builds on something 00:02:10.590 --> 00:02:12.949 called stochastic neighbor embedding, which was 00:02:12.949 --> 00:02:15.330 originally developed by Jeffrey Hinton and Sam 00:02:15.330 --> 00:02:18.469 Rolwis. And then later, Lawrence Vandermaten, 00:02:18.650 --> 00:02:22.110 working alongside Hinton, proposed the T distributed 00:02:22.110 --> 00:02:24.610 variant that, you know, really became the industry 00:02:24.610 --> 00:02:27.550 standard. In the formal language of the field, 00:02:27.689 --> 00:02:31.110 it is a nonlinear dimensionality reduction technique. 00:02:31.330 --> 00:02:33.909 Wait, I have to stop you there because nonlinear 00:02:33.909 --> 00:02:36.289 dimensionality reduction is exactly the kind 00:02:36.289 --> 00:02:39.500 of phrase that makes people like immediately 00:02:39.500 --> 00:02:41.560 turn off their brains. Fair enough. It's a mouthful. 00:02:41.680 --> 00:02:44.280 Yeah. Let me try an analogy here to ground this 00:02:44.280 --> 00:02:48.139 for the listener. So imagine you are tasked with 00:02:48.139 --> 00:02:50.780 organizing a massive party. OK. Let's say there 00:02:50.780 --> 00:02:53.400 are a million guests crammed into a giant convention 00:02:53.400 --> 00:02:55.879 center. And your job is to group them together 00:02:55.879 --> 00:02:58.319 on a flat, two -dimensional map of the room. 00:02:58.560 --> 00:03:01.280 A seating chart from hell. Right. Exactly. But 00:03:01.280 --> 00:03:02.939 you aren't just grouping them by their age or 00:03:02.939 --> 00:03:04.680 their hometown. Right. You have to group them 00:03:04.680 --> 00:03:07.599 by, say, 500 different personality traits simultaneously. 00:03:07.770 --> 00:03:11.210 And that is your high dimensional space. Each 00:03:11.210 --> 00:03:13.590 individual guest at the party is a data point. 00:03:13.969 --> 00:03:17.169 And those 500 distinct traits, those are the 00:03:17.169 --> 00:03:20.610 500 dimensions. Right. But here's where my brain 00:03:20.610 --> 00:03:23.330 completely breaks trying to draw that map. Like 00:03:23.330 --> 00:03:25.430 if I put all the heavy metal fans in one corner, 00:03:25.569 --> 00:03:28.590 that's great. Sure. But what if Half of those 00:03:28.590 --> 00:03:30.969 heavy metal fans are also obsessed with baking 00:03:30.969 --> 00:03:33.509 sourdough bread, and the other half are amateur 00:03:33.509 --> 00:03:36.469 botanists. Yeah, they get split up. Exactly. 00:03:36.810 --> 00:03:38.949 And what if the botanists share sleep habits 00:03:38.949 --> 00:03:41.129 with the classical music fans who are all the 00:03:41.129 --> 00:03:42.810 way on the other side of the room? You can't 00:03:42.810 --> 00:03:45.370 just squish 500 overlapping interests onto a 00:03:45.370 --> 00:03:47.750 flat piece of paper without tearing those relationships 00:03:47.750 --> 00:03:50.370 apart. You've just hit on the exact mathematical 00:03:50.370 --> 00:03:53.430 problem TSNE is designed to solve. Oh, wow. It 00:03:53.430 --> 00:03:56.349 acts as the ultimate party planner for this impossible 00:03:56.349 --> 00:03:58.569 scenario. What's fascinating here is that the 00:03:58.569 --> 00:04:01.490 algorithm completely abandons the idea of fixed 00:04:01.490 --> 00:04:04.330 rigid geometry. What do you mean by rigid geometry? 00:04:04.789 --> 00:04:07.849 Like, instead of trying to use a ruler to measure 00:04:07.849 --> 00:04:10.229 the distance between these people's traits, it 00:04:10.229 --> 00:04:13.669 uses probability. It asks a much more fluid question. 00:04:13.810 --> 00:04:16.629 It says, based on these 500 traits, what are 00:04:16.629 --> 00:04:18.629 the odds that these two specific people would 00:04:18.629 --> 00:04:20.750 find each other in this massive crowd and start 00:04:20.750 --> 00:04:23.959 talking? Oh, OK. So it trades a ruler for a set 00:04:23.959 --> 00:04:26.360 of odds. Exactly. How does that actually play 00:04:26.360 --> 00:04:28.579 out in the math, though? The source material 00:04:28.579 --> 00:04:31.139 breaks the process down into two main stages, 00:04:31.199 --> 00:04:33.560 starting with that high dimensional space. Yeah. 00:04:33.579 --> 00:04:36.560 So first, TSNE looks at the original data of 00:04:36.560 --> 00:04:40.100 those 500 trait party guests. And it computes 00:04:40.100 --> 00:04:42.480 probabilities that are proportional to how similar 00:04:42.480 --> 00:04:45.639 the objects are. OK. To do this, it centers a 00:04:45.639 --> 00:04:48.339 Gaussian distribution, which you can just picture 00:04:48.339 --> 00:04:51.230 as a classic bell curve. Right, a standard bell 00:04:51.230 --> 00:04:54.370 curve. Over every single data point. The algorithm 00:04:54.370 --> 00:04:56.350 essentially says, if I were to randomly pick 00:04:56.350 --> 00:04:58.509 a neighbor for the specific point based on the 00:04:58.509 --> 00:05:00.810 shape of this bell curve, what is the conditional 00:05:00.810 --> 00:05:02.810 probability I would pick this other specific 00:05:02.810 --> 00:05:05.189 point? So objects that share a lot of traits 00:05:05.189 --> 00:05:07.709 get a very high probability of being neighbors. 00:05:08.250 --> 00:05:10.930 objects with nothing in common get a microscopic 00:05:10.930 --> 00:05:13.589 probability. It sounds like it's building this 00:05:13.589 --> 00:05:17.370 massive invisible web of percentages in the high 00:05:17.370 --> 00:05:20.129 dimensional space. Like everyone has a specific 00:05:20.129 --> 00:05:21.810 percentage chance of standing next to everyone 00:05:21.810 --> 00:05:25.709 else. That is stage one completed. Now, the algorithm 00:05:25.709 --> 00:05:28.670 has to move to stage two. It takes a blank, flat, 00:05:28.769 --> 00:05:31.129 two -dimensional map and scatters new, low -dimensional 00:05:31.129 --> 00:05:33.250 points onto it. Just randomly. Just scatters 00:05:33.250 --> 00:05:35.750 them out. The ultimate goal is to move those 00:05:35.750 --> 00:05:38.290 flat points around until the web of probabilities 00:05:38.290 --> 00:05:40.870 on the flat map matches the web of probabilities 00:05:40.870 --> 00:05:43.769 in the 500 -dimensional space as closely as physically 00:05:43.769 --> 00:05:46.250 possible. Okay. Now, to connect those two stages, 00:05:46.389 --> 00:05:49.209 the text introduces a mechanism called minimizing 00:05:49.209 --> 00:05:54.199 the Kohlbach -Leibler divergence. or KL divergence 00:05:54.199 --> 00:05:56.300 using gradient descent. Yes. Let me see if I 00:05:56.300 --> 00:05:58.920 can visualize this one. Is KL divergence basically 00:05:58.920 --> 00:06:01.100 acting like a strict referee? A referee. Yeah, 00:06:01.399 --> 00:06:03.899 like the referee is constantly watching the flat 00:06:03.899 --> 00:06:06.220 map and comparing it to the high dimensional 00:06:06.220 --> 00:06:08.959 space. And if the map puts two people next to 00:06:08.959 --> 00:06:10.519 each other who actually have nothing in common, 00:06:10.980 --> 00:06:13.399 the referee throws a flag and assigns a penalty 00:06:13.399 --> 00:06:16.649 score. I like that. And gradient descent is just 00:06:16.649 --> 00:06:19.529 the mathematical process of tweaking the map 00:06:19.529 --> 00:06:22.709 over and over to minimize the referee's penalties. 00:06:23.009 --> 00:06:25.990 The referee analogy for KL divergence is spot 00:06:25.990 --> 00:06:28.670 -on. I mean, technically it is an asymmetric 00:06:28.670 --> 00:06:31.569 measure of how one probability distribution diverges 00:06:31.569 --> 00:06:34.329 from a second expected distribution, but... Right. 00:06:34.550 --> 00:06:37.129 Referee is easier. But let's upgrade your idea 00:06:37.129 --> 00:06:39.649 of gradient descent. It's often described as 00:06:39.649 --> 00:06:42.550 taking tiny steps down a mathematical hill, but 00:06:42.550 --> 00:06:45.079 in the context of TSNE... it's much more visceral 00:06:45.079 --> 00:06:47.920 than that. Imagine the points on your flat map 00:06:47.920 --> 00:06:50.920 are all connected by a complex system of physical 00:06:50.920 --> 00:06:53.939 springs. Springs, like actual coiled tension 00:06:53.939 --> 00:06:57.180 springs. Exactly. When the KL divergence referee 00:06:57.180 --> 00:06:59.600 throws a flag because two points are placed poorly, 00:07:00.079 --> 00:07:02.319 it's like adding massive tension to the springs 00:07:02.319 --> 00:07:05.399 connecting them. So gradient descent is the process 00:07:05.399 --> 00:07:08.800 of those springs. violently snapping and yanking 00:07:08.800 --> 00:07:11.420 the points across the map to relieve the tension. 00:07:11.639 --> 00:07:14.339 That's a great image. Yeah. The algorithm continually 00:07:14.339 --> 00:07:16.360 calculates the gradient, which is the direction 00:07:16.360 --> 00:07:18.959 of the pole, and updates the map, letting the 00:07:18.959 --> 00:07:21.199 points push and pull each other until the entire 00:07:21.199 --> 00:07:23.600 system settles into a state of minimal tension. 00:07:24.079 --> 00:07:27.980 That sounds incredibly chaotic. and mathematically 00:07:27.980 --> 00:07:30.319 exhausting for a computer to calculate. Like 00:07:30.319 --> 00:07:32.120 every single point is pulling on every other 00:07:32.120 --> 00:07:34.500 point constantly. It is intensely demanding. 00:07:34.839 --> 00:07:36.939 The source actually notes that for a data set 00:07:36.939 --> 00:07:40.899 with n elements, standard TSNE runs in what computer 00:07:40.899 --> 00:07:44.019 scientists call O of n squared time and requires 00:07:44.019 --> 00:07:46.879 O of n squared space. Meaning if you double the 00:07:46.879 --> 00:07:49.370 amount of data, The computational cost doesn't 00:07:49.370 --> 00:07:52.009 just double, it quadruples. Precisely. If you 00:07:52.009 --> 00:07:54.310 have a thousand data points, the computer is 00:07:54.310 --> 00:07:56.829 managing a million calculations. Right. If you 00:07:56.829 --> 00:07:58.529 scale that up to a million data points, you're 00:07:58.529 --> 00:08:00.709 suddenly asking the machine to handle a trillion 00:08:00.709 --> 00:08:03.430 calculations. The memory and processing power 00:08:03.430 --> 00:08:05.850 required become just a massive bottleneck as 00:08:05.850 --> 00:08:08.790 the data set grows. So assuming you have, like, 00:08:08.949 --> 00:08:11.430 a supercomputer that can handle the springs snapping 00:08:11.430 --> 00:08:14.529 back and forth a trillion times, what does this 00:08:14.529 --> 00:08:17.610 all mean for the actual map? Like how does it 00:08:17.610 --> 00:08:20.310 avoid just lumping everyone together in the middle? 00:08:20.430 --> 00:08:22.540 What do you mean? I mean, if everything shares 00:08:22.540 --> 00:08:24.899 at least some tiny similarity with everything 00:08:24.899 --> 00:08:27.600 else, wouldn't the tension just crush all the 00:08:27.600 --> 00:08:30.740 points into one dense overlapping black hole 00:08:30.740 --> 00:08:32.720 in the center of the screen? That black hole 00:08:32.720 --> 00:08:34.860 scenario is exactly what would happen without 00:08:34.860 --> 00:08:37.340 a few very clever mathematical interventions. 00:08:37.940 --> 00:08:40.639 To prevent the map from collapsing in on itself, 00:08:41.220 --> 00:08:44.279 TSNE relies on a user -defined parameter called 00:08:44.279 --> 00:08:47.559 perplexity. Perplexity? Yeah. Which is, ironically, 00:08:47.639 --> 00:08:49.700 how I feel when I try to read statistical mathematics. 00:08:49.720 --> 00:08:52.970 Yeah, it's a great name. In this context, perplexity 00:08:52.970 --> 00:08:55.250 is a number you choose before running the algorithm, 00:08:55.629 --> 00:08:57.990 typically set somewhere between 5 and 50. Okay. 00:08:58.269 --> 00:09:00.429 The technical definition involves matching the 00:09:00.429 --> 00:09:02.649 Shannon entropy of the conditional probabilities, 00:09:03.210 --> 00:09:05.389 but functionally you can interpret perplexity 00:09:05.389 --> 00:09:07.649 as a smooth measure of the effective number of 00:09:07.649 --> 00:09:09.990 neighbors a point has. Okay, let me translate 00:09:09.990 --> 00:09:11.809 that real quick. You're basically giving the 00:09:11.809 --> 00:09:14.049 algorithm an attention span. You're telling it, 00:09:14.129 --> 00:09:16.759 hey, Only focus on the closest 30 people to this 00:09:16.759 --> 00:09:19.440 point and safely ignore the thousands of other 00:09:19.440 --> 00:09:21.620 people who are further away. That is exactly 00:09:21.620 --> 00:09:23.879 what it does. And the algorithm adapts to the 00:09:23.879 --> 00:09:26.639 density of the data to make it happen. It adjusts 00:09:26.639 --> 00:09:29.159 the bandwidth of those Gaussian bell curves we 00:09:29.159 --> 00:09:31.399 talked about earlier. So they change size. Yeah. 00:09:31.559 --> 00:09:34.419 In a really crowded part of the high -dimensional 00:09:34.419 --> 00:09:37.600 space, it shrinks the bell curve to focus only 00:09:37.600 --> 00:09:40.919 on the immediate neighbors. In a sparse, empty 00:09:40.919 --> 00:09:43.759 area, it widens the bell curve to cast a larger 00:09:43.759 --> 00:09:46.919 net. That's smart. It ensures that every single 00:09:46.919 --> 00:09:49.519 point gets to care about the exact same effective 00:09:49.519 --> 00:09:51.759 number of neighbors, regardless of how packed 00:09:51.759 --> 00:09:54.000 the data is. So it adjusts its own zoom lens 00:09:54.000 --> 00:09:55.840 depending on the crowd. That's really cool. But 00:09:55.840 --> 00:09:57.919 the source material mentions another huge obstacle 00:09:57.919 --> 00:10:00.379 the algorithm has to overcome, something incredibly 00:10:00.379 --> 00:10:03.399 ominous. sounding, the curse of dimensionality. 00:10:03.480 --> 00:10:08.080 Ah, yes. The curse of dimensionality is a foundational 00:10:08.080 --> 00:10:11.139 nightmare in data science. When you use regular 00:10:11.139 --> 00:10:13.200 Euclidean distance. Like just measuring with 00:10:13.200 --> 00:10:15.879 a ruler. Right, the simple straight line distance 00:10:15.879 --> 00:10:18.519 we use in the physical world to measure the space 00:10:18.519 --> 00:10:21.620 between two objects. It completely loses its 00:10:21.620 --> 00:10:24.379 meaning in high dimensions. How does distance 00:10:24.379 --> 00:10:26.840 lose its meaning? I mean, a mile's a mile, isn't 00:10:26.840 --> 00:10:29.450 it? Well, in three dimensions, yes. But in high 00:10:29.450 --> 00:10:32.590 dimensions, volume expands exponentially. Think 00:10:32.590 --> 00:10:35.649 of a multi -dimensional orange. OK. As you add 00:10:35.649 --> 00:10:38.610 hundreds of dimensions, the math dictates that 00:10:38.610 --> 00:10:41.009 almost all of the volume of that orange gets 00:10:41.009 --> 00:10:44.070 pushed to the very outer surface. If it were 00:10:44.070 --> 00:10:47.129 a 500 -dimensional orange, it would be 99 % peel 00:10:47.129 --> 00:10:50.549 and almost zero juice. Wait, really? So the data 00:10:50.549 --> 00:10:53.429 points all migrate to the edges? Yes. And because 00:10:53.429 --> 00:10:55.669 everything is pushed to the vast outer crust 00:10:55.669 --> 00:10:58.889 of the space, almost all points seem completely 00:10:58.889 --> 00:11:01.730 equidistant from each other. If distances lose 00:11:01.730 --> 00:11:04.110 their ability to discriminate, the probabilities 00:11:04.110 --> 00:11:06.409 of things being neighbors become too similar. 00:11:06.990 --> 00:11:08.909 Asymptotically, they just converge to a constant 00:11:08.909 --> 00:11:11.409 number. So if everyone is equally far away from 00:11:11.409 --> 00:11:13.129 you, you don't actually have any neighbors. The 00:11:13.129 --> 00:11:15.090 whole concept of a neighborhood just breaks down. 00:11:15.470 --> 00:11:18.850 Exactly. To fix this on the final flat map, Vanermaten 00:11:18.850 --> 00:11:21.940 and Hinton did something ingenious. they completely 00:11:21.940 --> 00:11:24.659 abandoned the Gaussian bell curve for the low 00:11:24.659 --> 00:11:26.679 dimensional map. OK, what did they use instead? 00:11:26.860 --> 00:11:29.539 They swapped it out for a heavy -tailed student 00:11:29.539 --> 00:11:33.340 t distribution, specifically a Cauchy distribution 00:11:33.340 --> 00:11:36.700 with one degree of freedom. This is actually 00:11:36.700 --> 00:11:40.210 where the t in TSNE comes from. Oh. Okay, let's 00:11:40.210 --> 00:11:42.870 visualize a heavy tail. If a normal bell curve 00:11:42.870 --> 00:11:45.450 looks like a hill, where the slopes swoop all 00:11:45.450 --> 00:11:47.889 the way down to touch the floor, this Cauchy 00:11:47.889 --> 00:11:49.590 distribution looks like a hill where the slopes 00:11:49.590 --> 00:11:51.769 hover above the ground. Right. Like they stretch 00:11:51.769 --> 00:11:54.970 out infinitely without ever touching zero. What 00:11:54.970 --> 00:11:57.490 does that actually achieve though? It artificially 00:11:57.490 --> 00:12:00.470 inflates the space. Because the tails hover above 00:12:00.470 --> 00:12:03.070 the ground, there is a much higher mathematical 00:12:03.070 --> 00:12:05.870 probability of finding data points way out on 00:12:05.870 --> 00:12:08.629 the fringes. It essentially gives the algorithm 00:12:08.629 --> 00:12:11.529 the permission it needs to push dissimilar objects 00:12:11.529 --> 00:12:13.909 much, much further apart on the flat map than 00:12:13.909 --> 00:12:15.730 they strictly are in the high -dimensional space. 00:12:16.070 --> 00:12:19.009 Oh, I see. It gives the springs permission to 00:12:19.009 --> 00:12:22.309 stretch. It artificially shoves groups away from 00:12:22.309 --> 00:12:24.710 each other to keep the visual clean, preventing 00:12:24.710 --> 00:12:27.090 that overlapping black hole we were worried about. 00:12:27.250 --> 00:12:30.529 Yes, it creates those beautiful, distinct visual 00:12:30.529 --> 00:12:34.519 islands of data that TSNE is famous for. Here's 00:12:34.519 --> 00:12:36.399 where it gets really interesting, though, because, 00:12:36.500 --> 00:12:38.480 I mean, we've been deep in the theoretical math 00:12:38.480 --> 00:12:42.220 for a while now. Gaussian kernels, Cauchy distributions, 00:12:42.720 --> 00:12:45.100 O of n squared complexity. We've been in the 00:12:45.100 --> 00:12:47.299 weeds. Yeah, but this isn't just an academic 00:12:47.299 --> 00:12:49.830 exercise happening on a chalkboard. The real 00:12:49.830 --> 00:12:52.409 -world applications of this algorithm are astonishing. 00:12:52.610 --> 00:12:54.769 Like, when you take this ability to find hidden 00:12:54.769 --> 00:12:57.409 islands of data and apply it to actual human 00:12:57.409 --> 00:13:00.090 problems, it is quite literally saving lives. 00:13:00.330 --> 00:13:03.090 Oh, definitely. The range of fields relying on 00:13:03.090 --> 00:13:05.809 TSNE to see hidden patterns is just staggering. 00:13:06.049 --> 00:13:08.429 Take medicine, for example. The source highlights 00:13:08.429 --> 00:13:11.610 researchers using TSNE for analyzing EEG signals 00:13:11.610 --> 00:13:14.110 to detect epileptic seizures. Which makes perfect 00:13:14.110 --> 00:13:16.950 sense when you think about it. And EEG is recording 00:13:16.950 --> 00:13:19.340 the chaotic, high -dimensional electrical noise 00:13:19.340 --> 00:13:22.580 of the entire human brain millions of overlapping 00:13:22.580 --> 00:13:25.100 signals. To a human eye looking at a raw chart, 00:13:25.440 --> 00:13:28.620 it's just a wall of static. But T -SNE can map 00:13:28.620 --> 00:13:30.919 that electrical chaos and visually group the 00:13:30.919 --> 00:13:34.039 moments in time that look similar. It pulls the 00:13:34.039 --> 00:13:36.700 distinct, hidden signature of a seizure out of 00:13:36.700 --> 00:13:39.480 the static and plots it as an isolated island 00:13:39.480 --> 00:13:42.080 on a map. It's incredible. The text also emphasizes 00:13:42.080 --> 00:13:45.139 its use in exploring breast cancer data, specifically 00:13:45.139 --> 00:13:48.340 computer -aided diagnosis, or CADEX. Wait, how 00:13:48.340 --> 00:13:50.980 does the algorithm map a tumor? Well, tumor doesn't 00:13:50.980 --> 00:13:53.320 just have one or two features. When doctors analyze 00:13:53.320 --> 00:13:55.539 tissue, they're looking at cellular density, 00:13:56.000 --> 00:13:58.279 the thickness of cell walls, genetic markers, 00:13:58.779 --> 00:14:01.419 dozens or hundreds of microscopic variables. 00:14:01.759 --> 00:14:04.340 Ah, okay. That is a high dimensional space. Exactly. 00:14:04.779 --> 00:14:07.120 TSNE flattens all of those variables. It allows 00:14:07.120 --> 00:14:09.700 a researcher to plot a new patient's tumor profile 00:14:09.700 --> 00:14:12.340 on a screen and see instantly if it visually 00:14:12.340 --> 00:14:14.820 lands on the island of known benign tumors or 00:14:14.820 --> 00:14:17.340 if it clusters with the malignant ones. It takes 00:14:17.340 --> 00:14:19.840 the microscopic and makes it entirely visual. 00:14:20.000 --> 00:14:23.039 And it completely jumps industries, too. In technology 00:14:23.039 --> 00:14:25.899 and computer security, researchers use it to 00:14:25.899 --> 00:14:28.639 analyze the behavior of off -the -shelf anti 00:14:28.639 --> 00:14:32.200 -virus engines, like grouping how different software 00:14:32.200 --> 00:14:35.580 reacts to millions of lines of malicious code. 00:14:35.820 --> 00:14:38.279 It's heavily utilized in arts and culture too. 00:14:38.639 --> 00:14:41.340 Natural language processing uses T -S -N -E to 00:14:41.340 --> 00:14:44.120 generate word embeddings from 19th century literature. 00:14:44.360 --> 00:14:47.240 I love this example so much. It maps the vocabulary 00:14:47.240 --> 00:14:50.000 habits of authors. It plots how often they use 00:14:50.000 --> 00:14:52.559 specific prepositions or adjectives. Suddenly 00:14:52.559 --> 00:14:54.679 you can take an anonymous piece of text, run 00:14:54.679 --> 00:14:57.360 it through T -S -N -E, and watch it visually 00:14:57.360 --> 00:14:59.639 cluster right next to Charles Dickens. Because 00:14:59.639 --> 00:15:02.519 the algorithm recognized his subconscious high 00:15:02.519 --> 00:15:05.419 -dimensional word choice fingerprint. Yes. to 00:15:05.419 --> 00:15:07.659 learn features from music audio using deep belief 00:15:07.659 --> 00:15:10.159 networks. Earth scientists use it for geological 00:15:10.159 --> 00:15:13.179 domain interpretation, identifying complex material 00:15:13.179 --> 00:15:15.480 types in geochemical data scattered across the 00:15:15.480 --> 00:15:17.539 globe. From the electrical storms in our brains 00:15:17.539 --> 00:15:20.379 to 19th century literature to the literal dirt 00:15:20.379 --> 00:15:22.679 under our feet. The primary takeaway here is 00:15:22.679 --> 00:15:26.419 that TSNE is not just a math trick. It is a fundamental 00:15:26.419 --> 00:15:29.500 lens. When professionals across these entirely 00:15:29.500 --> 00:15:31.659 different disciplines are drowning in variables, 00:15:32.320 --> 00:15:35.519 TSNE acts as a translator. It converts abstract 00:15:35.519 --> 00:15:38.320 numbers into spatial intuition, giving researchers 00:15:38.320 --> 00:15:40.879 a kind of superhuman sight. But, and this is 00:15:40.879 --> 00:15:44.399 a massive, but, the source material has an entire 00:15:44.399 --> 00:15:47.820 section dedicated to the outputs of TSNE that 00:15:47.820 --> 00:15:51.259 serves as a giant flashing warning label. Yes. 00:15:51.620 --> 00:15:53.379 This raises an important question, maybe the 00:15:53.379 --> 00:15:55.080 most important question of our entire discussion. 00:15:55.580 --> 00:15:57.500 Given everything we know about how the algorithm 00:15:57.500 --> 00:16:00.120 artificially inflates space and uses heavy tails, 00:16:00.889 --> 00:16:03.590 How much should we trust our own eyes when we 00:16:03.590 --> 00:16:05.649 look at a TSNE map? Wait, so you're telling me 00:16:05.649 --> 00:16:07.950 the visual clusters we see on these maps, those 00:16:07.950 --> 00:16:10.590 beautiful distinct islands of data that are helping 00:16:10.590 --> 00:16:13.029 doctors and geologists, might be completely fake? 00:16:13.129 --> 00:16:15.070 They absolutely can be, and this is where critical 00:16:15.070 --> 00:16:17.470 thinking becomes mandatory. According to the 00:16:17.470 --> 00:16:20.230 source, TSNE plots often seem to display clusters, 00:16:20.649 --> 00:16:23.190 but those visual groupings are heavily manipulated 00:16:23.190 --> 00:16:25.549 by the chosen parameterization. You mean the 00:16:25.549 --> 00:16:28.419 settings? Right. Remember that perplexity number 00:16:28.419 --> 00:16:31.799 you have to choose, the attention span. If you 00:16:31.799 --> 00:16:34.860 set that number wrong for your specific data 00:16:34.860 --> 00:16:39.360 set, TSAE can and will produce visual clusters 00:16:39.360 --> 00:16:43.259 even in data that has absolutely no clear grouping 00:16:43.259 --> 00:16:46.570 in reality. So it will just invent quirks. because 00:16:46.570 --> 00:16:48.789 it's trying so hard to push things apart with 00:16:48.789 --> 00:16:51.230 that heavy -tailed t -distribution. Like, it 00:16:51.230 --> 00:16:53.950 wants to make a map so badly, it will draw borders 00:16:53.950 --> 00:16:56.049 where none exist. Yes, it will show you false 00:16:56.049 --> 00:16:59.409 findings. But the distortion gets even more counterintuitive 00:16:59.409 --> 00:17:02.230 than that. Let's say you do have real mathematically 00:17:02.230 --> 00:17:05.089 verified clusters. On a TSNE map, you might see 00:17:05.089 --> 00:17:08.029 one cluster that is huge and spread out and another 00:17:08.029 --> 00:17:10.849 that is tiny and dense. You might see two clusters 00:17:10.849 --> 00:17:12.710 right next to each other and a third one way 00:17:12.710 --> 00:17:14.529 off in the corner of the screen. Naturally looking 00:17:14.529 --> 00:17:16.049 at that, my brain immediately at least says, 00:17:16.170 --> 00:17:18.809 OK, the big cluster has more variance inside 00:17:18.809 --> 00:17:20.509 of it, and the two clusters close together are 00:17:20.509 --> 00:17:22.789 closely related, while the one far away is an 00:17:22.789 --> 00:17:25.289 outlier. And your brain would be completely fundamentally 00:17:25.289 --> 00:17:28.349 wrong. The source explicitly states that the 00:17:28.349 --> 00:17:31.430 size of clusters produced by TSNE is mathematically 00:17:31.430 --> 00:17:34.390 not informative, and neither is the distance 00:17:34.390 --> 00:17:36.150 between different clusters. Are you kidding? 00:17:36.430 --> 00:17:39.930 Nope. The algorithm distorts the macrogeography 00:17:39.930 --> 00:17:42.109 of the map to preserve the local neighborhoods. 00:17:42.430 --> 00:17:45.170 The heavy tail inflates space unpredictably. 00:17:45.390 --> 00:17:49.109 You cannot use a ruler on a TSN plot. You cannot 00:17:49.109 --> 00:17:52.430 say cluster A is closer to cluster B than cluster 00:17:52.430 --> 00:17:56.109 C. That is wild. The big picture is essentially 00:17:56.109 --> 00:17:58.910 a highly distorted illusion. So it successfully 00:17:58.910 --> 00:18:02.109 brings the data down into two dimensions, but 00:18:02.109 --> 00:18:04.289 it fundamentally warps the global distances just 00:18:04.289 --> 00:18:06.410 to make the local neighborhoods look good. Exactly. 00:18:06.490 --> 00:18:08.910 So if the distances are meaningless and the clusters 00:18:08.910 --> 00:18:11.930 might be fake, what is the solution? How do researchers 00:18:11.930 --> 00:18:14.049 actually use this without getting fooled by their 00:18:14.049 --> 00:18:16.589 own data? The solution is a process the text 00:18:16.589 --> 00:18:19.289 calls interactive exploration. You cannot just 00:18:19.289 --> 00:18:21.430 run the TSNA algorithm once, print out the picture, 00:18:21.509 --> 00:18:22.970 and publish your paper. You have to actively 00:18:22.970 --> 00:18:24.750 play with the parameters. You have to run it 00:18:24.750 --> 00:18:27.349 with different perplexities, validate the findings 00:18:27.349 --> 00:18:30.109 against other analytical methods, and truly understand 00:18:30.109 --> 00:18:32.890 the math beneath the image. Which totally explains 00:18:32.890 --> 00:18:35.190 why the software section of the article highlights 00:18:35.190 --> 00:18:37.529 tools that are specifically designed for this 00:18:37.529 --> 00:18:40.420 kind of iteration. Because of that brutal O of 00:18:40.420 --> 00:18:42.700 N squared computation time we mentioned earlier, 00:18:43.099 --> 00:18:45.019 developers have built approximation methods. 00:18:45.200 --> 00:18:48.519 Right, to speed things up. Yeah. There is a C++ 00:18:48.519 --> 00:18:50.960 implementation called Barnes -Hutt, available 00:18:50.960 --> 00:18:53.579 directly from Vandermaten, which groups distant 00:18:53.579 --> 00:18:56.200 points together as a single massive point to 00:18:56.200 --> 00:18:59.660 save calculation time. Yes, and the R package, 00:18:59.960 --> 00:19:03.799 Artsny, or ELKI, which also utilizes that Barnes 00:19:03.799 --> 00:19:06.259 -Hutt approximation to make the algorithm viable 00:19:06.259 --> 00:19:08.619 for massive data sets. And Python users, they 00:19:08.619 --> 00:19:11.220 rely on scikit -learn, which is hugely popular 00:19:11.220 --> 00:19:13.779 and handles both exact solutions and the Barnes 00:19:13.779 --> 00:19:16.319 -Hutt approximation. There's TensorBoard, the 00:19:16.319 --> 00:19:19.240 Julia package, T -Series. The point is, all of 00:19:19.240 --> 00:19:21.480 these tools are being built not to generate a 00:19:21.480 --> 00:19:24.880 single static image, but for progressive visual 00:19:24.880 --> 00:19:27.180 analytics. Exactly. They are built so you can 00:19:27.180 --> 00:19:29.380 turn the dials in real time and watch how the 00:19:29.380 --> 00:19:32.160 map changes. Because if the map radically transforms 00:19:32.160 --> 00:19:34.380 and your beautiful clusters just disappear the 00:19:34.380 --> 00:19:36.559 moment you change the propensity from 20 to 30, 00:19:37.180 --> 00:19:38.819 those clusters probably weren't real in the first 00:19:38.819 --> 00:19:42.140 place. Exactly. The truth of the data has to 00:19:42.140 --> 00:19:45.039 be robust across different parameters. It has 00:19:45.039 --> 00:19:46.700 been mathematically proven that with the right 00:19:46.700 --> 00:19:50.220 parameter choices, TSNE can recover well -separated 00:19:50.220 --> 00:19:52.539 clusters, but you have to do the rigorous work 00:19:52.539 --> 00:19:54.940 to find those correct settings. It demands an 00:19:54.940 --> 00:19:58.160 active, highly skeptical user. So to summarize 00:19:58.160 --> 00:20:01.119 our deep dive today, TSE &E is this brilliantly 00:20:01.119 --> 00:20:04.019 complex, beautifully flawed translator. It takes 00:20:04.019 --> 00:20:06.180 the incomprehensible scale of high dimensional 00:20:06.180 --> 00:20:08.539 space, whether that's hundreds of variables in 00:20:08.539 --> 00:20:11.480 a breast cancer tumor or 500 personality traits 00:20:11.480 --> 00:20:14.200 at a massive convention. And it uses probabilities 00:20:14.200 --> 00:20:17.000 and heavy tail distributions to squish that reality 00:20:17.000 --> 00:20:19.420 down into a 2D map we can actually comprehend. 00:20:19.609 --> 00:20:22.470 It really is a tool that has fundamentally revolutionized 00:20:22.470 --> 00:20:25.190 data visualization, but it demands that we do 00:20:25.190 --> 00:20:27.769 not take its visual outputs at face value. It 00:20:27.769 --> 00:20:29.910 serves as a perfect example of why we can never 00:20:29.910 --> 00:20:32.609 let algorithms do our thinking for us. It provides 00:20:32.609 --> 00:20:35.009 a unique perspective, but it does not provide 00:20:35.009 --> 00:20:37.369 an absolute truth. Right. Which brings me back 00:20:37.369 --> 00:20:39.289 to where we started. We talked about how our 00:20:39.289 --> 00:20:41.710 brains evolved for three -dimensional space, 00:20:42.170 --> 00:20:44.789 how we are biologically wired to look at the 00:20:44.789 --> 00:20:46.769 physical world and immediately find structure. 00:20:46.960 --> 00:20:49.279 We look up at a random scattering of stars and 00:20:49.279 --> 00:20:51.579 we see a hunter with a belt. We see faces in 00:20:51.579 --> 00:20:54.400 the clouds. We are deeply wired pattern recognition 00:20:54.400 --> 00:20:57.539 machines. We will trust our eyes over abstract 00:20:57.539 --> 00:21:00.519 numbers almost every single time. And that leaves 00:21:00.519 --> 00:21:02.819 a lingering question for you to mull over. We've 00:21:02.819 --> 00:21:05.200 just learned that a TSNE map will show you cluster 00:21:05.200 --> 00:21:07.839 sizes and distances that look incredibly meaningful. 00:21:08.380 --> 00:21:10.859 But mathematically? They are just an illusion 00:21:10.859 --> 00:21:14.079 of the translation process. So in an era where 00:21:14.079 --> 00:21:17.660 we increasingly rely on complex algorithms to 00:21:17.660 --> 00:21:20.440 compress impossible hyperdimensional reality 00:21:20.440 --> 00:21:22.420 into something our primate brains can digest, 00:21:23.099 --> 00:21:25.839 are we actually using these visualizations to 00:21:25.839 --> 00:21:28.500 uncover the hard truth of the data? Or are we 00:21:28.500 --> 00:21:30.460 just using them to paint a picture that our human 00:21:30.460 --> 00:21:33.380 brains are biologically desperate to see? A very 00:21:33.380 --> 00:21:36.039 necessary reminder to always question the lens 00:21:36.039 --> 00:21:38.220 through which we view the world. Thank you for 00:21:38.220 --> 00:21:41.259 joining us on this custom deep dive. Keep exploring, 00:21:41.779 --> 00:21:44.160 keep tweaking those parameters, and most importantly, 00:21:44.400 --> 00:21:46.059 keep questioning the data around you.