#Principal Components

[haveyoureadthisfanfic]

Summary: Anyone could last two months in prison. After an adventure in 1969 goes wrong, River has to infiltrate an isolated base in the US desert to rescue the Doctor from captivity at the hands of military scientists. By the time she discovers the lengths they have gone to learn the Doctor's secrets, it may be too late to save either of them.

Author: @eveeleven11-blog

[platypu]

[donumanimae]

*reduces your dimensions*

[juliebowie]

Step-by-Step Guide to Principal Component Analysis (PCA)

A comprehensive guide to performing Principal Component Analysis (PCA). Follow the step-by-step process to understand how PCA reduces data dimensionality and aids in data visualization and analysis.

[prajwalyyy22]

principal component analysis (PCA)

Dive into "What is Principal Component Analysis?" Simplify data intricacies, revealing key insights through effective dim

[maklodes]

I think “alcohol and salads” is the funniest PCA-based dietary pattern, but I’m open to changing my mind. "Southern" is also kinda funny.

[seat-safety-switch]

Here's the thing about kids: they'll work really hard, for not a lot of money. Child labour has been an essential component of the gettin'-stuff infrastructure since children were invented, and I figured it was high time I got my cut, too.

As opposed as I am to private high schools (they cost money,) I can't resist a chance to convince my parole officer I am indeed applying to jobs. And so it was that fateful morning when I got hired to replace Ms. Nettles, the former drama teacher, after she got in her Gremlin X and left the country entirely rather than do another minute of educating the leaders of tomorrow. The pay was shit, sure, but "theatre teacher" sounds a lot better in a courtroom than "freelance scumbag."

For the first couple days, it really wasn't that bad. Band/drama kids, like when I was in high school, were largely self-organizing. They built their own sets. They read the textbook and did their own exercises. They didn't complain too much when I told them that my "method" was to sit in the dimly-lit back of the room, put on dark glasses, and sleep while they worked hard to rehearse the big play. As far as they knew, all this was normal. Until it wasn't.

On the night of the big play, I dressed up. I did the gladhanding. The principal in particular was greatly impressed, telling me that he has heard fantastic things about my students and I was likely to be lifted aloft as a god of entertainment, eligible for a $0.25 cent per hour raise (not including grading, prep, and commute time) and revered forever. Just as long as the class production of Atlas Shrugged went off without a hitch.

Here's the thing about child labour, though: it's cheap for a reason. Turns out, without me being there to teach them what to do, the kids actually read the book. And then they got mad at each other about the book, and they decided to do their own version. If I had been awake at any point during class over the last four months, I probably could have stopped the development of, or at least the staging of, Atlas Fucked.

Things could have gone worse. I managed to pivot blame onto their free-thinking history teacher, who was no doubt filling their minds with Communist indoctrination, and slipped out the back door. A new drama teacher would replace me, ready to put on a production where the kids (and by extension their parents) could be told the things they already believed. I didn't leave empty-handed, though. In addition to the meagre salary I extracted, I also got to loot the principal's office while he was busy watching the show. Got a pretty nice stapler.

[worrywarwrites]

LET'S TALK COSTUMES YALL!

I don't completely understand the dislike of the Wembley production too well (It's a non-replica production yall, for what it is it's a lot of fun!) but I have seen that a major point of contention for people seems to be the costumes, so I wanted to create a post discussing why I think they are done very well.

First off, they are wonderfully colorful- one of the things that always concerns me in costuming is a disappearance of color in favor of darker neutral colors, but even the characters that have closer to neutral pallets- Rusty, Momma, the Components- all still have elements of color within their designs, and different textures and shapes to make them visually interesting. As this musical is a dream being had by a little kid, the colors also help reflect this as well- Control is an imaginative child, whose made up world reflects that.

The three main engines (Rusty, Greaseball, Electra) all have very distinct appearances, marking them as principal figures and representative of the three different types of engine we see- diesel, steam, and electric. All three have unique color pallets and silhouettes- the exception being Rusty, who shares similar design elements with Momma (though not quite the same colors). The are the main three racers the story revolves around, and they stand out accordingly.

The thing about the other costumes that interests me, however, is how despite the fact that the rest of the characters in the show are all different colors (with the exception of the Components, whose costumes denote them as a group unique to Electra), there are certain design elements used on the other engines, coaches, and freights that helps denote them as such.

The champion engines are the easiest example here- they all have identical costume elements, just done in different colors. All of them have fin-like hairstyles, and identical plating: shoulder pieces that when an actors hands are at their sides can stretch up to their ears, a rounded breastplate with the symbol of the engine in question, and two pieces for the legs.

The coaches also have this- despite being a myriad of colors and having elements unique to their design, they are a couple through lines- namely a piece around the waist than fans out similar to a skirt, and padding on the shoulders (except for Pearl, but she's got other stuff going on there). They also have more form fitting pieces on their legs- similar more to regular pants or leggings, which makes the detail at the waist and the padding at the shoulders the widest parts of the silhouette.

The freights also have a very similar construction of their costumes- oversized pants and large vests with shoulder plating, and then smaller pieces for the arms- they all very clearly do the same job, despite being different colors and with different patterns (Hydra is not an exception to this, but there are subtle differences signifying how he differs from the others- the plating on his arms is not as bulky as the others, the colors on his pants are inverted, and the vest comes down to his waist rather than stopping below his ribs, giving a smoother silhouette and less bulky appearance, to name a few examples).

And of course, the Components- all trucks like the freight, but their main job in the show isn't what they carry- it's to make Electra look good. As such, they all very clearly fit Electra's aesthetic in a way that none of the other coaches or freight fit the other engines- complementary silver and white to their blue and silver, with the only personalization their belts and the shape of the protrusions from their plating. (They aren't the focus of the next picture but I love it too much not to put here in some fashion.)

All of this is deliberate attention to detail- as the majority of theatre-goers are not going to be intimately familiar with the characters, and the train types, and the roles, and the story, and- you get the idea. The shapes of a character's costume helps denote them into a group- if nothing else, an audience member can tell you "oh, that's an engine" or "that's freight". It also helps people sitting further away to track the action a little better- costume details and textures will become invisible at a distance, but bright colors, large shapes and consistent silhouettes help everyone have a good time.

So, if you didn't know anything about the musical, what could you tell me about the trains in this picture?

[bloodyshadow1]

So I made a post about Adaine being the principal after killing Arthur Aguefort in a duel. And if that happens I think it would be fun for the bad kids to join her as teachers so here's what I think they teach

Kristen- Cleric teacher obviously. I think she's the most powerful and best cleric in the world, or at the very least Elmville even if she stumbles a lot. I think her background as helioic/solesian, who created her own god and found then revived another gives her a very unique perspective for any young clerics out there. I also think as someone who worships a pantheon it would work like Yolanda giving up her path of following a single god to be more fair to the students she teaches, unlike Bobby Dawn. Kristen has made as many mistakes as you can as a cleric so she would be a very good person to teach kids who might have anxiety about their choices.

Fabian- Bard Teacher, dance and sword. Corsica is a young woman as the fighter teacher so there's no real reason to replace her when the bad kids come of age. Fabian also drifted away from fighter so hard to bard it's clear where his heart is even if he's still an amazing fighter. I think he would be the teacher that brags about being the future and present of dance, along with being the Oracool of Dance to his students. He also has made a lot of steps from his stumbles in his school days and assures his students it's okay to fail, it's okay to wallow but you do have to pick yourself up still. Seacaster manor is still used as a study hall for any students who need it and his is the teacher willing to help any and all students, no matter the class or grade

Gorgug- Barbarian teacher. While I think artificing has his heart more, I could see Gorgug as an amazing Barbarian teacher. His goal is to undo a lot of the toxic aspects of rage and being a barbarian that people like Porter tried to force upon the class and the students taking it. He teaches about the positives of rage, that while it's a strong weapon, it can be an amazing shield to protect people. He is also the main multiclass advisor, he never refuses an MCAT request, he does ask questions but to let students talk about their interests not to make thing think their ideas are stupid or pointless

Riz- Rogue teacher. I think Riz starts to work for the CoC (Council of Chosen) for a bit after graduation, but doesn't like it since it feels more like Narc shit than spy work like his dad did. He's more fair than Yolanda, he is on school grounds more so kids have a chance to find him instead of having to go to a town miles away to find Eugenia. He focuses on the practical application of being a rogue, stressing that it's more than just damage for sneak attack. Being a rogue is about team work to make sneak attack easier, knowing your terrain to making hiding easier and not to jump into lava when you're not fire resistant or immune, investigating things not just focus on killing people

Fig- Sorcery teacher. Obviously she wouldn't be the bard teacher. She didn't go to bard classes as a student, why would she go as a teacher, despite being one of the most famous musicians in Spire. At first it seems like she's just another Jace, you know just hanging with her students instead of really teaching because sorcery is innate. But she's actually very good with them, she actually has experience in knowing what it's like to get powers from your blood instead of hard work. she also encourages her students to try multiclassing since they have time at school, she doesn't want them wasting the time they have when their young. Hackysack is fun, but they should try things when they're young and can get easy A's so try other class.

Adaine- Before she became principal she takes over for Tiberia as the wizarding teacher. she is much kinder and sympathetic than the previous teacher. She also doesn't make her students buy their own spell components and she makes sure that they know that they can explore other disciplines. Everyone thinks she's the sweet gentle wizard teacher until one of her students get bullied and she throws the other kid off them, or a monster attacks the school and she just decks it in the face exploding it's skull from the force of the blow. I also think she recommends that her students get exercise more than any previous wizard teacher. Studying and reading is important, but spells aren't everything, sometimes a healthy lifestyle can save you more than just magic.

[writerandbaka]

The jackal and the witch AU ～ Tighnari and Cyno 💚💜

I have sketched out a reference sheet for witch Tighnari and jackal Cyno! Soon I'll draw those of other characters as well for future chapters! ฅ(◕ᴥ◕)ฅ

And as promised, here are my headcanons for this AU:

Magic is basically a component of every living being and manifests itself in different amounts and shapes in different individuals

Magic is invisible to humans. However, some humans are able to perceive it

Humans who know how to use their own magic and that of their surroundings, shaping it to their liking, are called "witches"

"Witch" is a generic word used for people of any gender without distinction (gentleman, ladies, non-binary specimen etc…)

Through spells, witches can shape magic to alter reality

There are mainly two types of spells: those that are free and uncontrolled, and those that are infused in potions

A free spell is easier because it applies directly to reality, which is thus modified at will. However, it’s more difficult to be controlled and managed if you don’t have good control over your magic

A spell infused in a potion is more controlled and specific than a free one. On the other hand, however, it's more difficult to achieve the desired effect this way

Generally, spells are temporary. That means that the magic that shapes and changes reality tends to resume its original form within a certain period of time, returning reality to its original state too

A permanent spell is consequently more complicated and difficult to accomplish. Permanently altering reality requires a good deal of magical power to force the magic of the environment to change shape forever

To perform a spell, the witch's magic influences the external magic, and weaving them together can have a different effect on reality

The witch's personal emotions are very important and act as a catalyst to manage and control magic itself. If one doesn’t have good control of their magic, when they use it, the environment magic can take over from the witch, taking command of the course of the spell and dragging the witch to its will

Spirits are creatures able to see magic, being themselves made of pure magic

Spirits come from the spirit realm, a realm separate from the earthly realm of Teyvat. They can descend to earth only when the veil between the two realms thins, during full moon nights

Spirits can take corporeal bodies only through a contract with a witch, thus becoming "familiars"

The form the familiars take depends on many factors, the character of the witch, their amount of magical power, etc. But they are always only animal forms

To enter into a contract, the witch and familiar set their own conditions (a wish, specific needs, etc.) and when these are approved or met by both parties, the contract is finally sealed

The contract between a witch and a familiar is also manifested by two small objects carried by both of them, which can be jewelry, accessories, etc.

Having a familiar is not mandatory for a witch. The spirit simply helps them control their magical power by giving them an extra dose of magic to draw on and helping them stabilize their own

The witch and the familiar share strong emotions and feelings through their bond

The witch and the familiar cannot be excessively physically distant from each other for long periods of time

The contract between a familiar and a witch binds them inextricably until the death of one of them, usually the witch. In some cases, spirits too can also die if their magic is absorbed or corrupted due to a curse

Curses are nothing more than enchantments or spells whose effects are usually negative for the creature they are aimed at

Curses may be the cause of the presence of exceptions to what has just been written so far 

The Akademiya is a witchcraft school, where students of any age can be admitted to learn to study magic

The council of Sages, or senior professors, are bigoted people who are in charge of school management, often bypassing the principal when the latter is not physically present

There is tension between the principal and the current council of Sages, for a variety of reasons

So, no visions for this AU, but each character still has different aptitudes for certain types of elemental magic rather than others

That’s all!!✨

I won't spoil anything more about the plot, but these are pretty much the things to keep in mind as the story progresses. All of them will be picked up as we go along at various points, so don't worry, I will specify everything again at the right time, so that you can appreciate the fic even without the need of this post (｡•̀ᴗ-)✧

Oh btw, If you haven't read it yet or if this sketch has made you curious about this AU, here is the first chapter of the Ao3 fic I am talking about! The next chapter will be posted on Monday and is already basically ready! Can't wait for you to read it!!!🪄🌱💕

[whencyclopedia]

Boeing B-29 Superfortress

The Boeing B-29 Superfortress was a four-engined, long-range bomber of the United States Air Force. The largest of all Second World War (1939-45) bombers, B-29s were used to strike Japanese targets from the summer of 1944. In August 1945, the B-29s 'Enola Gay' and 'Bockscar' each dropped an atomic bomb on Hiroshima and Nagasaki, respectively, thereby ending the war.

Development

In the 1930s, the United States Army Air Corps (USAAC) required a long-range strategic bomber that could attack enemy targets thousands of miles from the aircraft's home base. One of the problems to make such an aircraft a reality was to find engines which were powerful enough for the task. The project to design and build a long-range, high-altitude precision bomber, or VLR (Very Long Range) as such aircraft became known, was greatly accelerated following the invasion of Poland in 1939 by Nazi Germany and the outbreak of WWII. In January 1940, five aircraft companies were tasked with designing a VLR bomber. Four companies came back with a design proposal: Consolidated, Douglas, Lockhead, and Boeing. After two of the companies later withdrew, only Consolidated and Boeing won construction contracts in September 1940. Ultimately, each company built three prototypes. Boeing's construction plans were more advanced since it had already been working on modifications of its existing Boeing B-17 Flying Fortress design. Boeing received an order of 1,500 VLRs and promised these aircraft would be ready within three years.

Following the Japanese attack on Pearl Harbour in Hawaii, home of the US Pacific naval fleet, on 7 December 1941, the need for VLRs in the vast theatre of the Pacific Ocean suddenly became a necessity. The first Boing VLR prototype, called XB-29, flew on 21 September 1942. The very large wings of the craft were designed to help it land at lower speeds, and tricycle landing gears helped bear the tremendous weight. 14 test aircraft began to fly from June 1943. The planes were built at four principal plants: Renton, Wichita, Marietta, and Omaha. Boeing, Bell, and Martin were just three of the main companies involved, but there were thousands of others providing components and partial assembly. The B-29 project "was the largest aircraft manufacturing project undertaken in the USA during World War II" (Mondey, 29). It was also the most expensive. From the autumn of 1943, the first B-29 bombers were delivered to US air bases.

B-29 Superfortress in Flight

US Air Force (Public Domain)

Continue reading...

[deconstructthesoup]

Thinking about Fantasy High and The Seven again and---

I love the dichotomy between the way Brennan plays Kalvaxus in the Fantasy High seasons and the way he played him in The Seven. Because, yeah, he was the BBEG for Freshman Year, he was a powerful red dragon, he was the guy who ate Riz's dad... but to the Bad Kids, he was, first and foremost, Goldenrod. He was their vice principal who they made fun of, and when he turned out to be a villain, they were absolutely merciless in their takedown of him. So, Brennan played him to be a little bit goofy, with the "THIS RULES!" line when he transforms back into a dragon and the whole libertarian spiel. And, of course, he winds up getting turned into a pirate ship, and he's just a beaten-down, pathetic asshole when we see him in Hell.

But in The Seven? In Danielle's Time & Space sequence?

He's terrifying. He's a menacing dracolich who peers straight into their insecurities and mocks them for it. None of that gleeful little mania at being rich, none of that Goldenrod energy---no, he's a goddamn nightmare.

And that's how The Seven see him.

He's not their hardass vice principal who seemed pretty well-meaning yet over his head, who they cheerfully teased in their teenager fashion and promptly turned that good-natured teasing to full Vicious Mockery when they realized he was legitimately evil. He's the guy who kidnapped them, imprisoned them in gems, and then turned them into sacrificial spell components. They lost months off of their lives, got separated from their family and friends, and probably would've gotten eaten if his plan had succeeded.

So of course he's so much more scary in that scene in The Seven than he was in Freshman Year. Of course every single line that comes from his mouth is absolutely chilling, of course he goes full menacing dragon.

...That being said, if we get a second season of The Seven, I think they should get to go to Hell and throw a rager on the Goldenrod that absolutely trashes it.

[askvectorprime]

Where do the names "Autobot" and "Decepticon" even come from? Are there any sort of root words that go with them?

Dear Etymology Enthusiast,

This answer is complicated by language barriers that span galaxies. As Galvatron alluded to—albeit in tones I would never use—Cybertronian words can be very linguistically dense; a translation that conveyed every nuance of our equivalent for "Autobot" would take over seventeen minutes for a human to say! As such, "Autobot" and "Decepticon" are only approximations of the neocybex names of these factions.

In many universes, my faction is named for the ideals of freedom and autonomy—hence, "Autobot" is derived from the term "autonomous". Sometimes this reflects a casting off of Quintesson rule or triumph over a caste system, but in other contexts—sometimes simultaneously—it reflects a darker facet of Cybertronian history. A famous bot once said that autonomy was a gift, a spark of sentience kindled by Primus himself. That bot's name was Nova Prime, and he used that belief to justify the subjugation of hundreds of alien worlds.

The suffix translated as "-bot" encompasses ideas such as "person", "individual", "independent agent". It could be considered an adaptation of the common English-language "man", of course—you might be familiar with the Aerialmen, the Dinomen, and the Sparkamen—but "bot" conveys that it most commonly refers to mechanical lifeforms. While typically used in the names of teams and factions, occasionally an individual might be called "Dinobot" or "Dreadbot"; such sobriquets can be seen as similar to a human being carrying a family name as their first name, such as "Jackson".

As for "Decepticon"… much has been said of the phrase "you are being deceived." In many universal clusters, this is indeed the earliest origin of the term. "Decepticon" suffers to a greater degree from the imperfections of localization. In many universes, Cybertronian language uses nuances related to subject and object that fail to translate, especially when neologism is concerned; "Decepticon" principally suggests "deceptive" in English, but in its original Cybertronix, the waveform can simultaneously be read as "the deceived".

The "-con" suffix is not dissimilar to "-bot", though it carries subtly but significantly different implications. "Person" is an adequate translation, but its meaning is much broader, not being restricted to living creatures; you may know of data-cons, information storage devices commonly used in my home reality. The closest equivalent to the suffix in your language would be "entity"—or, more bluntly, "thing". As such, the translation "-con" is derived from your language's "construct", a created object or idea.

The reasoning for the use of this suffix varies across the multiverse. On versions of Cybertron where Functionism took hold, Cybertronians of lower labor castes, or with alternate modes considered fit only for use by others, were more likely to have "con" names or be assigned categories like "Constructicon", "Agricon" or "Recordicon". Conversely, in universes where the Decepticons originate as a military junta, the use of "-con" carries the suggestion of component; all Decepticons are considered to be a part of Megatron's war machine. These implications, of course, carry over to the Mini-Cons. While I am proud to count Safeguard as a friend and partner, for much of my world's history, Decepticon and Autobot alike treated his kind as "smart tools", as mere objects to be collected. Regardless, the Great War created extreme political polarization of the "-con" suffix, and nearly no self-described Autobot adopts it; even as Decepticons freely use "bot" to describe themselves, "con" is almost exclusively used by Autobots as a term of animosity.

One more suffix you may have heard of is "-tron"; here, the root is "positron"—which, before the introduction of microscope alt-modes, we simply understood to be the stuff of sparks. The Cybertron factions of realities like the G1 World and BT World draw their names from a well of indigeneity; unlike the invading, colonizing Quintessons, the Cybertrons are the true sparks of the planet and derive their name thus. The Destrons, then, are destructive sparks who oppose the planet. Naturally, "-bot" and "-con" recur in these worlds too, following similar etymological patterns.

[juliebowie]

Understanding Principal Component Analysis (PCA)

The world of data is vast and complex. Machine Learning thrives on this data, but with great power comes great responsibility (to manage all those features!). This is where Principal Component Analysis (PCA) steps in, offering a powerful technique for simplifying complex datasets in Machine Learning.

What is Principal Component Analysis?

Imagine a room filled with clothes. Each piece of clothing represents a feature in your data. PCA helps you organize this room by identifying the most important categories (like shirts, pants, dresses) and arranging them efficiently.

It does this by transforming your data into a lower-dimensional space while capturing the most significant information. This not only simplifies analysis but also improves the performance of Machine Learning algorithms.

Fundamentals of Principal Component Analysis (PCA)

At its core, Principal Component Analysis (PCA) is a technique used in Machine Learning for dimensionality reduction. Imagine a room filled with clothes, each piece representing a feature in your data.

PCA helps organize this room by identifying the most important categories (like shirts, pants, dresses) and arranging them efficiently in a smaller space. Here’s a breakdown of the fundamental steps involved in PCA:

Standardization

PCA assumes your data is centered around a mean of zero and has equal variances. Standardization ensures this by subtracting the mean from each feature and scaling them to have a unit variance. This creates a level playing field for all features, preventing biases due to different scales.

Covariance Matrix

This matrix captures the relationships between all features in your data. A high covariance value between two features indicates they tend to move together (e.g., height and weight). Conversely, a low covariance suggests they are relatively independent.

Eigenvectors and Eigenvalues

PCA finds a set of directions (eigenvectors) that explain the most variance in your data. Each eigenvector is associated with an eigenvalue, which represents the proportion of variance it captures.

Think of eigenvectors as new axes along which your data can be arranged, and eigenvalues as measures of how “important” those axes are in capturing the spread of your data points.

Component Selection

You choose the most informative eigenvectors (based on their corresponding eigenvalues) to create your new, lower-dimensional space. These eigenvectors are often referred to as “principal components” because they capture the essence of your original data.

By selecting the top eigenvectors with the highest eigenvalues, you retain the most important variations in your data while discarding less significant ones.

Understanding these fundamentals is crucial for effectively using PCA in your Machine Learning projects. It allows you to interpret the results and make informed decisions about the number of components to retain for optimal performance.

Applications of PCA in Machine Learning

PCA is a versatile tool with a wide range of applications:

Dimensionality Reduction

As mentioned earlier, PCA helps reduce the number of features in your data, making it easier to visualize, analyze, and use in Machine Learning models.

Feature Engineering

PCA creates new, uncorrelated features (principal components) that can be more informative than the originals for specific tasks.

Anomaly Detection

By identifying patterns in the principal components, PCA can help you detect outliers and unusual data points.

Image Compression

PCA plays a role in compressing images by discarding less important components, reducing file size without significant visual degradation.

Recommendation Systems

PCA can be used to analyze user preferences and recommend relevant products or services based on underlying patterns.

Implementing PCA in Machine Learning Projects

While the core concepts of PCA are crucial, its real power lies in its practical application. This section dives into how to implement PCA in your Machine Learning projects using Python libraries like Scikit-learn.

Prerequisites

Basic understanding of Python programming

Familiarity with Machine Learning concepts

Libraries

We’ll be using the following libraries:

Pandas: Data manipulation

Numpy: Numerical computations

Scikit-learn: Machine Learning algorithms (specifically PCA from decomposition)

Note: Make sure you have these libraries installed using pip install pandas, numpy, scikit-learn.

Sample Dataset

Let’s consider a dataset with customer information, including features like age, income, spending habits (various categories), and location. We want to use PCA to reduce dimensionality before feeding the data into a recommendation system.

Step 1: Import libraries and data

Step 2: Separate features and target (optional)

In this example, we’re focusing on dimensionality reduction, so we don’t necessarily need a target variable. However, if your task involves prediction, separate the features (explanatory variables) and target variable.

Step 3: Standardize the data

PCA is sensitive to the scale of features. Standardize the data using StandardScaler from scikit-learn.

Step 4: Create the PCA object

Instantiate a PCA object, specifying the desired number of components (we’ll discuss this later) or leaving it blank for an initial analysis.

Step 5: Fit the PCA model

Train the PCA model on the standardized features.

Step 6: Analyze explained variance

PCA outputs the explained variance ratio (explained_variance_ratio_) for each principal component. This represents the proportion of variance captured by that component.

Step 7: Choose the number of components (n_components)

Here’s the crux of PCA implementation. You need to decide how many principal components to retain. There’s no single answer, but consider these factors:

Explained variance: Aim for components that capture a significant portion of the total variance (e.g., 80–90%).

Information loss: Retaining too few components might discard valuable information.

Model complexity: Using too many components might increase model complexity without significant benefit.

A common approach is to iteratively fit PCA models with different n_components and analyze the explained variance. You can also use tools like the scree plot to visualize the “elbow” where the explained variance plateaus.

Step 8: Transform the data

Once you’ve chosen the number of components, create a new PCA object with that specific value and transform the data into the principal component space.

Note: The transformed_data now contains your data projected onto the new, lower-dimensional space defined by the principal components.

Step 9: Use the transformed data

You can now use the transformed_data for further analysis or train your machine learning model with these reduced features.

Additional Tips:

Explore visualization techniques like plotting the principal components to understand the underlying structure of your data.

Remember that PCA assumes linear relationships between features. If your data exhibits non-linearity, consider alternative dimensionality reduction techniques.

By following these steps, you can effectively implement PCA in your machine learning projects to unlock the benefits of dimensionality reduction and enhance your models’ performance.

Frequently Asked Questions

How Much Dimensionality Reduction is Too Much?

There’s no one-size-fits-all answer. It depends on your data and the information you want to retain. Evaluation metrics can help you determine the optimal number of components.

Can PCA Handle Non-linear Relationships?

No, PCA works best with linear relationships between features. For non-linear data, consider alternative dimensionality reduction techniques.

Does PCA Improve Model Accuracy?

Not always directly. However, by simplifying data and reducing noise, PCA can often lead to better performing Machine Learning models.

Conclusion

PCA is a powerful tool that simplifies complex data, making it a valuable asset in your Machine Learning toolkit. By understanding its core concepts and applications, you can leverage PCA to unlock insights and enhance the performance of your Machine Learning projects.

Ready to take your Machine Learning journey further?

Enrol in our free introductory course on Machine Learning Fundamentals! Learn the basics, explore various algorithms, and unlock the potential of data in your projects.

[talonabraxas]

"Qabalah" The Tree Of Life And The Qliphoth. T. Ketola The Four Worlds Spiritual, Mental, Astral, Physical

The colour-related pages in this site are organised according to the Hebrew names for the ‘Four Worlds’ of the Qabalah/Kabbalah: Atziluth, Briah, Yetzirah and Assiah. The extensive symbolic structure of the Tree — including the Colour Scales used to make the Trees in Colour — is built around these ‘Four Worlds.’ There are other versions of these Worlds to be found, but these are the ones I learned through study with The Servants of the Light.

The Luminous Tree is principally about colour, although everything on the Tree is interrelated so other aspects will slip in — and each component part has numerous attributes. For those not yet familiar with colour in the modern Qabalah of the Western Mystery Schools, in the 1800s the Hermetic Order of the Golden Dawn determined a different set of colours for each of the Sephira and each of the Paths in all Four Worlds. This site exists to present, research and consider that fact.

Although elegant and cohesive, the Qabalah is inherently complex and can be confusing, especially when starting out. However sometimes things can be made a bit clearer without oversimplifying and further understand grows from there.

In an interview with Sounds True (that no longer appears on their website), Dolores Ashcroft-Nowicki discussed Pathworking and mentioned the Four Levels in a way that helped me better understand the Four Worlds. She called them:

The Spiritual The Mental The Astral The Physical

In the same interview, she also said: “…We’ve got these four [levels] — the physical, the astral, the mental, and the spiritual. And not only that, there are spaces between those levels. Dimensions that exist between them.” The same also applies to the Tree.