WEBVTT 00:00:00.000 --> 00:00:03.060 You know, sometimes you look at your digital 00:00:03.060 --> 00:00:06.080 life and it... It honestly feels like there's 00:00:06.080 --> 00:00:08.640 this invisible sorting hat just quietly putting 00:00:08.640 --> 00:00:10.939 everything into neat little boxes. Oh, absolutely. 00:00:11.240 --> 00:00:14.800 Yeah, it creates this, um, this illusion of intuition, 00:00:14.800 --> 00:00:17.079 I guess. Right, like you take a hundred photos 00:00:17.079 --> 00:00:19.500 on a weekend trip and suddenly your phone is 00:00:19.500 --> 00:00:21.760 perfectly grouped, you know, all the pictures 00:00:21.760 --> 00:00:25.019 of your dog into one distinct folder. Yeah, or 00:00:25.019 --> 00:00:27.579 you log onto a retailer's website and it feels 00:00:27.579 --> 00:00:30.079 like they know exactly which specific demographic 00:00:30.079 --> 00:00:32.659 bucket you fall into. It's unnerving, like they're 00:00:32.659 --> 00:00:35.119 pitching you products that are just way too accurate 00:00:35.119 --> 00:00:37.140 to your tastes. It really makes you feel like 00:00:37.140 --> 00:00:40.299 the machine just naturally understands the the 00:00:40.299 --> 00:00:42.880 nuanced shape of your life, you know, your habits, 00:00:43.079 --> 00:00:45.420 your preferences. But I mean, it's not magic. 00:00:45.619 --> 00:00:48.799 It's geometry. And today we are taking a deep 00:00:48.799 --> 00:00:51.659 dive into the very blueprint of that geometry. 00:00:52.119 --> 00:00:54.600 It's a fascinating subject. It really is. We're 00:00:54.600 --> 00:00:56.859 pulling from this comprehensive Wikipedia deep 00:00:56.859 --> 00:01:01.009 dive on a a mathematical workhorse called k -means 00:01:01.009 --> 00:01:03.170 clustering. Yeah, which is basically the engine 00:01:03.170 --> 00:01:05.829 behind so much of that sorting. Exactly. And 00:01:05.829 --> 00:01:08.549 our mission today is to figure out exactly how 00:01:08.549 --> 00:01:11.650 this invisible algorithm forces order onto our 00:01:11.650 --> 00:01:15.890 chaotic lives, translate its incredibly dense 00:01:15.890 --> 00:01:19.269 math into a clear mental model, and just reveal 00:01:19.269 --> 00:01:21.909 how it physically organizes the digital world 00:01:21.909 --> 00:01:25.750 around you. It's a phenomenal topic because it 00:01:25.750 --> 00:01:28.629 really exposes the tension between raw, messy 00:01:28.629 --> 00:01:31.510 human data and the machine's desperate need for 00:01:31.510 --> 00:01:34.269 order. Yes. The machine needs its boxes. Exactly. 00:01:34.549 --> 00:01:37.310 You are taking a chaotic universe of information 00:01:37.310 --> 00:01:40.689 and commanding the math to draw hard, rigid boundaries 00:01:40.689 --> 00:01:43.209 just to make sense of it all. OK, let's unpack 00:01:43.209 --> 00:01:45.250 this because before we can understand where this 00:01:45.250 --> 00:01:47.010 algorithm is secretly operating in your life, 00:01:47.090 --> 00:01:49.250 whether it's grouping your photos or targeting 00:01:49.250 --> 00:01:51.129 your ads, we really have to understand what it's 00:01:51.129 --> 00:01:53.569 actually doing data on a fundamental level. Right, 00:01:53.750 --> 00:01:56.209 the mechanics of it. Yeah. Let's start with that 00:01:56.209 --> 00:01:58.489 name. K means clustering. I mean, the jargon 00:01:58.489 --> 00:02:00.890 is thick right out of the gate. It sounds intimidating 00:02:00.890 --> 00:02:03.950 for sure, but it's surprisingly literal once 00:02:03.950 --> 00:02:06.150 you strip away the math speak. Okay, lay it on 00:02:06.150 --> 00:02:09.169 me. So the K is simply a placeholder variable. 00:02:09.409 --> 00:02:12.550 It literally just stands for the exact number 00:02:12.729 --> 00:02:15.789 of clusters or groups that you wanna sort your 00:02:15.789 --> 00:02:18.810 data into. And you, the human operator, have 00:02:18.810 --> 00:02:22.069 to decide K. Like if you have a massive database 00:02:22.069 --> 00:02:24.550 of customers and you wanna sort them into, say, 00:02:25.030 --> 00:02:27.810 five distinct groups for five different email 00:02:27.810 --> 00:02:30.669 campaigns. Then K equals five. Exactly, K equals 00:02:30.669 --> 00:02:33.009 five. So K is just the number of boxes we are 00:02:33.009 --> 00:02:37.270 forcing the data into. And the means part, I'm 00:02:37.270 --> 00:02:39.090 assuming that's not about the algorithm being 00:02:39.090 --> 00:02:42.340 like... aggressive or mean? No, not quite. Means 00:02:42.340 --> 00:02:44.780 refers to the mathematical center point of those 00:02:44.780 --> 00:02:47.240 groups, the centroid. Centroid, that sounds like 00:02:47.240 --> 00:02:49.759 a transformer. It kind of does, but if you imagine 00:02:49.759 --> 00:02:52.560 like plotting a scatter plot of a thousand data 00:02:52.560 --> 00:02:56.580 points on a graph, the mean is the literal physical 00:02:56.580 --> 00:02:59.419 center of mass for a specific group of those 00:02:59.419 --> 00:03:01.219 points. So it's like the geographic heart of 00:03:01.219 --> 00:03:02.879 the cluster. That's a perfect way to put it, 00:03:02.960 --> 00:03:04.939 yes. And the way the algorithm actually finds 00:03:04.939 --> 00:03:07.479 these geographical hearts is through what the 00:03:07.479 --> 00:03:09.360 source material calls the standard algorithm. 00:03:09.530 --> 00:03:12.469 which is also known as Lloyd's algorithm. Right. 00:03:12.550 --> 00:03:14.969 Named after Stuart Lloyd. Yeah. And it's essentially 00:03:14.969 --> 00:03:17.909 this continuous iterative two -step dance. You 00:03:17.909 --> 00:03:19.930 have step one, which is the assignment step, 00:03:20.289 --> 00:03:23.289 and step two, the update step. Let's visualize 00:03:23.289 --> 00:03:25.490 that assignment step first because it's pretty 00:03:25.490 --> 00:03:29.349 wild. The algorithm takes your K number. Let's 00:03:29.349 --> 00:03:32.080 say you chose three. And it literally throws 00:03:32.080 --> 00:03:35.139 down three center points onto your graph of data. 00:03:35.139 --> 00:03:37.659 Just drops them in randomly. This boom, boom, 00:03:37.699 --> 00:03:40.960 boom. Exactly. Then it looks at every single 00:03:40.960 --> 00:03:43.680 piece of data on that board and assigns it to 00:03:43.680 --> 00:03:45.840 whichever of those three center points it is 00:03:45.840 --> 00:03:48.599 physically closest to. And what happens mathematically 00:03:48.599 --> 00:03:51.520 when it does that is absolutely wild. Like, the 00:03:51.520 --> 00:03:54.419 source notes that this assignment process mathematically 00:03:54.419 --> 00:03:57.379 partitions the entire data space into geometric 00:03:57.379 --> 00:04:00.870 regions called Voronoi cells. Which, if you've 00:04:00.870 --> 00:04:03.629 never seen a voronoi diagram, picture a beautiful 00:04:03.629 --> 00:04:05.849 stained glass window. That stained glass visual 00:04:05.849 --> 00:04:07.969 is perfect, actually, because it highlights the 00:04:07.969 --> 00:04:11.319 rigidity of the math. When the algorithm assigns 00:04:11.319 --> 00:04:14.259 a data point to its closest center, it is effectively 00:04:14.259 --> 00:04:18.019 drawing a hard microscopic boundary line exactly 00:04:18.019 --> 00:04:20.680 halfway between two competing centers. Oh, wow. 00:04:20.759 --> 00:04:23.360 Yeah, it creates these polygonal tiles that fit 00:04:23.360 --> 00:04:26.680 perfectly together with zero overlap. Like you 00:04:26.680 --> 00:04:29.220 are either inside the glass tile for center A, 00:04:29.540 --> 00:04:31.360 or you're inside the glass tile for center B. 00:04:31.360 --> 00:04:33.860 There is no gray area. But the algorithm doesn't 00:04:33.860 --> 00:04:36.779 just stop once it draws that stained glass window. 00:04:37.199 --> 00:04:40.329 That brings us to step two. the update step. 00:04:40.529 --> 00:04:42.810 Right, because the center has changed. Exactly. 00:04:43.110 --> 00:04:45.009 Because you just assigned a whole bunch of random 00:04:45.009 --> 00:04:47.930 data points to a cluster, the actual literal 00:04:47.930 --> 00:04:51.110 center of mass of that new group has probably 00:04:51.110 --> 00:04:52.970 shifted away from where you originally dropped 00:04:52.970 --> 00:04:55.009 your center point. It definitely has. So the 00:04:55.009 --> 00:04:57.569 algorithm has to recalculate the mean. It literally 00:04:57.569 --> 00:05:01.209 drags the center point to the true middle of 00:05:01.209 --> 00:05:04.509 its newly assigned cluster. Which, um... immediately 00:05:04.509 --> 00:05:06.769 invalidates the stained glass window you just 00:05:06.769 --> 00:05:09.569 drew. Exactly. I was trying to wrap my head around 00:05:09.569 --> 00:05:11.610 this endless loop of assigning and updating, 00:05:12.129 --> 00:05:14.589 and I came up with an analogy. Well, let's hear 00:05:14.589 --> 00:05:17.410 it. Okay. Imagine you are hosting this incredibly 00:05:17.410 --> 00:05:21.569 chaotic dinner party in a massive open ballroom. 00:05:21.589 --> 00:05:24.829 Okay. And you need to sort your hundreds of million 00:05:24.829 --> 00:05:27.930 guests into K number of tables. Okay. Let's stick 00:05:27.930 --> 00:05:30.329 with K equals three. Three giant round tables. 00:05:30.509 --> 00:05:33.620 A true logistical nightmare for any host. Total 00:05:33.620 --> 00:05:36.079 nightmare. People are just standing around randomly. 00:05:36.800 --> 00:05:39.639 So you physically drop three tables in random 00:05:39.639 --> 00:05:42.079 spots across the ballroom. Just drag them out 00:05:42.079 --> 00:05:44.720 there. Yeah. Then you get on a microphone and 00:05:44.720 --> 00:05:47.100 tell everyone, hey, go sit at the table that 00:05:47.100 --> 00:05:49.779 you are currently standing closest to. That is 00:05:49.779 --> 00:05:51.680 our assignment step. And everyone scrambles, 00:05:51.699 --> 00:05:53.620 and the room is instantly divided into three 00:05:53.620 --> 00:05:56.680 distinct crowds based purely on proximity. Right. 00:05:56.879 --> 00:05:59.379 But once everyone sits down, you look around 00:05:59.379 --> 00:06:02.220 and realize the conversational energy is completely 00:06:02.220 --> 00:06:05.220 off -center. Naturally. Like the actual dense 00:06:05.220 --> 00:06:08.720 core of the crowd at table one is heavily skewed, 00:06:09.379 --> 00:06:11.240 say 20 feet to the left of where the physical 00:06:11.240 --> 00:06:13.100 table actually is. Okay, I see where this is 00:06:13.100 --> 00:06:15.220 going. So to make sure everyone can hear each 00:06:15.220 --> 00:06:17.980 other, you grab the physical table and you literally 00:06:17.980 --> 00:06:20.939 drag it across the floor to the exact center 00:06:20.939 --> 00:06:23.079 of where that specific group is currently sitting. 00:06:23.620 --> 00:06:26.360 You update the center. But by dragging table 00:06:26.360 --> 00:06:30.079 1 20 feet to the left, you just changed the geography 00:06:30.079 --> 00:06:32.699 of the entire ballroom. Exactly. Because you 00:06:32.699 --> 00:06:35.120 moved the tables, a guest who was sitting on 00:06:35.120 --> 00:06:37.639 the edge of table 1 might certainly look around 00:06:37.639 --> 00:06:40.980 and realize, wait. Because table two also got 00:06:40.980 --> 00:06:43.439 dragged over this way. I'm actually physically 00:06:43.439 --> 00:06:46.240 closer to table two now, right the boundary shifted 00:06:46.240 --> 00:06:49.519 Yeah, so they stand up abandon table one and 00:06:49.519 --> 00:06:52.220 walk over to table two They are reassigning themselves 00:06:52.220 --> 00:06:54.779 based on the new geometry Yes, and you just keep 00:06:54.779 --> 00:06:56.920 doing this over and over people reassigning themselves 00:06:56.920 --> 00:06:59.579 to the closest table and you Dragging the physical 00:06:59.579 --> 00:07:01.600 tables to the new center of whatever the group 00:07:01.600 --> 00:07:04.779 looks like until it stabilizes exactly you repeat 00:07:04.779 --> 00:07:07.500 this exhausting dance until finally the table 00:07:07.500 --> 00:07:10.620 stopped moving and Absolutely nobody needs to 00:07:10.620 --> 00:07:13.209 stand up and switch tables anymore. That analogy 00:07:13.209 --> 00:07:16.670 captures the mechanics flawlessly. And it actually 00:07:16.670 --> 00:07:19.589 brings us to the underlying math that drives 00:07:19.589 --> 00:07:22.430 all that table moving. Oh, boy. OK, bring on 00:07:22.430 --> 00:07:24.610 the math. Don't worry, it's not too bad. The 00:07:24.610 --> 00:07:26.850 algorithm's ultimate objective is built on a 00:07:26.850 --> 00:07:29.209 concept called within cluster sum of squares, 00:07:29.629 --> 00:07:33.029 or WCSS. OK, within cluster sum of squares sounds 00:07:33.029 --> 00:07:35.370 like a terrifying question on a graduate level 00:07:35.370 --> 00:07:38.149 math exam. It does, yeah. But your dinner party 00:07:38.149 --> 00:07:41.350 actually decodes it perfectly. The algorithm's 00:07:41.350 --> 00:07:44.639 entire underlying goal is to minimize variance. 00:07:45.819 --> 00:07:47.920 It wants to make sure that everyone sitting at 00:07:47.920 --> 00:07:50.779 a given table is as physically close to the center 00:07:50.779 --> 00:07:53.420 of their table as mathematically possible, and 00:07:53.420 --> 00:07:56.100 it calculates this using what are called squared 00:07:56.100 --> 00:07:59.079 Euclidean distances. Why are we squaring the 00:07:59.079 --> 00:08:01.860 distance? If I am five feet away from the table, 00:08:01.939 --> 00:08:04.680 why does the man need to square that to 25? Because 00:08:04.680 --> 00:08:08.379 squaring heavily penalizes outliers. Oh, interesting. 00:08:08.560 --> 00:08:10.959 Yeah. Think about your dinner party. If a guest 00:08:10.959 --> 00:08:12.779 is sitting two feet away from the center of the 00:08:12.779 --> 00:08:15.980 table, two squared is four penalty points. The 00:08:15.980 --> 00:08:17.699 algorithm doesn't mind that too much. Right. 00:08:17.740 --> 00:08:20.360 Four is a small penalty. But if a guest is stranded 00:08:20.360 --> 00:08:22.519 way out in the hallway, 10 feet away from the 00:08:22.519 --> 00:08:26.079 table, 10 squared is 100 penalty points. Oh, 00:08:26.120 --> 00:08:29.540 wow. So it ramps up fast. Exactly. The math panics. 00:08:29.620 --> 00:08:33.039 It hates large numbers. So it will... aggressively 00:08:33.039 --> 00:08:36.360 drag the table toward that stranded guest to 00:08:36.360 --> 00:08:39.000 minimize that massive squared penalty. Okay, 00:08:39.000 --> 00:08:41.059 that makes total sense. Yeah, minimizing the 00:08:41.059 --> 00:08:44.460 WCSS simply means the algorithm has manipulated 00:08:44.460 --> 00:08:47.460 the room until it found the absolute tightest, 00:08:47.460 --> 00:08:50.779 most compact groups possible. It is so elegantly 00:08:50.779 --> 00:08:52.960 simple when you visualize the mechanics like 00:08:52.960 --> 00:08:56.080 that. But, you know, knowing how elegantly it 00:08:56.080 --> 00:08:58.700 forces order onto a room really makes you wonder 00:08:58.700 --> 00:09:00.740 who actually came up with this. Yeah, the history 00:09:00.740 --> 00:09:03.509 is fascinating. And more importantly, why, despite 00:09:03.509 --> 00:09:06.149 being run on literal supercomputers today, it 00:09:06.149 --> 00:09:08.389 almost never finds the perfect mathematical answer. 00:09:08.649 --> 00:09:10.990 Well, the history here is surprisingly old for 00:09:10.990 --> 00:09:12.950 something that serves as a foundational pillar 00:09:12.950 --> 00:09:15.090 of modern machine learning. How old are we talking? 00:09:15.250 --> 00:09:17.269 The standard algorithm was first proposed by 00:09:17.269 --> 00:09:19.409 a researcher named Stuart Lloyd at Bell Labs 00:09:19.409 --> 00:09:23.590 all the way back in 1957. 1957. Yeah. Though 00:09:23.590 --> 00:09:25.470 interestingly, he didn't formally publish it 00:09:25.470 --> 00:09:28.429 in a journal until 1982. What was he even trying 00:09:28.429 --> 00:09:31.269 to do in 1957 that required sorting data like 00:09:31.269 --> 00:09:33.230 this? I mean, they barely had computers. Right, 00:09:33.289 --> 00:09:35.649 he was working on pulse code modulation. Okay, 00:09:35.769 --> 00:09:38.220 what is that? Basically, this is the early mathematics 00:09:38.220 --> 00:09:41.240 of taking a smooth, continuous analog signal 00:09:41.240 --> 00:09:43.840 like a human voice traveling over a telephone 00:09:43.840 --> 00:09:47.179 wire and chopping it up into discrete, manageable 00:09:47.179 --> 00:09:50.139 digital chunks. Ah, so turning sound into data. 00:09:50.399 --> 00:09:53.299 Exactly. He needed a mathematical way to find 00:09:53.299 --> 00:09:55.440 the most representative means of those sound 00:09:55.440 --> 00:09:58.340 waves to digitize them efficiently. And it wasn't 00:09:58.340 --> 00:10:00.899 even called K -Means back then, right? The source 00:10:00.899 --> 00:10:03.399 says James McQueen finally coined the term K 00:10:03.399 --> 00:10:06.480 -Means a decade later in 1967. That is correct. 00:10:07.039 --> 00:10:10.299 But here is the massive catch with Stuart Lloyd's 00:10:10.299 --> 00:10:11.860 brilliant algorithm. I knew there was a catch. 00:10:12.190 --> 00:10:14.889 Finding the absolute mathematically perfect optimal 00:10:14.889 --> 00:10:18.370 solution for K means meaning the guaranteed absolute 00:10:18.370 --> 00:10:20.889 lowest possible variance across your entire data 00:10:20.889 --> 00:10:23.509 set is what computer scientists call NP -hard. 00:10:23.730 --> 00:10:25.970 NP -hard. Which translates to what, practically 00:10:25.970 --> 00:10:28.289 speaking? Just incredibly difficult to solve. 00:10:28.509 --> 00:10:31.289 Beyond difficult, it implies a combinatorial 00:10:31.289 --> 00:10:33.990 explosion. A combinatorial explosion. OK. Even 00:10:33.990 --> 00:10:36.070 if you just have a simple two -dimensional flat 00:10:36.070 --> 00:10:38.990 graph with a few dozen data points, checking 00:10:38.990 --> 00:10:42.009 every single possible cluster combination to 00:10:42.009 --> 00:10:44.850 guarantee you have the absolute best one can 00:10:44.850 --> 00:10:48.179 take exponential time. Wait, seriously? Just 00:10:48.179 --> 00:10:51.259 for a few dozen points. Imagine trying to arrange 00:10:51.259 --> 00:10:53.960 a seating chart for a wedding with 10 ,000 guests, 00:10:54.299 --> 00:10:56.659 and you have to mathematically check every single 00:10:56.659 --> 00:10:59.539 possible combination of who sits where before 00:10:59.539 --> 00:11:01.340 you make a decision. That sounds like actual 00:11:01.340 --> 00:11:04.659 torture. It is. As you add more dimensions or 00:11:04.659 --> 00:11:06.919 more clusters, it would literally take the age 00:11:06.919 --> 00:11:09.039 of the universe to compute the perfect answer. 00:11:09.259 --> 00:11:11.679 Wait, I have to push back here. Sure. If finding 00:11:11.679 --> 00:11:14.639 the perfect, mathematically true answer takes 00:11:14.639 --> 00:11:16.960 an eternity, even for modern cloud computing 00:11:16.960 --> 00:11:20.399 servers, why is this algorithm so overwhelmingly 00:11:20.399 --> 00:11:22.980 popular? Why do we use it to compress images 00:11:22.980 --> 00:11:25.480 and target marketing if it can't actually guarantee 00:11:25.480 --> 00:11:29.080 the right answer? That is the brilliant, pragmatic 00:11:29.080 --> 00:11:31.639 compromise of k -means. It relies heavily on 00:11:31.639 --> 00:11:34.960 heuristics. Heuristics. Rule of fun stuff. Exactly. 00:11:35.700 --> 00:11:38.440 Because finding the global optimum, the absolute 00:11:38.440 --> 00:11:40.879 best answer in the universe, is computationally 00:11:40.879 --> 00:11:43.899 impossible, the algorithm happily settles for 00:11:43.899 --> 00:11:46.460 a local optimum. A local optimum. Yeah. It finds 00:11:46.460 --> 00:11:48.940 an answer that is good enough for its immediate 00:11:48.940 --> 00:11:51.419 surroundings, and then it simply stops looking. 00:11:51.639 --> 00:11:53.419 It's the good enough algorithm. It literally 00:11:53.419 --> 00:11:55.360 just throws its hands up and says, hey, this 00:11:55.360 --> 00:11:57.720 was fine. Let's go to lunch. If we connect this 00:11:57.720 --> 00:12:00.320 to the bigger picture, that is exactly what you 00:12:00.320 --> 00:12:03.649 want in the real world of massive petabyte scale 00:12:03.649 --> 00:12:06.330 data sets. You just need it to work fast. Right. 00:12:06.330 --> 00:12:09.710 You don't usually need the perfect fundamental 00:12:09.710 --> 00:12:12.330 mathematical truth of the universe. You just 00:12:12.330 --> 00:12:14.710 need a highly functional grouping and you need 00:12:14.710 --> 00:12:17.710 it in three seconds. Makes sense. Lloyd's algorithm 00:12:17.710 --> 00:12:20.529 is famous because it usually converges on a local 00:12:20.529 --> 00:12:23.909 optimum in just a dozen or so iterations of that 00:12:23.909 --> 00:12:26.929 table moving dance. It is incredibly ruthlessly 00:12:26.929 --> 00:12:29.750 efficient. But OK, if it is settling for a local 00:12:29.750 --> 00:12:33.039 optimum, a good enough answer based on its immediate 00:12:33.039 --> 00:12:36.500 surroundings, then where it starts, the search 00:12:36.500 --> 00:12:39.440 must matter immensely. Oh, absolutely. Going 00:12:39.440 --> 00:12:42.139 back to the dinner party, if I accidentally drop 00:12:42.139 --> 00:12:44.600 all three tables bunched up in the far right 00:12:44.600 --> 00:12:47.200 corner of the ballroom, the final grouping of 00:12:47.200 --> 00:12:49.600 guests is going to look vastly different than 00:12:49.600 --> 00:12:51.679 if I had spread the tables evenly across the 00:12:51.679 --> 00:12:53.940 room to begin with. You have zeroed in on one 00:12:53.940 --> 00:12:56.940 of the most heavily researched areas of k -means 00:12:56.940 --> 00:13:00.000 clustering, initialization. where you drop the 00:13:00.000 --> 00:13:02.740 tables. Exactly. Where you place those starting 00:13:02.740 --> 00:13:05.720 centers drastically dictates the final outcome. 00:13:06.440 --> 00:13:09.460 The source details a few highly specific ways 00:13:09.460 --> 00:13:11.960 data scientists try to handle this. Like what? 00:13:12.360 --> 00:13:14.740 For instance, there's the 4G method. Yeah. This 00:13:14.740 --> 00:13:17.659 is where you randomly pick k actual data points 00:13:17.659 --> 00:13:19.840 from your data set and use them as your starting 00:13:19.840 --> 00:13:22.159 centers. OK. So in the dinner party, that would 00:13:22.159 --> 00:13:25.080 be like closing my eyes. pointing at three random 00:13:25.080 --> 00:13:27.679 guests and just dropping the heavy tables directly 00:13:27.679 --> 00:13:31.179 onto their toes. Ouch. But yes, exactly. Because 00:13:31.179 --> 00:13:33.620 you are picking existing data points, it tends 00:13:33.620 --> 00:13:36.539 to spread the initial means out somewhat naturally 00:13:36.539 --> 00:13:39.139 across where the data actually lives. Right, 00:13:39.240 --> 00:13:40.940 because guests aren't usually standing in the 00:13:40.940 --> 00:13:43.480 walls. Exactly. But then there is an alternative 00:13:43.480 --> 00:13:45.220 approach called the random partition method. 00:13:45.620 --> 00:13:48.259 This one takes a totally different route. It 00:13:48.259 --> 00:13:51.000 randomly assigns every single point in the data 00:13:51.000 --> 00:13:54.049 set to a cluster first, before there are even 00:13:54.049 --> 00:13:57.169 any centers, and then calculates the center of 00:13:57.169 --> 00:13:59.710 those completely random jumbled assignments. 00:14:00.169 --> 00:14:02.409 Wait, if everything is totally jumbled across 00:14:02.409 --> 00:14:05.389 the entire room, wouldn't the center of those 00:14:05.389 --> 00:14:08.769 random groups all just average out to the exact 00:14:08.769 --> 00:14:11.590 middle of the ballroom? Yes, they all start bunched 00:14:11.590 --> 00:14:13.809 up in the exact center of the room and slowly 00:14:13.809 --> 00:14:15.830 have to drift outwards to find their crowds. 00:14:16.299 --> 00:14:19.059 That seems inefficient. It's a slow drift, and 00:14:19.059 --> 00:14:21.700 it is actually incredibly risky. If you start 00:14:21.700 --> 00:14:24.019 them all tightly packed in the middle, they might 00:14:24.019 --> 00:14:26.659 get trapped in a really poor local optimum and 00:14:26.659 --> 00:14:29.519 fail to capture groups on the outer edges. That 00:14:29.519 --> 00:14:32.080 is why researchers rarely run k -means just once. 00:14:32.200 --> 00:14:34.460 They will run the algorithm 50 times with 50 00:14:34.460 --> 00:14:36.559 different random starting points and then just 00:14:36.559 --> 00:14:38.580 pick the resulting map that has the tightest 00:14:38.580 --> 00:14:41.879 mathematical variance. Okay, so because this 00:14:41.879 --> 00:14:44.580 algorithm relies on these aggressive mathematical 00:14:44.580 --> 00:14:47.720 shortcuts, these good enough heuristics and random 00:14:47.720 --> 00:14:50.399 starting points, it must have some serious blind 00:14:50.399 --> 00:14:52.580 spots. It definitely does. And here's where it 00:14:52.580 --> 00:14:56.120 gets really interesting. When commines encounters 00:14:56.120 --> 00:14:59.269 the messy unpredictable shapes of real -world 00:14:59.269 --> 00:15:02.690 data, it can make some hilarious and deeply problematic 00:15:02.690 --> 00:15:05.710 mistakes. Oh, it absolutely does. The algorithm 00:15:05.710 --> 00:15:08.529 has strict, uncompromising assumptions built 00:15:08.529 --> 00:15:11.009 into its geometry. Like what kind of assumptions? 00:15:11.110 --> 00:15:14.590 It assumes that clusters are sphere - like, perfectly 00:15:14.590 --> 00:15:17.009 round, symmetrical bubbles, and it assumes that 00:15:17.009 --> 00:15:19.429 they are all of roughly similar size. Fierce 00:15:19.429 --> 00:15:21.970 and equal sizes. Yeah. And when real -world data 00:15:21.970 --> 00:15:24.649 violates those geometric assumptions, commines 00:15:24.649 --> 00:15:27.629 fails completely and aggressively. The Wikipedia 00:15:27.629 --> 00:15:30.090 source gives a fantastic, almost comical example 00:15:30.090 --> 00:15:32.610 of this called the mouse dataset. Yes, the mouse. 00:15:32.889 --> 00:15:35.870 Imagine plotting thousands of data points on 00:15:35.870 --> 00:15:38.750 a graph and they happen to form the exact shape 00:15:38.750 --> 00:15:41.149 of a Mickey Mouse head. You know, you have a 00:15:41.149 --> 00:15:43.529 massive, incredibly dense circle of points at 00:15:43.529 --> 00:15:46.690 the bottom representing the head and two much 00:15:46.690 --> 00:15:49.669 smaller, less dense circles at the top left and 00:15:49.669 --> 00:15:52.750 top right representing the ears. It is a brilliant 00:15:52.750 --> 00:15:55.750 visual representation of three distinct clusters. 00:15:56.370 --> 00:15:59.309 Any human being looks at that graph and instantly, 00:15:59.830 --> 00:16:01.850 intuitively says, oh, there are three groups 00:16:01.850 --> 00:16:05.330 here. One giant head, two tiny ears. Exactly. 00:16:05.509 --> 00:16:08.309 It's obvious. But if you tell Cosneys to find 00:16:08.309 --> 00:16:11.200 three clusters in that data, it completely butchers 00:16:11.200 --> 00:16:13.340 the mouse. It really does. Because it strictly 00:16:13.340 --> 00:16:15.279 assumes that clusters must be of similar size 00:16:15.279 --> 00:16:17.539 and perfectly spherical. It cannot comprehend 00:16:17.539 --> 00:16:19.480 that the head is massive and the ears are small, 00:16:19.799 --> 00:16:22.039 so it just violently chops the entire image into 00:16:22.039 --> 00:16:24.720 three roughly equal -sized chunks. Yeah, it's 00:16:24.720 --> 00:16:27.320 brutal. It will slice a voronoi boundary line 00:16:27.320 --> 00:16:28.960 right through the middle of the massive head, 00:16:29.559 --> 00:16:31.120 stealing thousands of points from the face just 00:16:31.120 --> 00:16:33.179 to make the ear clusters bigger and mathematically 00:16:33.179 --> 00:16:36.450 equal. It is entirely blind to the density of 00:16:36.450 --> 00:16:39.029 the points or the distinct unequal shapes of 00:16:39.029 --> 00:16:42.190 reality. It only sees its desperate need to draw 00:16:42.190 --> 00:16:44.809 equidistant lines. Right, it just wants balance. 00:16:45.090 --> 00:16:46.950 And it struggles just as much with shapes that 00:16:46.950 --> 00:16:49.909 aren't perfectly round. The text brings up another 00:16:49.909 --> 00:16:53.629 famous benchmark in machine learning, the Iris 00:16:53.629 --> 00:16:56.029 flower dataset. Right, I've heard of this one. 00:16:56.110 --> 00:16:59.110 This is a classic dataset containing petal and 00:16:59.110 --> 00:17:02.029 sepal measurements of three distinct real -world 00:17:02.029 --> 00:17:05.990 species of Iris. But if you feed that data into 00:17:05.990 --> 00:17:08.549 k -means and tell it to find three clusters, 00:17:09.089 --> 00:17:11.609 it routinely fails to separate the actual botanical 00:17:11.609 --> 00:17:14.190 species correctly. Yeah, and the reason why reveals 00:17:14.190 --> 00:17:16.789 the limitation of the sphere assumption. In the 00:17:16.789 --> 00:17:19.150 data, two of those iris species have somewhat 00:17:19.150 --> 00:17:21.069 similar measurements, so their data points kind 00:17:21.069 --> 00:17:23.009 of bleed into each other on the graph. So they 00:17:23.009 --> 00:17:25.089 don't look like neat little circles. Exactly. 00:17:25.309 --> 00:17:27.210 Instead of forming two separate circles, they 00:17:27.210 --> 00:17:31.019 form one long, stretched -out oblong shape. K 00:17:31.019 --> 00:17:34.059 -means looks at that long oval -shaped cluster. 00:17:34.539 --> 00:17:36.559 And because its fundamental math desperately 00:17:36.559 --> 00:17:39.940 wants to draw perfect spheres, it will literally 00:17:39.940 --> 00:17:43.579 chop that visible continuous oval perfectly in 00:17:43.579 --> 00:17:46.799 half. It is literally forcing its rigid worldview 00:17:46.799 --> 00:17:49.220 onto the data rather than listening to what the 00:17:49.220 --> 00:17:51.720 data's natural shape is actually telling it. 00:17:51.819 --> 00:17:54.900 Which highlights the absolute biggest, most glaring 00:17:54.900 --> 00:17:57.940 flaw of K -means clustering, the K -conundrum. 00:17:57.960 --> 00:18:01.019 Oh, right, the K -conundrum. the human operator 00:18:01.019 --> 00:18:03.460 have to tell the algorithm exactly how many clusters 00:18:03.460 --> 00:18:06.299 exist before it is even allowed to look at the 00:18:06.299 --> 00:18:09.059 data. That seems entirely backward. If the whole 00:18:09.059 --> 00:18:11.319 point of using an advanced machine learning algorithm 00:18:11.319 --> 00:18:13.380 is to discover hidden patterns in my massive 00:18:13.380 --> 00:18:15.720 data set, how on earth am I supposed to know 00:18:15.720 --> 00:18:17.619 how many patterns there are before I even start? 00:18:17.720 --> 00:18:20.519 It is a massive structural limitation. If you 00:18:20.519 --> 00:18:23.480 blindly guess k equals 3 on that iris data set, 00:18:23.960 --> 00:18:26.569 it chops a natural cluster in half. If you guess 00:18:26.569 --> 00:18:29.390 K equals 2, it would actually capture the geometric 00:18:29.390 --> 00:18:31.990 structure much better, grouping the two overlapping 00:18:31.990 --> 00:18:34.690 species together into one big bubble. But then 00:18:34.690 --> 00:18:37.049 you fundamentally miss the biological fact that 00:18:37.049 --> 00:18:40.269 there are three classes of flowers. So how do 00:18:40.269 --> 00:18:44.190 data scientists deal with this K conundrum? Do 00:18:44.190 --> 00:18:46.849 they just guess and... Hope for the best? Well, 00:18:46.950 --> 00:18:49.450 they use a variety of diagnostic checks to try 00:18:49.450 --> 00:18:52.410 and mathematically estimate k. The source outlines 00:18:52.410 --> 00:18:55.190 several techniques. Like what? There is the elbow 00:18:55.190 --> 00:18:57.990 method, where you run the algorithm for k equals 00:18:57.990 --> 00:19:00.769 1, then 2, then 3, and you plot the variance 00:19:00.769 --> 00:19:03.329 on a line graph. You look for a sharp bend or 00:19:03.329 --> 00:19:06.349 an elbow in the line to find the sweet spot of 00:19:06.349 --> 00:19:08.390 diminishing returns. OK, that sounds reasonable. 00:19:08.529 --> 00:19:10.970 But the text explicitly notes this is considered 00:19:10.970 --> 00:19:13.950 highly unreliable in practice because real -world 00:19:13.950 --> 00:19:16.779 data rarely produces a sharp, obvious elbow. 00:19:16.980 --> 00:19:18.920 It's more of a gentle curve. So if the elbow 00:19:18.920 --> 00:19:21.180 is too blurry, what else is there? There's the 00:19:21.180 --> 00:19:23.799 silhouette score, which evaluates how tightly 00:19:23.799 --> 00:19:26.559 knit an object is to its own cluster compared 00:19:26.559 --> 00:19:28.579 to how close it is to the neighboring cluster. 00:19:28.880 --> 00:19:31.720 Or you have the gap statistic, which compares 00:19:31.720 --> 00:19:34.319 your data's clustering against a random null 00:19:34.319 --> 00:19:37.700 distribution. Wait, a null distribution? Are 00:19:37.700 --> 00:19:39.480 you saying the algorithm essentially creates 00:19:39.480 --> 00:19:42.880 a totally random fake data set? just to see if 00:19:42.880 --> 00:19:44.880 its real clusters are actually statistically 00:19:44.880 --> 00:19:47.819 meaningful or just a random mathematical coincidence. 00:19:48.039 --> 00:19:50.559 That is a perfect translation. Yes. It generates 00:19:50.559 --> 00:19:53.680 a totally uniform box of random noise, clusters 00:19:53.680 --> 00:19:56.140 it, and compares the variance to your actual 00:19:56.140 --> 00:19:58.980 data. Oh, wow. If your data clusters way tighter 00:19:58.980 --> 00:20:00.559 than the random noise, you've probably found 00:20:00.559 --> 00:20:03.400 a good k. But the reality is, all of these are 00:20:03.400 --> 00:20:05.539 just sophisticated mathematical ways of trying 00:20:05.539 --> 00:20:08.380 to justify the k you've chosen. None of them 00:20:08.380 --> 00:20:10.700 are magic bullets. OK, so let me summarize this. 00:20:10.940 --> 00:20:13.680 The algorithm stubbornly forces all data into 00:20:13.680 --> 00:20:16.519 perfect spheres. It completely struggles with 00:20:16.519 --> 00:20:19.099 overlapping shapes. It violently chops mouse 00:20:19.099 --> 00:20:22.140 heads into thirds to maintain equal sizes. And 00:20:22.140 --> 00:20:24.160 it forces you to guess the answer before you 00:20:24.160 --> 00:20:26.160 even start the test. That's a pretty damning 00:20:26.160 --> 00:20:28.319 summary, but yes. If it is this mathematically 00:20:28.319 --> 00:20:31.180 flawed and rigid, why on earth is it used everywhere 00:20:31.180 --> 00:20:33.920 in modern technology? Because when it is applied 00:20:33.920 --> 00:20:36.359 correctly and you understand its limitations, 00:20:36.880 --> 00:20:39.819 it is an incredibly powerful tool for simplification. 00:20:40.359 --> 00:20:43.240 It reduces complex high -dimensional reality 00:20:43.240 --> 00:20:46.359 into manageable chunks better than almost anything 00:20:46.359 --> 00:20:48.660 else. Let's talk about those real -world applications 00:20:48.660 --> 00:20:50.319 because this is where the algorithm actually 00:20:50.319 --> 00:20:53.619 touches the listener's daily life. The first 00:20:53.619 --> 00:20:57.059 major one mentioned is vector quantization, which 00:20:57.059 --> 00:21:00.579 is essentially a very fancy academic way of saying 00:21:00.579 --> 00:21:03.130 image compression. What's fascinating here is 00:21:03.130 --> 00:21:06.309 how commines treat something visual, like colors, 00:21:06.809 --> 00:21:09.750 as pure mathematical coordinates. Colors as math. 00:21:09.950 --> 00:21:12.400 Okay. Imagine a high -definition photograph on 00:21:12.400 --> 00:21:15.079 your phone. It might have millions of distinct, 00:21:15.299 --> 00:21:18.200 subtle color variations. Millions of pixels, 00:21:18.380 --> 00:21:20.420 each representing a slightly different data point 00:21:20.420 --> 00:21:22.940 of red, green, and blue. Right, ton of data. 00:21:23.220 --> 00:21:25.579 Storing the exact hex code for every single pixel 00:21:25.579 --> 00:21:27.440 takes a massive amount of memory. But if I'm 00:21:27.440 --> 00:21:30.160 a web developer and I need that high -res image 00:21:30.160 --> 00:21:32.740 to load instantly on a user's slow cell connection, 00:21:33.180 --> 00:21:35.200 I can't be sending millions of unique colors 00:21:35.200 --> 00:21:37.519 over the network. It would take forever. Exactly. 00:21:37.579 --> 00:21:40.660 So you run the image through K -means. You tell 00:21:40.660 --> 00:21:43.779 the algorithm, I only want 64 colors to represent 00:21:43.779 --> 00:21:47.339 this entire massive image. So k equals 64. Yep. 00:21:48.119 --> 00:21:51.119 The algorithm maps out every pixel, and it finds 00:21:51.119 --> 00:21:54.180 the 64 mathematical centers of all the colors 00:21:54.180 --> 00:21:57.460 in that photo. It groups millions of similar 00:21:57.460 --> 00:22:00.579 subtle shades of reds, blues, and greens into 00:22:00.579 --> 00:22:03.339 64 distinct Voronoi cells. And then it strips 00:22:03.339 --> 00:22:06.019 away all the nuance, it says. Every single pixel 00:22:06.019 --> 00:22:08.839 that got assigned to this specific subtle shade 00:22:08.839 --> 00:22:11.559 of ocean blue is now going to be forced to become 00:22:11.559 --> 00:22:14.619 exactly this one. Uniform centroid shade of blue. 00:22:14.759 --> 00:22:17.559 Yes. It drastically reduces the file size because 00:22:17.559 --> 00:22:19.559 the computer no longer has to remember millions 00:22:19.559 --> 00:22:22.039 of colors. It only has to store a tiny palette 00:22:22.039 --> 00:22:24.759 of K colors and a simple map of which pixel gets 00:22:24.759 --> 00:22:27.140 painted which color. That's brilliant. And human 00:22:27.140 --> 00:22:28.819 eyes often can't even tell the difference because 00:22:28.819 --> 00:22:30.920 the algorithmic centroids capture the visual 00:22:30.920 --> 00:22:33.960 essence of the image so accurately. That is wild. 00:22:34.160 --> 00:22:37.200 It is essentially creating a custom, hyper -efficient 00:22:37.200 --> 00:22:40.359 paint -by -numbers kit for every single image 00:22:40.359 --> 00:22:42.359 on the internet. That's exactly what it is. What 00:22:42.359 --> 00:22:45.200 about applications beyond just pixels and images? 00:22:46.240 --> 00:22:48.720 The source also dives into cluster analysis, 00:22:49.299 --> 00:22:53.000 specifically market segmentation. This is a classic 00:22:53.000 --> 00:22:56.240 foundational business application. Major retailers 00:22:56.240 --> 00:22:59.440 have massive sprawling databases of customer 00:22:59.440 --> 00:23:01.259 behavior. Oh yeah, they know everything. They 00:23:01.259 --> 00:23:04.579 really do. They know your age, your income, your 00:23:04.579 --> 00:23:07.359 purchase history, how many milliseconds you hover 00:23:07.359 --> 00:23:10.640 over a specific product. They run k -means to 00:23:10.640 --> 00:23:13.380 group these millions of chaotic individual customers. 00:23:13.740 --> 00:23:16.019 Sorting us into buckets. Right. They might test 00:23:16.019 --> 00:23:18.380 the data and find that k equals four gives them 00:23:18.380 --> 00:23:21.480 four highly actionable customer profiles. the 00:23:21.480 --> 00:23:24.240 bargain hunters, the impulse buyers, the brand 00:23:24.240 --> 00:23:26.720 loyalists, and the seasonal shoppers. And because 00:23:26.720 --> 00:23:29.759 K -Means draws those rigid, hard, voronoi boundary 00:23:29.759 --> 00:23:31.900 lines we talked about, you could have a situation 00:23:31.900 --> 00:23:34.220 where two neighbors buy almost the exact same 00:23:34.220 --> 00:23:36.680 things, but because one neighbor buys slightly 00:23:36.680 --> 00:23:39.299 more coffee, they cross a millimeter over that 00:23:39.299 --> 00:23:41.640 mathematical boundary line. Exactly. Suddenly, 00:23:41.779 --> 00:23:44.200 the algorithm places them in two entirely different 00:23:44.200 --> 00:23:46.680 voronoi cells. One gets targeted with late -night 00:23:46.680 --> 00:23:49.619 flash sale emails as an impulse buyer, and the 00:23:49.619 --> 00:23:53.440 other gets loyalty rewards. It simplifies millions 00:23:53.440 --> 00:23:57.240 of nuanced, complex individuals into K number 00:23:57.240 --> 00:24:00.279 of manageable, highly targeted marketing campaigns. 00:24:01.099 --> 00:24:03.579 The text also mentions a really fascinating modern 00:24:03.579 --> 00:24:06.059 application, feature learning and natural language 00:24:06.059 --> 00:24:09.029 processing, or NLP. Yes, this is quite advanced 00:24:09.029 --> 00:24:11.410 and incredibly relevant right now. With all the 00:24:11.410 --> 00:24:14.809 AI models everywhere. Exactly. In NLP, before 00:24:14.809 --> 00:24:17.609 you can train a massive complex deep learning 00:24:17.609 --> 00:24:20.670 model or an AI neural network to understand human 00:24:20.670 --> 00:24:23.599 tech, say, Figuring out if a specific word in 00:24:23.599 --> 00:24:26.500 a sentence is a person, a place, or a corporate 00:24:26.500 --> 00:24:29.759 entity, you can use k -means as a sort of pre 00:24:29.759 --> 00:24:32.359 -processing rough draft. So instead of forcing 00:24:32.359 --> 00:24:34.160 the neural network to read the dictionary and 00:24:34.160 --> 00:24:36.579 learn everything from scratch, k -means acts 00:24:36.579 --> 00:24:39.069 like a cheat sheet. That is exactly what it does. 00:24:39.210 --> 00:24:41.549 You mathematically map words as physical points 00:24:41.549 --> 00:24:44.049 in a multidimensional space. You use k -means 00:24:44.049 --> 00:24:46.089 to cluster words that frequently hang out together 00:24:46.089 --> 00:24:48.410 in similar sentences. It groups them together 00:24:48.410 --> 00:24:50.670 into Voronoi cells. That makes total sense. The 00:24:50.670 --> 00:24:52.529 neural network, then, doesn't have to learn the 00:24:52.529 --> 00:24:54.650 definition of every single word in isolation. 00:24:55.089 --> 00:24:57.529 It can look at the clusters k -means build and 00:24:57.529 --> 00:25:01.349 say, ah, bank, money, and vault are all in the 00:25:01.349 --> 00:25:03.980 same neighborhood. They function similarly. It 00:25:03.980 --> 00:25:06.500 provides a foundational layer of understanding 00:25:06.500 --> 00:25:09.240 for the AI. So bring this all back to you listening 00:25:09.240 --> 00:25:12.500 right now. When you are scrolling online and 00:25:12.500 --> 00:25:16.299 you receive a hyper -specific targeted ad that 00:25:16.299 --> 00:25:19.519 feels like it read your mind, or when a website 00:25:19.519 --> 00:25:22.119 loads a beautiful complex image instantly on 00:25:22.119 --> 00:25:24.980 your phone, or when an AI seems to fundamentally 00:25:24.980 --> 00:25:28.019 understand the context of your prompt, you are 00:25:28.019 --> 00:25:30.640 directly benefiting from or being targeted by 00:25:30.640 --> 00:25:33.319 a k -mean centroid. You've been pulled into the 00:25:33.319 --> 00:25:36.180 orbit of a Voronoi cell. You are a complex data 00:25:36.180 --> 00:25:37.779 point that has been assigned to a mathematical 00:25:37.779 --> 00:25:40.079 mean. It's kind of humbling, honestly. It really 00:25:40.079 --> 00:25:42.579 is. So what does this all mean? We started back 00:25:42.579 --> 00:25:45.319 in 1957 with Stuart Lloyd at Bell Labs trying 00:25:45.319 --> 00:25:47.720 to chop up analog sound waves for pulse code 00:25:47.720 --> 00:25:51.240 modulation. A long time ago. Yeah. We explored 00:25:51.240 --> 00:25:54.759 the elegant, albeit NP -hard, geometry of Voronoi 00:25:54.759 --> 00:25:57.740 cells and the exhausting chaotic dinner party 00:25:57.740 --> 00:26:00.359 of assigning guests and dragging tables to minimize 00:26:00.359 --> 00:26:02.660 variance. We'll forget the mouse. Right. We saw 00:26:02.660 --> 00:26:05.019 how the algorithm completely butchers a mouse 00:26:05.019 --> 00:26:07.500 -shaped data set because of its rigid obsession 00:26:07.500 --> 00:26:10.059 with perfect spheres. And we uncovered how those 00:26:10.059 --> 00:26:12.660 very same rigid assumptions make it the hyper 00:26:12.660 --> 00:26:14.940 -efficient backbone of modern image compression 00:26:14.940 --> 00:26:18.039 and targeted marketing today. It truly is a testament 00:26:18.039 --> 00:26:20.619 to the power of heuristic thinking. In a modern 00:26:20.619 --> 00:26:23.180 world absolutely drowning in petabytes of data, 00:26:23.640 --> 00:26:26.559 finding a good enough local optimum is often 00:26:26.559 --> 00:26:29.539 far more valuable and computationally feasible 00:26:29.539 --> 00:26:32.779 than endlessly searching for perfect universal 00:26:32.779 --> 00:26:35.039 truth. It really is. But I want to leave you 00:26:35.039 --> 00:26:37.140 with one final thought, building on something 00:26:37.140 --> 00:26:39.680 tucked away near the very end of our source material. 00:26:39.880 --> 00:26:42.000 Oh, what's that? The text explicitly mentions 00:26:42.000 --> 00:26:44.480 that because k -means is so rigid, researchers 00:26:44.480 --> 00:26:46.599 eventually had to develop alternative algorithms 00:26:46.599 --> 00:26:50.069 to fix its geometric flaws. Algorithms like mean 00:26:50.069 --> 00:26:52.009 shift, which doesn't require you to guess the 00:26:52.009 --> 00:26:54.750 number of k -clusters beforehand, or the Gaussian 00:26:54.750 --> 00:26:57.470 mixture model. Which is a fascinating alternative. 00:26:57.529 --> 00:27:00.730 Right. Unlike k -means, which draws a hard rigid 00:27:00.730 --> 00:27:03.650 circle and says you are either 100 % in or out, 00:27:04.250 --> 00:27:06.670 a Gaussian mixture model looks at probability. 00:27:06.769 --> 00:27:09.470 It says, hey, this data point has a 70 % chance 00:27:09.470 --> 00:27:11.509 of belonging to this long stretched out oval 00:27:11.509 --> 00:27:14.509 group and a 30 % chance of belonging to the one 00:27:14.509 --> 00:27:17.240 next to it. It allows the boundaries to be soft 00:27:17.240 --> 00:27:19.720 and the shapes to stretch and warp based on the 00:27:19.720 --> 00:27:21.700 actual shape of the data. It allows the data 00:27:21.700 --> 00:27:23.839 to dictate the shape of the categories rather 00:27:23.839 --> 00:27:26.380 than forcing the categories onto the data. Exactly. 00:27:26.519 --> 00:27:28.859 And that is what I want you to ponder. In a world 00:27:28.859 --> 00:27:32.140 completely obsessed with categorization, K means 00:27:32.140 --> 00:27:35.539 forces data into a strict predefined number of 00:27:35.539 --> 00:27:38.500 boxes based on rigid mathematical boundary lines. 00:27:38.619 --> 00:27:41.930 Hard lines. Yeah. But human behavior, your behavior, 00:27:42.130 --> 00:27:44.289 the overlapping, incredibly messy data of the 00:27:44.289 --> 00:27:47.170 real world rarely fits into neat, equal -sized 00:27:47.170 --> 00:27:50.230 spheres. As you navigate the digital world today, 00:27:50.650 --> 00:27:53.089 and that invisible sorting hat quietly does its 00:27:53.089 --> 00:27:55.910 work, ask yourself, are the personalized digital 00:27:55.910 --> 00:27:57.769 experiences you're getting truly tailored to 00:27:57.769 --> 00:28:00.789 your unique, complex shape? Or were you just 00:28:00.789 --> 00:28:02.789 forced into a predetermined k -box because you 00:28:02.789 --> 00:28:04.509 happened to fall a millimeter on the wrong side 00:28:04.509 --> 00:28:06.329 of a marketer's mathematical boundary line?