Rhythm in learning is something that most people don't think about, mostly because they take it for granted. If you were educated in a structure-oriented country, like most countries in the West, this would be instilled in you (contrary to countries like Greece where disorder and lack of any functional structure reign supreme). However, even then you may not value it so much because it is not something you're conscious of always. The need to be aware of it and make conscious effort comes about when you are on your own, be it as a freelancer or a learner in a free-form kind of course (i.e. not a university course of a boot camp). And just like any other real needs, this needs to be fulfilled in one way or another.

The idea of this article came about from a real situation, namely a session with one of my mentees. Although she is a very conscientious learner and a very good mentee, she was struggling with rhythm, mostly due to external circumstances in her life. Having been there myself, I advised her accordingly. The distillation of this is what follows.

So, rhythm is not something you need to strive for as it's built-in yourself as an innate characteristic. In other words, it's natural, like breathing and should come by on its own. If it doesn't, it's because you've put something in its way. So, you just need to remove this obstacle and rhythm will start flowing again on its own. This action of removal may take some effort but it's a one-time thing (unless you are in a very demanding situation in your life, in which case you need to re-set your boundaries). But how does rhythm manifest in practice? It's all about being able to do something consistently, even if it's a small amount certain days.

In my experience with writing (a truly challenging task in the long run, particularly when there is a deadline looming over you), I make it a habit of writing a bit every day, even if it's just a single paragraph or the headings and subheadings structure of a new chapter. Sometimes I don't feel like working on a book at all, in which case I take the time to annotate the corresponding Jupyter notebooks or write an article on this blog. Whatever the case, I avoid idleness like the plague since it's the killer of rhythm.

When it comes to learning data science and A.I., rhythm manifests as follows. You cultivate the habit of reading/coding/writing something related to the topic of your study plan or course curriculum. Even a little bit can go a long way since it's not that bit that makes the difference but the maintenance of your momentum. It's generally harder to pick up something that has gone rusty in your mind, particularly coding. However, if you coded a bit the previous day, it's so much easier. If you get stuck somewhere, you can always work on another drill or project. The important thing is to never give up and go idle.

Frustration is oftentimes inevitable but if you leverage it properly, it can be a powerful force as it has elements of willpower in it, willpower that doesn't have a proper outlet and it trapped. This is what can cause the break of rhythm but what can also remedy it. You always have the energy to carry on, even at a slower pace sometimes. You just need to tap into it and apply yourself. That's when having a mentor can do wonders, yet even without one, you can still manage, but with a bit more effort. It's all up to you!

It may seem strange to have an article on this topic in this blog, but since hashgraph is a promising technology that I've already talked about in the past, it may be worthwhile to make an exception.

As you may have heard, the Hedera platform is a hashgraph-based network that promises high speeds, very low cost, and a high level of security in it. All this is through the use of a new technology that one of its founders, Dr. Leeman Baird, created over the years. The idea is to use a clever combination of the gossip protocol along with virtual voting to ensure consensus in a network of computers, keeping track of various transactions. Up until now, this network has been used with a series of other applications but as of this year, a financial application has also become available. This takes the form of a cryptocurrency called hbar, which promises to be a worthwhile alternative to the blockchain-based cryptos.

Whether hbar is going to make it or not remains to be seen, since BitCoin, Ethereum, Dash, and some other cryptos have attracted a large enough community to establish themselves, even if they are based on inferior technologies than hbar. Don't get me wrong, I think blockchain tech is amazing and may continue bringing about benefits to its users. Hashgraph, however, is superior in many ways, plus it has a legitimate company behind it, something that inspires confidence in many of its users. Some of these users are established companies such as Boeing, so it's not some hyped tech that may or may not exist a year from now.

Hbar is being traded as of last week (September 17th to be exact) on the internet, after several months of beta-testing. Currently, it is available for trade on major crypto exchange sites, such as Bittrex and it's at a very low price (around 0.036 USD per token), even lower than the ICO one (0.12  USD). You can monitor its price from the Hedera-based site www.hbarprice.com where you can also learn additional information about the company and the various services they offer.

Just like other innovative technologies, a hashgraph-based cryptocurrency seems a bit ahead of its time. In a way, it reminds me of the Julia language, which has been better in many ways than other data science programming platforms, yet it is still to receive the recognition it deserves. Whether this is due to the inertia of the tech people or the excessive promotion that its competitors receive is unknown. Whatever the case, those who make use of such technologies benefit even if the majority of people never fully accept them as worthwhile alternatives. So, I don't expect hbar to dominate the crypto market any time soon, but I'd be interested in following its course.

Throughout this blog, I've talked about all sorts of problems and how solving them can aid one's data science acumen as well as the development of the data science mindset. Problem-Solving skills rank high when it comes to the soft skills aspect of our craft, something I also mentioned in my latest video on O'Reilly. However, I haven't talked much about how you can hone this ability.

Enter Brilliant, a portal for all sorts of STEM-related courses and puzzles that can help you develop problem-solving, among other things. If you have even a vague interest in Math and the positive Sciences, Brilliant can help you grow this into a passion and even a skill-set in these disciplines. The most intriguing thing about all this is that it does so in a fun and engaging way.

Naturally, most of the stuff Brilliant offers comes with a price tag (if it didn't, I would be concerned!). However, the cost of using the resources this site offers is a quite reasonable one and overall good value for money. The best part is that by signing up there you can also help me cover some of the expenses of this blog, as long as you use this link here: www.brilliant.org/fds (FDS stands for Foxy Data Science, by the way). Also, if you are among the first 200 people to sign up you'll get a 20% discount, so time is definitely of the essence!

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What?
Translinearity is the super-set of what’s linear, so as to include what is not linear, in a meaningful manner. In data analytics, it includes all connections among data points and variables that make sense in order to maintain robustness (i.e. avoid any kind of over-fitting). Although fairly abstract, it is in essence what has brought about most modern fields of science, including Relativistic Physics. Naturally, when modeled appropriately, it can have an equally groundbreaking effect in all kinds of data analytics processes, including all the statistical ones as well as some machine learning processes. Effectively, a framework based on translinearity can bridge the different aspects of data science processes into a unified whole where everything can be sophisticated enough to be considered A.I. related while at the same time transparent enough, much like all statistical models.

Why?
Because we have reached the limits of what the linear approach has to offer through Statistics, Linear Algebra, etc. Also, the non-linear approach, although effective and accessible, are black boxes, something that may remain so for the foreseeable future. Also, the translinear approach can unveil aspects of the data that are inaccessible with the conventional methods at our disposal, while they can help cultivate a more holistic and more intuitive mindset, benefiting the data scientists as much as the projects it is applied on.

Where?
So far, Translinearity is implemented in the Julia ecosystem by myself. This is something I've been working on for the past decade or so. I have reason to believe that it is more than just a novelty as I have observed various artifacts concerning some of its methods, things that were previously considered impossible. One example is optimal binning of multi-dimensional data, developing a metric that can assess the similarity of data points in high dimensionality space, a new kind of normalization method that combines the benefits of the two existing ones (min-max and mean-std normalization, aka standardization), etc.

How?
Translinearity is made applicable through the systematic and meticulous development of a new data analytics framework, rooted in the principles and completely void of assumptions about the data. Everything in the data is discovered based on the data itself and is fully parametrized in the corresponding functions. Also, all the functions are optimized and build on each other. A bit more than 30 in total, the main methods of this model cover all the fundamentals of data analytics and open the way to the development of predictive analytics models too.

So what?
Translinearity opens new roads in data analytics rendering conventional approaches more or less obsolete. However, the key outcome of this new paradigm of data analytics is the possibility of a new kind of A.I. that is transparent and comprehensible, not merely comprehensive in terms of application domains. Translinearity is employed in the more advanced deep learning systems but it’s so well hidden that it escapes the user. However, if an A.I. system is built from the ground-up using translinear principles, it can maintain transparency and flexibility, to accompany high performance.

It's interesting how even though there are a zillion ways to assess the similarity between two vectors (each representing a single-dimensional data sample) when it comes to doing the same thing with matrices (each representing a whole sample of data) the metrics available are mediocre at best. It's really strange that when it comes to clustering, for example, where this is an important part of the whole process, we often revert to crude metrics like Silhouette Width to figure out if the clusters are similar enough or not. What if there was a way to assess similarity more scientifically, beyond such amateur heuristics?

Well, fortunately, there is a way, at least as of late. Enter the Congruency concept. This is basically the idea that you can explore the similarity of two n-dimensional samples through the systematic analysis of their components, given that the latter are orthogonal. If they are not orthogonal, it shouldn't be difficult to make them orthogonal, without any loss of information. Whatever the case, it's important to avoid any strong relationships among the variables involved as this can skew the whole process of assessing similarity.

The Congruency concept is something I came up with a few months ago but it wasn't until recently that I managed to implement it in a reliable and scalable way, using a new framework I've developed in Julia. The metric takes as inputs the two matrices and yields a float number as its output, between 0 and 1. The larger this number is the more similar (congruent) the two matrices are. Naturally, the metric was designed to be robust regardless of its dimensionality, though if there are a lot of noisy variables, they are bound to distort the result. That's why it performs some preprocessing first to ensure that the variables are independent and as useful as possible.

Applications of the Congruency metric (which I coined as dcon) go beyond clustering, however. Namely, it can be used in assessing sampling algorithms too (usually yielding values 0.95+ for a reliable sample) as well as synthetic data generation. Since the metric doesn't make any assumptions about the data, it can be used with all kinds of data, not just those following a particular set of distributions. Also, as it doesn't make use of all dimensions simultaneously, it is possible to avoid the curse of dimensionality altogether.

Things like Congruency may seem like ambitious heuristics and few people would trust it when the more established statistical heuristics exist as an option. However, there comes a time when a data scientist starts to question whether a statistic's / metric's age is sufficient for establishing its usefulness. After all, what is now old and established was once new and experimental, let's not forget that...