So let me give you an example of multidimensional scaling being applied to physical distance. So these are distances between different cities in the United States. And if I have the distances between cities, what I should be able to do is reproduce a map of the United States. So the input for producing this map are the intercity distances. The algorithm's going to crank, and it's trying to figure out, how do I put these cities on a two-dimensional space, because that's what I've indicated. But how do I do that in such a way that gets as close to the actual distances as possible. And so if you're using XL Stat for this, multidimensional scalings underanalyze the data, you're going to specify the proximity matrix, and you're going to specify, are you providing similarities or dissimilarities? So since we're providing distances, those are dissimilarities, right? More distance means they're further apart And so this is the first map that was spit out from the multidimensional scaling algorithm. And your first glance might say, well, that's a little bit off. But keep in mind, all that MDS is concerned with is getting the distance between cities correct, right? So how did it do in that regard? Well, Boston, Philadelphia, New York, DC are all close together. Orlando, Miami, Atlanta are relatively close together. San Francisco, LA close together. Seattle being pretty far away from the cities in the northeast. So it got the intercity distances, right? It just didn't get the rotation right. Well, let's flip this around a little bit and see if it looks a little bit better, right? If I turn the axis a bit, this is what we get. And that looks a little bit more like it should. So the accuracy of MDS, again, it's all based on distances between points. You can rotate and flip the map itself, that's not changing the distance between the points. And so when we look at this rotated version, well, it turns out that the algorithm did what it was supposed to. It took intercity distances, and it recreated essentially a map for us of those cities in the United States. So that was using intercity data, let's use survey data. So a study was done where there were 10 vehicles, and respondents were asked which pairs to rate the similarity of the pairs of vehicles. So which pair of vehicles were the most similar to each other? Which pairs of vehicles were the least similar to each other? And so that's what each respondent was asked, 45 possible pairs to rank them, right? And so that's what they were tasked with. And this is not just the brands. These are specific models that they were tasked with. But give us the ranking of which ones are most similar, which ones are most different from each other. And that's what we're going to try to produce a perceptual map with. And so this a sample of the ratings for a particular respondent. And you'll notice that this respondent indicated that what the Lexus and Infiniti models were the most similar to each other. The Porsche and the Chrysler minivan were the most different from each other. What we take, this is what each respondent is giving us if we take the average ratings across all of our respondents, that's going to become our dissimilarity matrix. So again, the higher the score in this case, the more different they are from each other. So that's why it's a dissimilarity matrix. And so if we take that and put it into the multidimensional scaling algorithm, this is the map that we ultimately end up with. And so we have the Chrysler minivan, the Volvo station wagon being somewhat similar to each other. BMW, Mercedes, tending to be seen as more similar to each other. Infinity and Lexus seen as more similar to each other. Porsche looks like it's the most different from all of the vehicles that had been put into this particular study. And so we'd want to look at art for these particular models, how might we be able to label the two axis, right? That would be a logical step for us to want to take. So for example, is left or right? That horizontal axis, perhaps that's the premium dimension. So the further I go right, that being more premium, maybe there's a comfort element to this particular map. And that's where getting additional information on the attribute perceptions can help shed light on how a particular brand is seen, right? So that auto example that I'd shown you earlier is taken from the same study, whereas that first map was first produced using switching data. What the authors had also done, we've conducted MDS but apply to social media data. So they took social media data. They produced some metric and then fed that dissimilarity matrix into the multidimensional scaling algorithm. And this map looks fairly similar to the one we saw earlier, a little bit of reshuffling. But you notice that Cadillac still close to Lincoln, still a little bit close to Jaguar, you kind of straddle that line. It's a luxury vehicle but also a domestic vehicle. If we look at the segment that we have, we typically have a domestic car segment. Import segment are more of the luxury segment. So you can use MDS for sever data, you can use MDS with social media data, you can use MDS with switching data. Pretty much any data that allows you to construct a brand dissimilarity measure, you can use MDS to produce these visuals Now, we've constructed a single perceptual map. Something to keep in mind, and this goes back to what we talked about in the segment on customer segmentation. What we're making the assumption right now is that all consumers have the same perceptions of the marketplace. And if that's the case, we can go, we can look at it on our maps and say, alright, well, were there are the bulk of consumers that we're able to target? Were there a potential opportunities for us? Was there less competition? How might we want to try to reposition ourselves? Yeah, that works if you're comfortable with the assumption that all consumers have the same perceptual map of the marketplace. But yeah, one problem that you might run into is if you have very different segment, if you have segments that see the industry differently, that see the competitive landscape differently. They may say that one segment might say that two brands are similar, another segment might say, no, I don't see those brands as being particularly similar. And so that's something you want to be cognizant of. If you're looking at very different segments, you may want to make sure that they see the marketplace in the same way. Otherwise, you lump all of those individuals, their responses into the same perceptual map. You're going to get to wash out all those differences, and you might get things that don't make that much sense. All right, so you do want to be careful. If you have market segments, you may want to consider running your MDS market by market just to verify that the market structure appears the same way, right? And so we've talked about ways that you can go about understanding how your seeing how do you score an attribute, how do your competitors score an attribute? It's going to help you see how you're perceived, how your competitors are perceived, may help you identify potential opportunities in the marketplace. All right, so what we can do. We understand our own perceptions, we see which brands are seen as similar to us, and find those potential opportunities. MDS perceptual maps allow you to do all of that. What they don't do is tell you, should I take steps to reposition my brand? And they don't tell you which dimensions are the most important to the consumers. That's where you would need to bring in additional information, right? So I will need additional data to say, which spots on the map have the biggest market potential? Should I reposition myself here? Well, it depends. Where am I currently positioned? How costly is it going to be to reposition myself? And what do I expect to gain by doing that repositioning? If we have additional information on, think of it as a heatmap. If it were a heatmap saying, here's the really hot area, and there's not that much competition, if you can move yourself there relatively easily, absolutely. But if you've got an open area, and it's ice cold, well, maybe there's a reason that it's an open area, because there were no consumers there. So you would need additional data to enrich what those maps can deliver, but that's an analysis you can conduct if you have access to that data. So you'll overlay the perceptual map with essentially demanded information.