Applied Multivariate Analysis: Let’s ease the things

--- Amey Acharya, MSC SDS

---

In my second semester of Data Science course, I got introduced to the topics of Applied Multivariate Analysis. They have some interesting applications in Machine Learning and Deep Learning. While studying them I got some interesting examples that will clear all your ideas about these topics.

In this blog I have tried to explain the concepts by giving some examples to ease the complexity of understanding them. My main priority while writing the blog is to explain the concepts in different and unique ways. I have tried to explain the concept of Principle Component Analysis (PCA), Clustering Analysis, Structural Equation Modelling (SEM), Multi-Dimensional Scaling (MDS).  

🚀🚀🚀🚀Principal Component Analysis: From Clumsy clothes to Clear and Maintained Wardrobe

Suppose you want to shift into a new apartment, and you’ve brought your wardrobe with you. Your wardrobe is a mess of shirts, pants, hats, socks, shoes all jumbled together. While packing your clothes, you want to organize it and only take what really matters. Here PCA algorithm works as your Personal Wardrobe Organizer.

Step 1: The Problem.

You have 100 pieces of clothing, and you’re overwhelmed. You don’t know where to start because every item feels essential. But really all the items are essential?

Step 2: PCA comes into mind.

First, PCA looks at your clothes and asks:

• What’s common among them?

• Are some items pretty much the same? (Do you really need 10 black t-shirts? Do you really need 15 pink crop-tops?)

• What are the biggest differences? (Summer vs. winter clothes?)

Step 3: Finding Principal Components.

PCA creates a plan:

• It checks your wardrobe for patterns. Maybe most of your clothes fall into just two categories: Comfort and Style.

• These categories act as your Principal Components. Instead of thinking about each shirt, shoe, or hat individually, you now think in terms of comfort and style.

Step 4: Dimensionality Reduction.

Out of your 100 pieces of clothing, PCA says:

• “Hey, 80% of your wardrobe is about comfort. The rest is about style.”

• So, instead of 100 items, focus on just the ones that maximize comfort and style say, 10 pieces.

This is like PCA reducing your data from 100 variables (all those shirts and shoes) to just 2 dimensions (comfort and style).

Step 5: The Result

Now your wardrobe is compact, organized and clean.

• If you want to dress for a cozy day? Focus on the “Comfort” principal component.

• If you want to dress for a party? Lean into the “style” component.

PCA is like Marie Kondo for data. It finds what “sparks joy” (important patterns) and helps you ditch the clutter (unimportant noise).

Next time you’re dealing with too much data (or too many clothes), think of PCA. Because life’s too short for messy wardrobes and messy datasets.

🚀🚀🚀🚀Clustering Analysis: How to Find Your Squad in a Room Full of Strangers

Imagine you’ve invited to a massive party. You walk in and see 100 people chatting, laughing, and dancing. You know no one, and you wonder, “How do I find my tribe here?”

Here Clustering Analysis comes into action. It’s a smart way to group people (or data) into clusters based on their similarities. Let me show you how it works at this party.

Step 1: The Problem

You want to find people you can vibe with, but the room is filled with diverse personalities like the artists, the cricket fans, the bookworms, the foodies, and many more. Walking up to each person to figure them out would take all night.

Step 2: Clustering comes into mind.

Here’s what clustering does:

1. It listens to the conversations, observes behaviors, and takes notes.

2. It looks for patterns: who’s talking about cricket, who’s talking about latest movies, who’s showing off their written Shayaris, etc.

3. It forms clusters groups of people with similar interests.

Step 3: Making of Clusters.

After observing for a while, Clustering Analysis gives you a idea:

• Cluster 1: The Cricket Fans are seating near the TV.

• Cluster 2: The artists are standing near the stairs.•

Cluster 3: The singers are singing at karaoke.•

Cluster 4: The Foodies are hanging out near the buffet.

Now, instead of guessing, you can head straight to the cluster that matches your vibe.

Step 4: Real-Life Applications of Clustering Analysis.

Just like at the party, clustering helps in real-world situations:

1. Customer Segmentation: Businesses group their customers based on their behavior, like frequent shoppers, bargain hunters, or loyal subscribers.

2. Healthcare: Doctors cluster their patients based on symptoms or medical history to personalize treatments.

3. Marketing: Netflix recommends movies by clustering users with similar viewing habits.

4. Education: Teachers group students by learning styles to customize teaching methods.

5. Social media: Platforms like Facebook group users by interests to show relevant ads.

6. Urban Planning: Cities cluster areas based on population density, income levels, or traffic patterns to plan infrastructure.

🚀🚀🚀🚀Let’s have a look on Structural Equation Modeling (SEM) in a different way!

SEM Demystified: Unlocking the Gossip Network of Relationships

Imagine you’re at a high school reunion. You walk in, and the place is buzzing with chatter. Everyone seems connected somehow with friends, rivals, classmates, seniors, etc. The dynamics are complicated, but you’re determined to understand who influences whom in this scene.

Now Structural Equation Modeling (SEM) comes into action: your gossip analyser. SEM is like the Sherlock Holmes of relationships. It doesn’t just look at surface-level connections; it digs deep to uncover the hidden links and causal effects between people (variables).

Step 1: The Problem.

At the reunion, you hear whispers like: 

“Alex is super confident because of Jamie.” 

“Jamie’s confidence depends on how often they talk to Taylor.” 

“Taylor only talks to Jamie when Alex isn’t around.”

These are complicated cause-and-effect relationships. You can’t just write them down as facts because you’re not sure about them. How can you show or map this web of influence of variables on each other?

Step 2: SEM come into action.

SEM steps in with a structured approach:

1. It assumes relationships based on your guesses or theory (e.g., “Jamie influences Alex”).

2. It collects data (e.g. observing who talks to whom, about whom, with whom and how often).

3. It uses mathematics to check if your assumptions hold true and adjusts all the relationships accordingly.

In short, SEM takes your gossip and turns it into evidence.

Step 3: How SEM Works.

SEM combines two Analysis:

1. Factor Analysis: Groups things that are similar but not directly measurable (like “confidence” being influenced by “talk frequency” and “smiles exchanged”).

2. Path Analysis: Draws arrows between factors to show who influences whom and how strong that influence is.

At the reunion, SEM would map out something like this:

• Alex → Jamie: “Alex boosts Jamie’s confidence by being a great friend.”

• Jamie → Taylor: “Jamie gets braver and talks to Taylor.”

• Alex ↔ Taylor: “When Alex and Taylor are both there, the vibe changes everything.”

Step 4: Real-Life Example.

Let’s leave the reunion and talk about something universal: Happiness.

Imagine you want to understand what makes people happy.

Your hunch is that:

• Income boosts Leisure Activities.

• Leisure Activities improve Health.

• Health and Leisure Activities both increase Happiness.

SEM would let you:

1. Test this theory with data.

2. Visualize it as a network of arrows (causal relationships).

3. Measure how strong each arrow (influence) is.

For example, SEM might reveal:

• Income indirectly improves happiness via more leisure activities and better health.

• Health has a stronger impact on happiness than income.

Step 5: Real-Life Applications of SEM.

SEM is like the detective of relationships. Here’s where it’s used:

1. Psychology: To study how self-esteem, relationships, and stress influence mental health.

2. Education: To understand how teaching methods, student motivation, and peer influence impact academic success.

3. Marketing: To uncover how brand trust, perceived quality, and price affect customer loyalty.

4. Healthcare: To study how diet, exercise, and mental health interact to influence well-being.

5. Social Sciences: To map complex societal interactions, like poverty, education, and social mobility.

Step 6: The Result.

With SEM, you don’t just guess who influences whom; you prove it. Whether it’s a high school reunion, happiness, or customer loyalty, SEM uncovers the hidden drama behind the scenes and helps you make informed decisions.

SEM is like your personal drama solver. It takes the tangled web of “he said, she said” and turns it into a clear, actionable story. It’s the science of relationships whether between people, variables, or concepts.

Next time you’re faced with a complex network of cause-and-effect relationships, think of SEM. Because every dataset has a story, and SEM helps you tell it.

🚀🚀🚀🚀Multi-Dimensional Scaling (MDS): Making Sense of a Crowded Metro Map

Imagine you’re visiting a new city, and someone hands you a complicated metro map with lot of stations. It’s overwhelming the distances between stations, the complex crisscrossing lines, and the sheer number of stops confuse you. Now, what if someone simplified this map, showing just the key stations and their relative positions while keeping it visually clear? That’s what Multi-Dimensional Scaling (MDS) does. It simplifies complex relationships while keeping the essence of it.

Step 1: The Problem

The metro map represents a dataset with many variables (like stations connected by different lines). The challenge is understanding how the stations relate to each other in terms of distance and position.

Step 2: MDS comes to action

MDS do these following things:

1. Looks at the actual distances between the stations (data points).

2. Rearranges them into a simpler, two-dimensional map while preserving the relative distances.

Imagine MDS laying out the stations in a way that you can see which are closer together, which are far apart, and how they relate to each other without needing to worry about every single detail.

Step 3: How MDS Works

MDS starts by asking:

• How far is Station A from Station B?

• Is Station C closer to A or B?

It then plots all the stations (data points) in a way that the distances on the map reflect their real-world distances as closely as possible.

Step 4: Real-Life Example:

Let’s apply MDS to your life.

You’re at a food festival, trying to decide what to eat. There are 20 food stalls offering cuisines from different countries. You’re overwhelmed!

• You taste a few dishes and rate how similar or different they feel to your taste preferences.

• MDS takes your ratings and creates a simple map showing cuisines grouped by similarity. You see that Indian and Thai foods are close together (spicy), while Italian and French are in another cluster (savory).

Now, you can navigate the festival with ease!

Step 5: Real-Life Applications of MDS

MDS is a master of simplifying complexity. Here’s where it shines:

1. Market Research: Mapping customer preferences based on product similarities.

2. Psychology: Visualizing how people perceive emotions or behaviors.

3. Genomics: Understanding relationships between genes or species based on genetic distance.

4. Social Media: Visualizing networks, like how close two people are in terms of mutual friends or interests.

5. Urban Planning: Representing traffic patterns or neighborhood similarities.

6. Sports Analytics: Grouping players based on performance metrics.

Step 6: The Result

With MDS, the metro map of your mind is simplified, and your decision-making becomes effortless. Whether it’s finding the best food stall, analyzing customer behavior, or understanding genetic similarities, MDS is your go-to guide for turning confusion into clarity.

MDS is like that friend who says, “Let’s simplify this mess!” It doesn’t throw away any important information but makes things easier to see and understand.

Next time you’re drowning in complexity, think of MDS. It’ll map out your data (or life) in a way that’s clear, concise, and actionable.