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Random forests A single decision tree can learn quite complex functions. However, in many ways it will be prone to overfitting—learning rules that work only for the training set. One of the ways that we can adjust for this is to limit the number of rules that it learns. For instance, we could limit the depth of the tree to just three layers. Such a tree will learn the best rules for splitting the dataset at a global level, but won't learn highly specific rules that separate the dataset into highly accurate groups. This trade-off results in trees that may have a good generalization, but overall slightly poorer performance.

To compensate for this, we could create many decision trees and then ask each to predict the class value. We could take a majority vote and use that answer as our overall prediction. There are two problems with the aforementioned procedure.

The first problem is that building decision trees is largely deterministic—using the same input will result in the same output each time. We only have one training dataset, which means our input will be the same if we try build multiple trees. We can address this by choosing a random subsample of our dataset, effectively creating new training sets. The second problem is that the features that are used for the first few decision nodes in our tree will be quite good. Even if we choose random subsamples of our training data, it is still quite possible that the decision trees built will be largely the same.

To compensate for this, we also choose a random subset of the features to perform our data splits on. Then, we have randomly built trees using randomly chosen samples, using randomly chosen features. This is a Random Forest and, perhaps unintuitively, this algorithm is very effective on many datasets. An introduction to online learning Online learning is the incremental updating of a model as new data arrives.

Algorithms that support online learning can be trained on one or a few samples at a time, and updated as new samples arrive. In contrast, algorithms that are not online require access to all of the data at once. The standard k-means algorithm is like this, as are most of the algorithms we have seen so far in this module. Online versions of algorithms have a means to partially update their model with only a few samples. Neural networks are a standard example of an algorithm that works in an online fashion. As a new sample is given to the neural network, the weights in the network are updated according to a learning rate, which is often a very small value such as 0.01.

This means that any single instance only makes a small change to the model. Neural networks can also be trained in batch mode, where a group of samples are given at once and the training is done in one step. Algorithms are faster in batch mode, but use more memory. In this same vein, we can slightly update the k-means centroids after a single or small batch of samples. To do this, we apply a learning rate to the centroid movement in the updating step of the k-means algorithm.

Assuming that samples are randomly chosen from the population, the centroids should tend to move towards the positions they would have in the standard, offline, and k-means algorithm. Online learning is related to streaming-based learning; however, there are some important differences. Grouping news articles The aim of this chapter is to discover trends in news articles by clustering, or grouping, them together. To do that, we will use the k-means algorithm, a classic machine-learning algorithm originally developed in 1957. Clustering is an unsupervised learning technique and we use clustering algorithms for exploring data.

Our dataset contains approximately 500 stories, and it would be quite arduous to examine each of those stories individually. Even if we used summary statistics, that is still a lot of data. Using clustering allows us to group similar stories together, and we can explore the themes in each cluster independently.

We use clustering techniques when we don't have a clear set of target classes for our data. In that sense, clustering algorithms have little direction in their learning. They learn according to some function, regardless of the underlying meaning of the data. For this reason, it is critical to choose good features.

In supervised learning, if you choose poor features, the learning algorithm can choose to not use those features. For instance, support vector machines will give little weight to features that aren't useful in classification. However, with clustering, all features are used in the final result— even if those features don't provide us with the answer we were looking for. When performing cluster analysis on real-world data, it is always a good idea to have a sense of what sorts of features will work for your scenario.

In this chapter, we will use the bag-of-words model. We are looking for topic-based groups, so we will use topic-based features to model the documents. We know those features work because of the work others have done in supervised versions of our problem.

In contrast, if we were to perform an authorship-based clustering, we would use features such as those found in the Chapter 9, Authorship Attribution experiment. Creating your own transformer As the complexity and type of dataset changes, you might find that you can't find an existing feature extraction transformer that fits your needs. We will see an example of this in Chapter 7, Discovering Accounts to Follow Using Graph Mining, where we create new features from graphs. It takes data of one form as input and returns data of another form as output. Transformers can be trained using some training dataset, and these trained parameters can be used to convert testing data.

It takes data of a specific format as input and returns data of another format as output. Note The curse of dimensionality It is important to mention that KNN is very susceptible to overfitting due to the curse of dimensionality. The curse of dimensionality describes the phenomenon where the feature space becomes increasingly sparse for an increasing number of dimensions of a fixed-size training dataset. Intuitively, we can think of even the closest neighbors being too far away in a high-dimensional space to give a good estimate. We have discussed the concept of regularization in the section about logistic regression as one way to avoid overfitting.

This will be discussed in more detail in the next chapter. Kernels When the data cannot be separated linearly, the trick is to embed it onto a higher dimensional space. What this means, with a lot of hand-waving about the details, is to add pseudo-features until the data is linearly separable . The trick is that we often compute the inner-produce of the samples when finding the best line to separate the dataset. Given a function that uses the dot product, we effectively manufacture new features without having to actually define those new features.

This is handy because we don't know what those features were going to be anyway. We can now compute what that dot product is and then just use that. The linear kernel is the most straightforward and is simply the dot product of the two sample feature vectors, the weight feature, and a bias value. There is also a polynomial kernel, which raises the dot product to a given degree . Others include the Gaussian and Sigmoidal functions. In our previous code sample, we tested between the linear kernel and the rbf kernels.

The end result from all this derivation is that these kernels effectively define a distance between two samples that is used in the classification of new samples in SVMs. In theory, any distance could be used, although it may not share the same characteristics that enable easy optimization of the SVM training. In scikit-learn's implementation of SVMs, we can define the kernel parameter to change which kernel function is used in computations, as we saw in the previous code sample. The user can select either Yes or No depending on whether they think the choice made by the machine-learning algorithm matches the choice they would have made. This is not scientifically accurate (it's ripe for observation bias), but it's good enough for playing around. Using my eyes, it succeeded about 84 percent of the time, which is better than my grade 12 average.

Not bad for our first ever machine learning experience, eh? You might be wondering, "what does this have to do with object-oriented programming? There isn't even one class in this code!". In some ways, you'd be right; neither coroutines nor generators are commonly considered object-oriented. However, the functions that create them return objects; in fact, you could think of those functions as constructors. The constructed object has appropriate send() and __next__() methods.

Basically, the coroutine/generator syntax is a syntax shortcut for a particular kind of object that would be quite verbose to create without it. This case study has been an exercise in bottom-up design. We created various lowlevel objects that did specific tasks and hooked them all together at the end.

I find this to be a common practice when developing with coroutines. The alternative, topdown design sometimes results in more monolithic pieces of code instead of unique individual pieces. In general, we want to find a happy medium between methods that are too large and methods that are too small and it's hard to see how they fit together.

This is true, of course, regardless of whether the iterator protocol is being used as we did here. Let's assume that we fit our model on a training dataset and use the same data to estimate how well it performs in practice. To find an acceptable bias-variance trade-off, we need to evaluate our model carefully. In this section, you will learn about an extremely handy tool, the Pipeline class in scikit-learn. It allows us to fit a model including an arbitrary number of transformation steps and apply it to make predictions about new data.

As a simple algorithm; if the height is more than x, the person is tall, otherwise they are short. Our training algorithm will then look at the data and decide on a good value for x. For the preceding dataset, a reasonable value would be 170 cm.

Anyone taller than 170 cm is considered tall by the algorithm. In the preceding dataset, we had an obvious feature type. We wanted to know if people are short or tall, so we collected their heights. This engineering feature is an important problem in data mining. In later chapters, we will discuss methods for choosing good features to collect in your dataset.

Ultimately, this step often requires some expert domain knowledge or at least some trial and error. It is called lazy not because of its apparent simplicity, but because it doesn't learn a discriminative function from the training data but memorizes the training dataset instead. This objective function is often a cost function that we want to minimize. In the case of Adaline, we can define the cost function to learn the weights as the Sum of Squared Errors between the calculated outcomes and the true class labels . Printing c.most_common gives the list of the top five most frequently occurring words. Ties are not handled well as only five are given and a very large number of words all share a tie for fifth place.

The first is to use the raw frequencies, as shown in the preceding example. This does have a drawback when documents vary in size from fewer words to many words, as the overall values will be very different. The second model is to use the normalized frequency, where each document's sum equals 1. This is a much better solution as the length of the document doesn't matter as much. The third type is to simply use binary features—a value is 1 if the word occurs at all and 0 if it doesn't. We will use binary representation in this chapter.

Another popular method for performing normalization is called term frequency - inverse document frequency, or tf-idf. In this weighting scheme, term counts are first normalized to frequencies and then divided by the number of documents in which it appears in the corpus. We will use tf-idf in Chapter 10, Clustering News Articles. There are a number of libraries for working with text data in Python.

We will use a major one, called Natural Language ToolKit . The scikit-learn library also has the CountVectorizer class that performs a similar action, and it is recommended you take a look at it . However the NLTK version has more options for word tokenization.

If you are doing natural language processing in python, NLTK is a great library to use. Our media player can play this object just as easily as one that extends AudioFile. Polymorphism is one of the most important reasons to use inheritance in many object-oriented contexts. Because any objects that supply the correct interface can be used interchangeably in Python, it reduces the need for polymorphic common superclasses. Inheritance can still be useful for sharing code but, if all that is being shared is the public interface, duck typing is all that is required. Of course, just because an object satisfies a particular interface does not mean it will simply work in all situations.

It has to fulfill that interface in a way that makes sense in the overall system. Just because an object provides a play() method does not mean it will automatically work with a media player. For example, our chess AI object from Chapter 1, Objectoriented Design, may have a play() method that moves a chess piece. Even though it satisfies the interface, this class would likely break in spectacular ways if we tried to plug it into a media player! Another useful feature of duck typing is that the duck-typed object only needs to provide those methods and attributes that are actually being accessed.

More succinctly, duck typing doesn't need to provide the entire interface of an object that is available, it only needs to fulfill the interface that is actually accessed. Compressing Data via Dimensionality Reduction—are the size n of the bootstrap sample and the number of features d that is randomly chosen for each split (step 2.1), respectively. Via the sample size n of the bootstrap sample, we control the bias-variance tradeoff of the random forest. By choosing a larger value for n, we decrease the randomness and thus the forest is more likely to overfit. On the other hand, we can reduce the degree of overfitting by choosing smaller values for n at the expense of the model performance. For the number of features d at each split, we want to choose a value that is smaller than the total number of features in the training set.

A reasonable default that is used in scikit-learn and other implementations is training set. Character n-grams We saw how function words can be used as features to predict the author of a document. An n-gram is a sequence of n objects, where n is a value . Word n-grams have been used in many studies, usually relating to the topic of the documents. However, character n-grams have proven to be of high quality for authorship attribution. Character n-grams are found in text documents by representing the document as a sequence of characters.

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Apple Watch Series 6 40Mm Bands Amazon

There are tons of Apple Watch band options, with a variety of options to suit different needs and watch sizes. You can go for the office-acceptable nylon strap or leather loop with a modern buckle, a ballroom-worthy link bracelet, a sport loop band made from soft silicone or a rugged woven nylon band. Heck, there are even Italian leather and rose gold options out there if you're feeling fancy. Different watch bands come with different closures as well, so if you're on the lookout for a stainless steel buckle or a magnetic clasp, chances are they exist. An official Apple accessory, the Apple Watch Sport Loop has a double-layer nylon design that features extra cushion and comfort, making it ideal for many activities and all-day wear. Nylon is breathable, so you can wear this Apple sport loop straight from a morning workout to a morning meeting.

This Apple watch strap also comes in a multitude of colors, so there's something for everyone. Apart from the sports loop, there is also an Apple sport band, solo loop, braided solo loop and Nike sport loop available in different color options. The Fitbit Inspire 2 is a great option if you want a fitness tracker with a slim design that's under $100. The wearable device has a 24/7 heart rate tracker and up to 10 days of battery life.

Standout features include breathing sessions, menstrual health tracking, on-screen smartphone notification and more than 20 exercise modes for real-time workout stats. Get a 12-month free trial of Fitbit Premium with the Fitbit app for personalized guidance, additional insight and sleep tools. Again, Apple's official Apple Watch model accessory bands are hardly cheap, but some are worth the price tag. The popular Milanese Loop band is a great choice when you want something more professional than silicone, but aren't into a leather strap. This Apple Watch strap comes in stainless steel, in rose gold, silver or black, which results in a flexible fit and comfortable yet sturdy band that you can wear with professional clothes.

Looking for a band that will make your smartwatch look like a stainless steel wristwatch? It has the sheen of a Timex or Fossil timepiece, and it's elegant enough to wear to a formal outing. It's available in over 10 colors, including gold, blue, black, grey, and rose gold. It comes with an adjustment tool so you can remove the band's links to shorten its size without visiting a jeweler.

This best-seller has a 4.4-star average rating based on over 13,000 reviews. A stainless-steel band really changes the look of your Apple Watch, giving it a more timeless appearance. Epuly's band is one of the best Apple Watch bands for those who want an all-metal look. You can select from black, silver, bronze, rose gold and a few other colors to coordinate with your clothes .

The watchband comes with a kit for removing links so you can customize the length to fit your wrist. If you have large wrists or long or muscular arms, you might find that many watch bands look oddly minuscule on you -- or they don't fit at all. Epic Bands solves this problem with its adjustable stainless steel link bands, which you can customize to fit any size wrist. The band itself is already rather hefty , and it fits wrists up to 8.7 inches as-is. If you need the band to fit a larger wrist, you can purchase additional links to make the watch band as long as you need. Though I'm the last to say $70 is inexpensive for a watch band, the Nomad Modern Strap, made for Horween leather, still helps you save compared to Apple Watch leather bands.

And, this leather option is still high quality, highly rated and provides a comfortable fit. Linked here is the genuine Apple Watch leather band in rustic brown with matte black hardware, but this leather bandcomes in other colors, too. It's not too flashy, but there is an iridescent pattern if you want to add a bit of pizzazz. The band is made from stainless steel mesh, so it has a metallic finish but provides a comfortable fit. It's also easy to clean—and for those of us who are sweaty—that's a big bonus! There are neutral color options like black and ballet pink, which is very similar to rose gold, as well as "cool" iridescent and gradient options.

Reviewers say the colors are true to the photo and the band doesn't pinch. A fitness tracker, smartwatch, fitness band or whatever you want to call it can be useful to wear for evening strolls, intense at-home workouts or just all day, every day. Bands come in a number of options including silicone, leather, nylon, and stainless steel, each of which fits different styles and occasions. A silicone band, for example, offers a more athletic look, and it's fully waterproof so you can work out with it. Nylon is similarly resilient and often water-resistant, while stainless steel is incredibly durable and offers a more polished look (but it's typically not great with water).

Leather bands are a classic option that's great for everyday wear but can be dressed up too. The Garmin Venu 2 was nearly crowned our favorite wearable of 2021. Its accurate fitness- and health-tracking features, as well as the company's revamped software, made for an overall compelling package.

But Garmin watches tend to fall far behind the competition when it comes to "smart" features. You can install third-party apps and watch faces, but there's traditionally been no support for voice assistants, phone calls, or other smartwatch staples. My mom and I have been twinning in our Pink Citrus Apple Watch Sports Bands for the past nine months. The silicone watch band doesn't get gross and sweaty while working out and it feels comfortable while sleeping. I prefer this version with the loops, although if you're not into adjustable bands, opt for the Solo Loop Apple Watch band instead.

The Regular Sport Band comes in two sizes — 44 mm and 40 mm — plus 12 colors, including Deep Navy and Cyprus Green. But if you want a different style than what Apple offers, or you want to save a lot of money, we've found a large handful of the best Apple Watch bands that aren't made by Apple. This includes three cool leather bands at different prices, a couple of steel bracelets that we really like, and a classic nylon band. We also have suggestions for decent knockoffs if you want to come close to the style of Apple's bands for lower prices, or if you want to convert your own standard watch bands to fit the Apple Watch. If you are looking for the classic leather watch band look, then this band is probably the one for you. This design is intended not to be too flashy, but still have a stylish, classy look to it.

The band is also 100% genuine leather offering a soft texture that is an equal mix of style and comfort. If you're looking for a watch band that is as exuberant and flashy as you, these patterns might be the right fit for you. There is a cheerful, multi-color cheetah print with blue, orange, pink, green, and yellow spots.

There's a chic geometric pattern with navy and gold triangles and a more classic cheetah print. Each watch band is made with smooth silicone for a lightweight and comfortable fit. The bands come in two sizes and reviewers love them so much many have multiple from this seller. This faux-snakeskin watch band is sophisticated and stylish.

Apple Watch Series 6 40Mm Bands I love the texture it adds to any outfit, and it looks great paired with both silver and gold jewelry . Though it's a bit prettier than other options on this list, reviewers confirm that the materials are high quality and worth the cost. However, my favorite thing about this band is that you can customize the color of the buckle and lugs to go with your favorite accessories. This real-leather band offers a more modern look than the traditional buckle, using the pin-and-tuck style instead. It's sturdy and built to last, unlike some inexpensive bands. It also has more holes than some other bands, providing a snugger fit on your wrist — critical for accurate fitness tracking.

It's available in dozens of colors; you can opt for traditional brown or black or get a little wild with blue, yellow or even a two-tone combo. Kate Spade has long been a popular fashion brand, thanks to its unique prints and designs. And the company's Kate Spade scalloped Apple Watch strap is no different. This watch strap comes in a variety of colors and patterns, and is made from leather to enhance its broader fashion appeal. A single-prong metal buckle makes this band feel like a standard watch strap. That said, because it comes from the Kate Spade brand, it's a little more expensive than many other watchbands; the least expensive costs $45.

Brighten up a standard stainless steel watch strap with one of these resin block models. For those who want to stick with the classic, simple smartwatch look, nylon is the way to go. This woven style can be extremely durable and long-lasting if you choose the right brand. Salty USA, a Utah-based company that makes Apple accessories, offers budget-friendly woven nylon Apple Watch bands in two sizes (38/40mm and 42/44mm) and they come in more than 20 colors. And while that's an excellent prospect in regards to fitness, it also makes it one of the most user-friendly and feature-rich everyday offerings, as well. Truth be told, you might never want to take this smartwatch off once you've put it on.

That's all the more true when you consider that it is only $339 (down from $399) right now. And if you're looking for deals on previous Apple Watch models, there are some of those happening as well. When you're shopping around, there are a couple of key things to consider.

The Milanese style of watch strap was, as you might expect, developed in Milan at the end of the 19th century. It's based on smooth stainless steel mesh woven on specialised Italian machines, and it will give your Apple Watch a very distinctive look indeed. Apple's own Milanese loop is pretty impressive too, and the same price at time of writing, but in our eyes, the Mintapple Milanese just pips it to the post. I know how useful it can be to have your watch on your wrist to keep track of time, students' schedules, the day of the week, and how many days until summer break.

This band is silicone, so it can be easily wiped down and sanitized, so even if you're working with younger children it'll work for you. Plus, you can personalize the band with your name among crayons, right next to other classic teacher icons like pencils and apples. The band is available in eight colors, so make it work with your style. If you are a fan of Star Wars, specifically the Mandalorian spinoff series, then this is a watch band to get excited about. This band is seemingly infinitely customizable with multiple colors and quite a few different sizes to choose from, and features multiple images from the Mandalorian series, including Baby Yoda.

The band is made of silicone, intended to be versatile and easily cleanable. Make sure to get this one if you want to make all the Star Wars fans in your life jealous. Etsy shoppers can't get enough of these vibrant nylon sports straps.

In addition to the two dozen colors and two band sizes available, several reviewers also rave about their "terrific quality" and "perfect fit." Hermès Birkin bags are notoriously hard to come across in stores, and the lofty price tag, which has gone up to $300,000 at auction, doesn't help, either. Fortunately, if you want to splurge on a Hermès leather product but don't want to spend tens of thousands of dollars, go for the leather Apple watch band instead.

The French fashion house teamed up with Apple in 2015 and currently offers leather Apple Watch bands in eight colors, including Rouge Piment, Barénia, Orange and Noir. We love the look and style of the WFEAGL Apple Watch Band — plus, you get a bunch of bang for your buck. A leather watchband is a classic, classy look that never goes out of style. There are 45 different leather and hardware color combinations, including some bands that have a little sparkle. This band is available in both the larger and the smaller Apple Watch size, suitable for any generation. The Nomad Sport Strap is a $40 silicone watchband that's designed to be worn while you're active and sweating.

Nomad says the material is both durable and comfortable, and the slate-gray finish over the black adds some design flair you won't find elsewhere. It's one of the best Apple Watch bands for sports that stands out more than the average silicone options. Leather watch straps don't need to be brown and bulky, and this stylish band is ideal for smaller wrists. Beads either side of the strap where it meets the watch allow for a slimmer fit while adding a chic feel. There's a large range of colors for both the leather and adapter fitting, and you can even get the strap monogrammed for extra style points. There are a lot of silicone Apple Watch bands out there, but there aren't many with this thick, textured design.

The tire-tread silicone on this Carterjett band makes it perfect for people who need durability in a band, and the rugged aesthetic is a bonus for outdoorsy or adventurous types. This watch strap comes in a variety of color option choices with sizes from small to extra-large. The mesh looks beautifully polished and feels smooth and comfortable to wear. The weaving appears slightly less likely to pick up hairs and dust in practice than its official Apple rival. Also, because it's fully magnetic, the Milanese Loop is wonderfully adjustable, ensuring a perfect fit. Overall then, this tasteful and sophisticated design is our top recommendation when it comes to stainless steel Apple Watch bands.

This watch band comes highly recommended from one of our editors! It's from Rifle Paper Co., so you know it's gorgeous and intricately detailed. I love the mix of shades of blue, especially as someone who always dresses casually. The metallic gold foil catches the light to add a bit of flash to an already detailed design. The band is made of silicone and pairs with Apple Watches from Series 1–6. It's also worth noting that if you prefer gold jewelry, the watch will look great with your other accessories since it's hardware is gold as well.

The leather has a brushed look, which is modern and stylish. Similar to how you can buy third-party cases for your phone. We do not sell or include any products made by or authorized by Apple. If you want a leather Apple Watch band, but are unwilling to spend a few hundred bucks on an Hermés version, try the Poppy instead. The Roux Granada leather watch band is made in France and sports a flexible magnetic closure so you can adjust your watch to your wrist size. You can order either a Small/Medium or Large/Extra Large watch band, both of which can fit a 40 or 44 mm Apple Watch face.

The classic band, available in a variety of neutral colors, tapers just slightly from the lugs. It's a plain design without ornamentation that will look good on most wrists and fit most styles. The stitching is noteworthy for such an inexpensive band, as it's perfectly aligned and spaced. We also like the contrasting light brown against the black or darker brown leather.

The leather itself has a matte finish and is lightly textured but not pebbly. The EPULY Apple Watch Band is a sharp and classic-looking watch band available in both sizes. It is undoubtedly appropriate for the office or any formal occasion.

Several leather watch bands for the Apple Watch promise to make you look more fashionable. But the Marge Plus Compatible is one of the best Apple Watch bands because it's designed to provide a leather option without needing you to empty your wallet. Here's another dressy option that offers to put a more elegant rose gold look on your wrist. The stainless steel mesh band uses a magnetic clasp to keep it securely in place and does additionally come available in silver and rose pink mesh looks.

So you have some options if you want to pick up an extra band or two. You can pick up this woven nylon and silicone thread band in six colors and uses a simple buckle to make it easy to adjust when you need a tighter fit or you need to whip it off quickly. It's fit for keeping on when you're working out and we'd say the green and the red options offer the strongest look depending on what color case you're rocking. Available in all Apple Watch sizes the Fitlink stainless steel metal strap is a classic option for anyone looking for a metal link band.