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Self Improvement, Health, Life, Psychology, Science.
with the spiritual objectives of the festival. One of the defining characteristics of 'satvik' foods is their low glycemic index (GI). The glycemic index is a measure that ranks carbohydrate-containing foods based on how they affect blood glucose levels. Foods with a low GI value are metabolized
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more slowly, resulting in a more gradual rise in blood sugar levels as opposed to a sharp spike. This slow and steady release of glucose is crucial for several reasons. Firstly, it ensures that the body receives a consistent energy supply, which can help in maintaining focus and preventing feelings
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of fatigue. More importantly, from a health perspective, a steady glucose release reduces the strain on the pancreas to produce insulin, thereby fostering improved insulin sensitivity. Over time, improved insulin sensitivity can reduce the risk of developing metabolic disorders like type 2
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diabetes. 'Satvik' foods commonly consumed during Navratri include fruits, nuts, dairy products, and certain flours like buckwheat or amaranth. Apart from their low GI, these foods offer another significant advantage: they are typically rich in dietary fiber. Dietary fiber plays a multifaceted role
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in digestive health. It adds bulk to stools, aiding in regular bowel movements and preventing constipation. Moreover, certain types of fiber act as prebiotics, serving as food for beneficial gut bacteria. The consumption of fiber-rich foods can lead to a positive modulation of the gut microbiota,
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fostering the growth of beneficial bacteria and inhibiting the proliferation of pathogenic strains. A balanced gut microbiota is increasingly being recognized for its wide-ranging benefits, from improved digestion and nutrient absorption to modulation of immune responses and potential protective
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effects against colorectal cancers. Furthermore, the emphasis on natural, unprocessed 'satvik' foods means that the diet is typically devoid of additives, preservatives, and excessive salts or sugars. This absence of additives can be beneficial for overall health, reducing the intake of potentially
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harmful chemicals and excessive sodium or refined sugars, which have been associated with various health issues when consumed in excess. While the shift towards 'satvik' foods during Navratri is rooted in spiritual and cultural practices, its implications for health are profound. These dietary
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choices, characterized by low GI values and rich fiber content, not only align with the festival's spiritual ethos but also offer tangible benefits for digestive health, insulin sensitivity, and overall well-being. However, as with all dietary practices, individual responses can vary, emphasizing
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the importance of being attuned to one's body and its unique needs. Navratri's fasting practice isn't merely a physiological endeavor; it significantly impacts the psychological and emotional realms of those who partake in it. This period of deliberate restraint and reflection underscores a
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deep-seated interplay between mind, body, and spirit, providing insights into the human psyche's resilience and adaptability. At the forefront of this psychological exploration is the exercise of cognitive discipline. Choosing to abstain from specific foods or even general sustenance requires a
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significant amount of willpower. This act is not just about curbing physical hunger; it's about mastering one's desires, impulses, and habitual tendencies. Such self-imposed restrictions can bolster an individual's sense of control over their own actions, thoughts, and emotions, leading to
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heightened self-awareness and mental clarity. The immersive spiritual environment that characterizes Navratri further amplifies this psychological experience. Engaging in prayers, meditations, and chants against the backdrop of fasting can heighten one's spiritual sensitivity. This deepened
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spiritual connection, coupled with the physical act of fasting, can set off a cascade of neurochemical changes within the brain. One such notable neurochemical response is the potential release of endorphins. Endorphins, often dubbed as the body's "feel-good" chemicals, are neurotransmitters that
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act on opiate receptors in the brain. They play a vital role in pain modulation and the induction of positive feelings. During periods of prolonged fasting and deep spiritual engagement, as observed during Navratri, there's a plausible surge in endorphin production. This surge can manifest in
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various psychological states, including a profound sense of euphoria, a deep-seated feeling of tranquility, and heightened introspection. Moreover, the endorphin release might also act as a natural coping mechanism. As the body undergoes the stress of fasting, endorphins can mitigate feelings of
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discomfort or pain, allowing individuals to navigate the fasting period with greater ease and comfort. The combined effect of these endogenous chemicals and the spiritual ambiance often leads individuals into a state of enhanced spiritual connectivity, deeper introspection, and a heightened sense
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of well-being. The psychological facets of Navratri fasting offer a captivating window into the strength and adaptability of the human psyche. By intertwining physical restraint with spiritual immersion, individuals embark on a journey that not only nourishes the soul but also offers profound
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insights into the mind's capabilities and intricacies. Navratri, while a deeply personal and spiritual experience for many, is also profoundly communal in its essence. Its observance transcends individual spirituality, reaching out and intertwining the threads of entire communities, reinforcing
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shared values, beliefs, and cultural traditions. The sociocultural ramifications of Navratri fasting and its associated rituals are multifaceted and pivotal to understanding the festival's broader significance within communities. A unique feature of Navratri is the shared rituals that are observed
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collectively. Whether it's the specific dietary practices or the vibrant dances like Garba and Dandiya, these synchronized activities become more than just individual expressions of devotion; they serve as powerful symbols of collective identity. When individuals come together, adorned in
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traditional attire, dancing in unison to the rhythmic beats, or partaking in specific meals, it reinforces a shared cultural heritage and identity. These moments act as tangible reminders of shared histories, narratives, and values, helping solidify the sense of belonging to a larger community.
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It's a celebration not just of the divine but of shared cultural roots and traditions that have been passed down through generations. Moreover, the very act of collective participation during Navratri creates an environment that fosters communal cohesion. Shared experiences, especially those deeply
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rooted in cultural and religious beliefs, have a unique way of binding people together. As families and communities come together for collective prayers, share meals, exchange stories, and participate in dances, it creates an environment of mutual trust and understanding. This shared sense of
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purpose, combined with the mutual respect and camaraderie observed during these rituals, engenders feelings of solidarity. Over time, such events can lead to the formation of a robust and cohesive community where members feel interconnected and interdependent. Navratri, with its rich tapestry of
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rituals, traditions, and practices, is emblematic of the confluence of faith and science, tradition and inquiry. At its heart, it is a festival of profound spiritual significance, a time for introspection, devotion, and reconnection with the divine. Yet, as we delve deeper into its various facets,
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it becomes evident that the practices associated with Navratri, particularly fasting, reverberate beyond the realms of spirituality, touching upon diverse scientific domains. The physiological adaptations that the body undergoes during fasting, from the shift to ketosis to cellular autophagy, are a
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testament to the body's remarkable resilience and adaptability. These changes, while instigated by a religious practice, offer insights into the intricate workings of the human metabolic system, shedding light on potential health benefits and the body's innate mechanisms for maintaining
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homeostasis. On the psychological front, the interplay of fasting with heightened spiritual engagement provides a window into the workings of the human psyche. The release of endorphins, the feelings of tranquility, and the deepened introspection are indicative of the complex neurochemical and
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emotional responses triggered by this confluence of physical and spiritual practices. From a sociocultural perspective, Navratri stands as a beacon of community, culture, and shared identity. The collective rituals, dances, and shared experiences serve as powerful reminders of shared histories and
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values, fostering community bonds and reinforcing a collective cultural identity. However, while the myriad benefits and implications of Navratri fasting are compelling, it's imperative to approach it with a nuanced perspective. Individual responses to fasting can vary widely, influenced by factors
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like age, health status, and genetic predispositions. As such, recognizing and respecting this individual variability becomes paramount. What benefits one individual might not necessarily benefit another, and as with all practices that impact health and well-being, personalized approaches and
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considerations are crucial. Navratri, in its essence, beautifully encapsulates the harmonious integration of faith and science, tradition and modernity. It serves as a reminder of the profound interconnectedness of mind, body, and spirit, and the intricate dance between individual practices and
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Artificial Intelligence, Robotics, Sensors.
Belo Horizonte, MG, Brasil, Photo by — @danielmonteirox Making sense from perception to machine and action This article is a brief look at the relationship between artificial intelligence (AI), sensors and robotics. It is not meant to be comprehensive, rather it explores rudimentary concepts. Many
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human-like operations may require some degree of artificial intelligence or machine learning to operate in the manner needed. Yet many robots are only programmed for a set task and given a few different eventualities. Yet to help a machine with an understanding of its spacial environment — in terms
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Artificial Intelligence, Robotics, Sensors.
of the perception, speech recognition or learning otherwise it can happen through sensory inputs. I have previously covered cameras, yet it can be microphones, wireless signals and much more. The machine has to recognise a set of human behavioural indications or to take information from the
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Artificial Intelligence, Robotics, Sensors.
environment it is situated to determine actions. Is it hot or cold, is that a human or machine, car or human, etc. Identifying objects can be one aspect, yet another one is to understand what set of events that should trigger a given action. The three if divided may serve different purposes. AI can
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Artificial Intelligence, Robotics, Sensors.
be programmed, robotics involving the wide aspects relating to the physical. You can see the almost uncanny movements of the robot hand trained by the team at OpenAI. OpenAI had then trained a neural network to solve the Rubik’s Cube in a simulation through the use of reinforcement learning. Domain
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Artificial Intelligence, Robotics, Sensors.
randomization enables networks trained solely in simulation to transfer to a real robot. This Automatic Domain Randomization (ADR), which endlessly generates progressively more difficult environments in simulation. They focus on challenging problems for ‘machines to master’. Perception. Dexterous
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manipulation. In addition to this they mention the concept of meta-learning. “We believe that meta-learning, or learning to learn, is an important prerequisite for building general-purpose systems, since it enables them to quickly adapt to changing conditions in their environments.” Robotics and AI
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serve different purposes. However these fields move closer in these type of contexts when complex manoeuvring is necessary. Robotics involves building robots, whereas AI deals with programming intelligence or making computers behave like humans. “Robotics is an interdisciplinary branch of
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engineering and research area for information engineering, computer engineering, computer science, mechanical engineering, electronic engineering and others. Robotics involves design, construction, operation, and use of robots.” To some extent a goal is to develop machines that can substitute for
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Artificial Intelligence, Robotics, Sensors.
humans and replicate human actions. However robots need motors and sensors in order to activate and perform basic operations. Sensors have become incredibly cheap and far easier to integrate into different systems whether on an industrial scale or private. As such with the increasing availability
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Artificial Intelligence, Robotics, Sensors.
of cheap sensors and possibilities to combine advanced software has been giving interesting results. Another example is Boston Dynamics, and their highlight reel from 2012–2019 shows the astonishing progress that is being made within this area. Their Spot model was launched recently and has been
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Artificial Intelligence, Robotics, Sensors.
popular. It may seem like this form of sensory intelligence is enough, yet it has been said we need far more for these type of robots to be operating in our homes. Still we let vacuum cleaners into our homes. There might be a possibility for other appliances as well although it may be in the
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Artificial Intelligence, Robotics, Sensors.
early-stages. Apparently the needs for health robotics has surged during the Coronavirus lockdown: Demand for health gadgets soars amid lockdowns | The Japan Times Fitness-tracking gadgets are selling out, home exercise classes have never been more popular and robotics crews
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are…www.japantimes.co.jp In addition to this robots are increasingly used in telemedicine. What America can learn from China's use of robots and telemedicine to combat the coronavirus After a passenger infected with the novel coronavirus boarded the Diamond Princess cruise ship in January, the
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virus…www.cnbc.com As well as to some extent — there are robots and drones used in this capacity to help in the strange battle against the spread of the Coronavirus. Robots And Drones Are Now Used To Fight COVID-19 As the coronavirus (COVID-19) spread from China to other countries, robots and
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Artificial Intelligence, Robotics, Sensors.
drones were deployed to provide critical…www.forbes.com A blog called TerraHawk described it with an illustration that I found helpful given what has been discussed above. Image by Terrahawk Software “Sensemaking or sense-making is the process by which people give meaning to their collective
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Artificial Intelligence, Robotics, Sensors.
experiences. It has been defined as “the ongoing retrospective development of plausible images that rationalize what people are doing.” In this way machines are programmed to attempt making sense of the environment to take appropriate actions. This is #500daysofAI and you are reading article 310. I
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
https://goo.gl/ihju1k 1. Introduction A recommender system refers to a system that is capable of predicting the future preference of a set of items for a user, and recommend the top items. One key reason why we need a recommender system in modern society is that people have too much options to use
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
from due to the prevalence of Internet. In the past, people used to shop in a physical store, in which the items available are limited. For instance, the number of movies that can be placed in a Blockbuster store depends on the size of that store. By contrast, nowadays, the Internet allows people
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
to access abundant resources online. Netflix, for example, has an enormous collection of movies. Although the amount of available information increased, a new problem arose as people had a hard time selecting the items they actually want to see. This is where the recommender system comes in. This
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article will give you a brief introduction to two typical ways for building a recommender system, Collaborative Filtering and Singular Value Decomposition. 2. Traditional Approach Traditionally, there are two methods to construct a recommender system : Content-based recommendation Collaborative
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Filtering The first one analyzes the nature of each item. For instance, recommending poets to a user by performing Natural Language Processing on the content of each poet. Collaborative Filtering, on the other hand, does not require any information about the items or the users themselves. It
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recommends items based on users’ past behavior. I will elaborate more on Collaborative Filtering in the following paragraphs. 3. Collaborative Filtering As mentioned above, Collaborative Filtering (CF) is a mean of recommendation based on users’ past behavior. There are two categories of CF:
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User-based: measure the similarity between target users and other users Item-based: measure the similarity between the items that target users rates/ interacts with and other items The key idea behind CF is that similar users share the same interest and that similar items are liked by a user.
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Assume there are m users and n items, we use a matrix with size m*n to denote the past behavior of users. Each cell in the matrix represents the associated opinion that a user holds. For instance, M_{i, j} denotes how user i likes item j. Such matrix is called utility matrix. CF is like filling the
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
blank (cell) in the utility matrix that a user has not seen/rated before based on the similarity between users or items. There are two types of opinions, explicit opinion and implicit opinion. The former one directly shows how a user rates that item (think of it as rating an app or a movie), while
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
the latter one only serves as a proxy which provides us heuristics about how an user likes an item (e.g. number of likes, clicks, visits). Explicit opinion is more straight-forward than the implicit one as we do not need to guess what does that number implies. For instance, there can be a song that
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user likes very much, but he listens to it only once because he was busy while he was listening to it. Without explicit opinion, we cannot be sure whether the user dislikes that item or not. However, most of the feedback that we collect from users are implicit. Thus, handling implicit feedback
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properly is very important, but that is out of the scope of this blog post. I’ll move on and discuss how CF works. User-based Collaborative Filtering We know that we need to compute the similarity between users in user-based CF. But how do we measure the similarity? There are two options, Pearson
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Correlation or cosine similarity. Let u_{i, k} denotes the similarity between user i and user k and v_{i, j} denotes the rating that user i gives to item j with v_{i, j} = ? if the user has not rated that item. These two methods can be expressed as the followings: Pearson Correlation
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(https://goo.gl/y93CsC) Cosine Similarity (https://goo.gl/y93CsC) Both measures are commonly used. The difference is that Pearson Correlation is invariant to adding a constant to all elements. Now, we can predict the users’ opinion on the unrated items with the below equation: Unrated Item
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Prediction (https://goo.gl/y93CsC) Let me illustrate it with a concrete example. In the following matrixes, each row represents a user, while the columns correspond to different movies except the last one which records the similarity between that user and the target user. Each cell represents the
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rating that the user gives to that movie. Assume user E is the target. Since user A and F do not share any movie ratings in common with user E, their similarities with user E are not defined in Pearson Correlation. Therefore, we only need to consider user B, C, and D. Based on Pearson Correlation,
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we can compute the following similarity. From the above table you can see that user D is very different from user E as the Pearson Correlation between them is negative. He rated Me Before You higher than his rating average, while user E did the opposite. Now, we can start to fill in the blank for
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the movies that user E has not rated based on other users. Although computing user-based CF is very simple, it suffers from several problems. One main issue is that users’ preference can change over time. It indicates that precomputing the matrix based on their neighboring users may lead to bad
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performance. To tackle this problem, we can apply item-based CF. Item-based Collaborative Filtering Instead of measuring the similarity between users, the item-based CF recommends items based on their similarity with the items that the target user rated. Likewise, the similarity can be computed
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with Pearson Correlation or Cosine Similarity. The major difference is that, with item-based collaborative filtering, we fill in the blank vertically, as oppose to the horizontal manner that user-based CF does. The following table shows how to do so for the movie Me Before You. It successfully
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avoids the problem posed by dynamic user preference as item-based CF is more static. However, several problems remain for this method. First, the main issue is scalability. The computation grows with both the customer and the product. The worst case complexity is O(mn) with m users and n items. In
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
addition, sparsity is another concern. Take a look at the above table again. Although there is only one user that rated both Matrix and Titanic rated, the similarity between them is 1. In extreme cases, we can have millions of users and the similarity between two fairly different movies could be
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
very high simply because they have similar rank for the only user who ranked them both. 4. Singular Value Decomposition One way to handle the scalability and sparsity issue created by CF is to leverage a latent factor model to capture the similarity between users and items. Essentially, we want to
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
turn the recommendation problem into an optimization problem. We can view it as how good we are in predicting the rating for items given a user. One common metric is Root Mean Square Error (RMSE). The lower the RMSE, the better the performance. Since we do not know the rating for the unseen items,
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
we will temporarily ignore them. Namely, we are only minimizing RMSE on the known entries in the utility matrix. To achieve minimal RMSE, Singular Value Decomposition (SVD) is adopted as shown in the below formula. Singular Matrix
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Decomposition(http://www.cs.carleton.edu/cs_comps/0607/recommend/recommender/images/svd2.png) X denotes the utility matrix, and U is a left singular matrix, representing the relationship between users and latent factors. S is a diagonal matrix describing the strength of each latent factor, while V
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
transpose is a right singular matrix, indicating the similarity between items and latent factors. Now, you might wonder what do I mean by latent factor here? It is a broad idea which describes a property or concept that a user or an item have. For instance, for music, latent factor can refer to the
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
genre that the music belongs to. SVD decreases the dimension of the utility matrix by extracting its latent factors. Essentially, we map each user and each item into a latent space with dimension r. Therefore, it helps us better understand the relationship between users and items as they become
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
directly comparable. The below figure illustrates this idea. SVD Maps Users and Items Into Latent Space (https://www.youtube.com/watch?v=E8aMcwmqsTg&list=PLLssT5z_DsK9JDLcT8T62VtzwyW9LNepV&index=55) SVD has a great property that it has the minimal reconstruction Sum of Square Error (SSE);
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
therefore, it is also commonly used in dimensionality reduction. The below formula replace X with A, and S with Σ. Sum of Square Error (https://www.youtube.com/watch?v=E8aMcwmqsTg&list=PLLssT5z_DsK9JDLcT8T62VtzwyW9LNepV&index=55) But how does this has to do with RMSE that I mentioned at the
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
beginning of this section? It turns out that RMSE and SSE are monotonically related. This means that the lower the SSE, the lower the RMSE. With the convenient property of SVD that it minimizes SSE, we know that it also minimizes RMSE. Thus, SVD is a great tool for this optimization problem. To
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
predict the unseen item for a user, we simply multiply U, Σ, and T. Python Scipy has a nice implementation of SVD for sparse matrix. >>> from scipy.sparse import csc_matrix >>> from scipy.sparse.linalg import svds >>> A = csc_matrix([[1, 0, 0], [5, 0, 2], [0, -1, 0], [0, 0, 3]], dtype=float) >>> u,
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Data Science, Recommender Systems, Collaborative Filtering, Artificial Intelligence, Machine Learning.
s, vt = svds(A, k=2) # k is the number of factors >>> s array([ 2.75193379, 5.6059665 ]) SVD handles the problem of scalability and sparsity posed by CF successfully. However, SVD is not without flaw. The main drawback of SVD is that there is no to little explanation to the reason that we recommend
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an item to an user. This can be a huge problem if users are eager to know why a specific item is recommended to them. I will talk more on that in the next blog post. 5. Conclusion I have discussed two typical methods for building a recommender system, Collaborative Filtering and Singular Value
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Decomposition. In the next blog post, I will continue to talk about some more advanced algorithms for building a recommender system. Should you have any problem or question regarding to this article, please do not hesitate to leave a comment below or drop me an email: [email protected]. If
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Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
Using quantum correlations to get out of jail I recently wrote a piece for Scientific American about how quantum entanglement isn’t that “spooky.” In it, I outlined a little problem that is solved when thinking about entanglement as correlated information. Due to various constraints such as word
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Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
limits and the fact that they weren’t going to let me put math in the article, I only alluded to the fact the problem could be solved if you knew a little bit of linear algebra. Well, anyway, I got a lot of messages from people confident they could handle the math, asking me for that solution. For
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Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
those people, I’ve tried to make the math as accessible as possible here: https://gist.github.com/csferrie/3facbbe18f977ace02a78474349b2ead. For everyone else, let me try to summarize the main takeaway message. First, let’s repeat the problem. Alice and Bob are implicated in a crime and are to be
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Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
questioned in separate rooms with no way to communicate. The investigators, trying to seem lenient, say they will be set free if they can corroborate each other’s story on more than 75% of the questions they are asked. They have two alibis, Charlie and Diane. Alice and Bob know that they are each
|
medium
| 6,956 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
going to be asked one of two questions: were you with Charlie? Or were you with Diane? They also know from an informant, Eve, that the investigators are trying to trap them. Eve has told them that to corroborate each other’s story, they must answer exactly the same if either of them is asked if
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medium
| 6,957 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
they were with Charlie, but differently if they are both asked if they were with Diane. The problem for Alice and Bob is that they can’t come up with a pre-determined strategy that wins more than 75% of the time. For example, Bob might suggest that Alice always says yes, and he will do the same,
|
medium
| 6,958 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
except when they are both asked about Diane. Of course, he can’t do that because he won’t know what question Alice is asked when they are separated. Any sort of if asked this, then definitely answer that idea won’t work. So, at the least, their strategy must be random if they have any chance of
|
medium
| 6,959 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
being set free. That’s where correlated information comes in. All classical information can be thought of as bits — answers to yes-or-no questions. To think about the problem in terms of information, as I suggested in the article, we start with the fact that Alice’s yes-or-no answer reveals a
|
medium
| 6,960 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
single bit. The point of mathematics is to simplify things that would require otherwise long-winded and complicated sentences. So, we replace the things we are talking about with symbols and numbers. If the bits are not known, then we write them as a list of probabilities (p1, p2, p3, …). If you
|
medium
| 6,961 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
recall your lessons on chance and probability, each of these symbols must represent a positive number, and they all have to add up to one. Before we know the chances of Alice saying yes or no, we can write her bit value as (p1, p2). Again, this is just a way more succinct way than writing (the
|
medium
| 6,962 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
probability that Alice says yes, the probability that Alice says no). Suppose, for example, Alice will either say yes or no with ½ probability. Succinctly, that’s represented as (½, ½). Both numbers are positive, and they add to one. Bob has two numbers as well. But, between the two of them, there
|
medium
| 6,963 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
are four possible pairs of answers, which would have a list of numbers like (q1, q2, q3, q4). Now, here’s the important point: if the list of four probabilities for the pair of them can’t be equally described as two separate lists of two numbers for each of them, then the information they share
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medium
| 6,964 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
must be correlated. Mathematically, you can take this as the definition of correlation. For example, (½, 0, 0, ½) represents the situation when Alice and Bob both say either yes or no with ½ probability. For Alice alone, she will say yes or no with ½ probability, and similarly for Bob, so their
|
medium
| 6,965 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
individual lists are (½, ½). But their individual lists don’t capture the fact that in this situation, the probability of yes-no or no-yes is 0 — you need the bigger list for that! You now know what correlation is. Luckily entanglement is not much different. Let’s start with qubits, the quantum
|
medium
| 6,966 |
Entanglement, Quantum Computing, Quantum Physics, Information Theory, Science.
analog of bits. Instead of two positive numbers that add up to one, a qubit is represented by two numbers (which could be negative) that add up to one after you square them. For example, (⅗, −⅘) represents a qubit. In decimal notation, that is (0.6, −0.8). Clearly, these are neither positive nor do
|
medium
| 6,967 |
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