There are plenty of graph based big data problems, which requires new machine learning solutions, few of them are as follows:

1. Genetic and genomic data annotation problems, there are very few attempts made to solve them with large scale machine learning techniques.
2. Chemical reaction prediction is another important and emerging area which can be performed using graph based machine learning techniques.
3. Social network based problems as influencer detection, friend recommendation, group recommendation areanother well known problems.
4. Bibliographic article and scholar article detection is another graph based big data problem which requires new machine learning techniques.
5. Job and candidate profile matching problem can also be seen as a graph based big data problem and right now various companies are working over it.

Let’s see:

Classification → Yes

Regression → Yes

Clustering → Self organizing Maps, so yes Neural networks can be applied.

Dimensionality reduction → Yes, see auto encoders.

Density estimation → Haven’t seen this happen, but might be wrong.

So Neural Networks have a solution to most ML problems, however that doesn’t mean it is always the best solution. A friend of mine recently did his master thesis on pose estimation in computer vision. Deep learning methods couldn’t beat the state of the art there. Furthermore, if you have very little data, deep learning may not be the way to go, since optimization is a bitch.

SNA can be considered as an application of graph mining. For SNA, your input data is the graph representing interactions of (e.g., interest graph) or between people (e.g., twitter follower graph) per the term "social". For graph mining, domain of the graph you want to study can be more diverse, including chemical, biological, or geographical graphs.

Moreover, SNA topics (e.g., influence, centrality, distance) generally require studying the social graph as a single data structure. Other graph mining applications may either work on a single large graph (e.g., identifying key proteins of a disease in the protein interaction network of an organism), or on a set of smaller graphs (e.g., looking for common patterns among the chemical structures of molecules).

There is a vast number of potential applications of machine learning to social networks, to mention a few that are particularly active areas:

Link prediction: Given an observed network of friendships, relationships, suggest new connections, infer latent links, etc. Facebook, LinkedIn and Twitter all have their own 'People you may know' feature and it's an active research topic in machine learning, too, where it's often referred to as learning from relational data or link prediction. Even at this year's ICML there were several papers concerned with this problem, search for 'link prediction' in this list for pointers: http://icml.cc/2012/papers/

Inferring Influence, predicting spread of information: There's big interest in this right now in business (it's useful for word-of-mouth marketing), politics (optimal targeting with political messages) and in the academic community. Basically you want to infer from data who has the power to influence others and swing opinions in select topics, and which set of people you want to target if you want to maximise the effective reach of your message in a given influence network.
Manuel Gomez Rodriguez, Jure Leskovec, Lada Adamic, Sinan Aral work on this topic, so do machine learning teams at for example PeerIndex (our company), Facebook, and elsewhere.

Sentiment analysis: Figure out that when someone says something in social media about something, is it a positive or negative message. Then you can take it further and analyse overall sentiment on an entire network, and try to model and predict how it changes over time. Some people like playing with the idea of correlating sentiment in social networks about a public company to changes in share prices, see for example Can Twitter sentiment analysis guide stock market investment?

Clustering and visualisation: There's a lot you can do with unsupervised learning, dimensionality reduction and visualisation in social networks. You can cluster people based on their connections, features, interests, etc. You can use various metric or non-metric embedding techniques to visualise communities of people.

To give you a brief introduction,

I am an engineer at Compellon, a fully autonomous predictive modeling technology platform which (primarily) uses concepts of Information theory for various phases of analysis. The technology is based on decades of research by our Chief scientist Dr. Nikolai Liachenko, an expert in Information Theory and AI.

Here's how information theory has been helping us analyze real customer data sets across different domains:

a) One of the basic ideas of Information theory is that the meaning and nature of data itself does not matter in terms of how much information it contains. Shannon states in his famous paper "A Mathematical Theory of Communication (1948)" that "the semantic aspects of communication are irrelevant to the engineering problem". This enables us to construct our analytical approach around informational measures (Shannon entropy, mutual information for example) and have it to be domain and data agnostic.

b) There has been interesting work about the using the "Information bottleneck" concept to uncover the "Deep neural net blackbox".

Original paper here: https://arxiv.org/pdf/1703.00810.pdf
I also recommend this very well written blog post.
https://blog.acolyer.org/2017/11/15/opening-the-black-box-of-deep-neural-networks-via-information-part-i/

Our technology uses a variant approach not only to "autonomously" diagnose our models but to improve their quality and efficiency and subject them to “noise-testing” using these “very generic” measures.

c) Using informational measures for analysis frees us from some of the assumptions that are made in conventional machine learning. We don't assume data to have properties such as independence or that some known probability distribution fits the data.
Here's an article describing some of the practical risks of those assumptionshttps://www.edge.org/response-detail/23856

Our experiments to predict rare events (high-sigma or "black swan") with this approach has shown very impressive results.

https://www.waterstechnology.com/industry-issues-initiatives/3464301/after-building-an-ai-black-swan-detector-compellon-mulls-path-forward

Conclusion:

Information theory concepts can immensely contribute to machine learning in practice (we have quite a few case studies and success stories of customers benefiting from our platform) and I believe it would provide an even bigger significant foundation for predictive science as we run into harder problems in this space.

Graph theory is fascinating for me and is useful in many pressing real-world problems, particularly those involving processes on networks. Some topics that might spark more interest:

Biology. Disease outbreak: Graph Theory Applied to Disease Transmission. Or search 'SI / SIS / SIR Model' (susceptible, infected, recovered)

Social Science. Information and decision-making. Search 'Voter Model'

Neurology. Studying the brain. https://pubs.rsna.org/doi/full/10.1148/radiol.11110380

Enjoy!

EDIT:

Note: I plan to edit this answer by adding applications I find interesting articles:

Network Theory Reveals The Hidden Link Between Trade And Military Alliances That Leads to Conflict-Free Stability

In social network analysis, there are several ways to calculate the importance or centrality of a node (person) in a graph. Some common methods include:

1. Degree centrality: This measures the number of connections a node has to other nodes. The node with the highest degree centrality is considered the most central.
2. Closeness centrality: This measures the average distance between a node and all other nodes in the graph. The node with the highest closeness centrality is considered the most central.
3. Betweenness centrality: This measures the number of times a node falls on the shortest path between other nodes. The node with the highest betweenness centrality is considered the most central.
4. Eigenvector centrality: This measures the centrality of a node based on the centrality of its neighbors. The node with the highest eigenvector centrality is considered the most central.
5. PageRank: This algorithm is used to rank web pages and it is based on the principle that more important pages are likely to receive more links from other web pages.

These are some of the most common ways to calculate the importance of a node in a social network graph. However, it is important to note that the best method to use depends on the specific context and research question.

According to my knowledge, the site with the most problems related to machine learning is Kaggle. Kaggle is a platform for data scientists and machine learning practitioners to share, learn, and compete. It is a great resource for learning about machine learning, but it can also be a source of problems.

One of the biggest problems with Kaggle is that it can be difficult to find high-quality data sets. There are many data sets available on Kaggle, but not all of them are created equal. Some data sets are poorly labeled, while others are simply not representative of the real world. This can make it difficult to train accurate machine learning models.

Another problem with Kaggle is that it can be difficult to find good competition ideas. There are many competitions on Kaggle, but not all of them are well-designed. Some competitions are too easy, while others are too difficult. This can make it difficult to find a competition that is both challenging and rewarding.

Finally, Kaggle can be a source of frustration for data scientists and machine learning practitioners. The competition can be fierce, and it can be difficult to stay ahead of the curve. This can lead to burnout and frustration.

Despite these problems, Kaggle is still a valuable resource for learning about machine learning. It is a great place to find data sets, competition ideas, and other resources. However, it is important to be aware of the problems with Kaggle and to take steps to mitigate them.

Here are some tips for avoiding problems with Kaggle:

• Be selective about the data sets you use: Not all data sets are created equal. Do your research and find data sets that are well-labeled and representative of the real world.
• Be selective about the competitions you enter: Not all competitions are well-designed. Do your research and find competitions that are challenging but not impossible.
• Take breaks: It is easy to get burned out when working on Kaggle. Take breaks to avoid burnout and frustration.

By following these tips, you can avoid problems with Kaggle and make the most of this valuable resource.

This is a great question!! For a bit of personal history, I am someone trained in classical information theory who is now working in the IBM Watson group, which emphasizes a lot machine learning skills. So almost every day I wonder about this question, trying to make my background relevant to the world I live in.

I think there are many good examples of connecting points, but we are really only scratching the surface and it is highly likely that the connections deepen soon.

For example, I have been impressed by the parallels between the target of RNNs (sequence prediction) with the equivalent work that has been going in information theory for decades. I am certain this is a fruitful direction to do research on; I would certainly pick it if I was a Ph.D. student.

Many famous algorithms used extensively in speech and natural language processing actually originated in information theory or close to it. Some names are the Viterbi algorithm, the BCJR algorithm, Baum-Welch, the Forward-Backward algorithm among the more famous ones. Belief propagation on graphical models is also extensively used in information theory as a decoding method for codes built on graphs.

For a different take on the relation, I suggest you look into the "information bottleneck" method which builds on rate-distortion theory to derive techniques that resemble latent variable models.

If I can think of more I will update the answer =)

Graph algorithms pop their head every so often. The back-propagation procedure, used to calculate the gradient of the parameters of a neural network, may be viewed as combinatorial algorithm .

I used graph algorithms (Barr, Shaw, et al.) to classify documents. Specifically, I turned the word2vec embedding into a correlation matrix (symmetric matrix with diagonal =1) and translated that matrix into a graph by decreeing an entry 0 if the corresponding entry is smaller in absolute value than some prescribed value, say 0.5, and 1 otherwise. The matrix served as a basis for discovering relations in text. For example, we used cluster editing to find groups of similar texts and maximal independence sets to identify number of unique topics.

Logic also flows in the opposite direction. Recently, procedures like struc2vec (and various other) were used to embed graphs (or vertices of graphs) into vectors in a finite dimensional Euclidean space. Resulting graph embedding is instrumental to investigate the underlying graph structure, or more specifically, it may provide a canonical way to measure similarity (or dissimilarity) between two graph.

Machine Learning, currently the most sought after skill in the computer science, has plethora of good courses over the internet.
Having a good understanding of the basics and the mathematics behind it is paramount for selecting the best Machine Learning model.Don’t worry you don’t need to be a PhD in Maths to dig deep.

Currently Andrew Ng’s Machine Learning course is on demand and is the right starting point for any beginner.
I would also recommend to check out Machine Learning course by University of Washington, as certain things can be better retained when explained with better graphics, and I believe that’s where the latter stands out.

Once the introduction to Regression, Classification and Clustering has been completed, the next step would be to advance further into the domain of Neural Networks. Deep Learning by Andrew Ng is by far the best course. Once this course is done it will give a holistic understanding of Machine Learning and its facets.

I would also recommend to check out Time Series , as it is not covered in any of the courses mentioned above, but knowing it would be a huge plus as it involves applying Machine Learning to time related data(very useful in Stock Market and company related Finances).

Even after finishing the courses, we have just come half way. From my experience I can vouch that the best of Machine Learning is understood only through discussion. Knowing which Machine Learning model to apply is always going to be a question. Having a strong understanding along with value added discussion is a bonus. Even after a model has been decided on, there are many questions that still needs to be answered in the development process.

In short Machine Learning unlike other facets, needs further tweaking and optimisation on the developer’s part according to the data which can be best understood only through discussion and implementation of the knowledge acquired.

Also check out Kaggle after the courses as it will give a hands on experience on real world data if you are still in college.

PS : For people interested in deeper understanding of the statistical maths involved in Machine Learning kindly refer to the Harvard Lecture Series on Statistics.

Edit 1 : fast.ai · Making neural nets uncool again is another must visit website which helps to build state of the art Machine Learning models on the fly.

Happy Learning!

I think Josep Lluis Larriba Pey gave a pretty comprehensive answer. Social network analysis is more than just analyzing data generated by social media networks. Social network analysis exists for a long time, and has its roots in graph theory.

It is importance as it maps the flow of goods, services, information between people, teams, organizations, etc. For me, the core of social network analysis is that aspects in our life are interconnected, and that interaction with one unit, influences interaction with a connected unit.

Before jumping on the bandwagon and doing a social network analysis, be clear on this: What are your nodes and what are your edges?

By creating a mathematical model of a social network, we can calculate the betweenness centrality of each individual node and estimate which node might influence the social network more than the rest of them. We can even calculate the shortest path for reaching node B from node A. These kind of parameters are used in finding key targets in terrorist organizations, calculating social score of a person (e.g. Klout ), etc. We can find out clusters among the social network and draw inferences regarding location or psychology. One study of high school students' social network indicated clusters based on ethnicity, color, etc.

Clustering is a machine learning algorithm that groups data points together. Its goal is to find natural groupings in data so that similar examples are close together and dissimilar examples are far apart. This can be useful for a variety of tasks, such as monitoring unusual activity in data streams, compressing data for storage, or visually exploring high-dimensional data. There are many different ways to perform clustering, and each has its own benefits and drawbacks.

There are various clustering algorithms available, which can be broadly classified into two types:

1. Connectivity-based clustering: This approach works by first creating a cluster of data points and then connecting similar points together to form larger clusters. The most common algorithm used for this purpose is the single-linkage algorithm.

2. Centroid-based clustering: This approach works by first finding the center (or centroid) of each cluster of data points and then connecting similar centroids together to form larger clusters. The most common algorithm used for this purpose is the k-means algorithm.

Clustering is the task of grouping data based on similarity criteria. Clustering is a essential part to learning. When we, humans, observe the world, what we constantly do is try to categorize things/events/signals into groups, as a means of understanding them. Studying clustering is one of the many ways in which we can attempt to recreate learning and intelligence within machines.

Clustering can also be seen as the unsupervised counterpart of classification. Knowing that data-points belong to a set of C classes is the same as saying that they can be clustered into C distinct groups that share the same properties. Clustering, in this sense, is trying to find ways in which the same set of points can be grouped. For instance, a classifier might be trained to recognize good payers and bad payers. A clusterer will, instead, show you that your payers can be grouped in several useful ways.

The primary difference between a hierarchical clustering approach and an agglomerative clustering approach is that in hierarchical clustering, the data set is initially divided into groups of single observations and then grouped together based on similarity or other criteria. In other words, it starts with many single clusters and works to group them together until a certain threshold of similarity is reached. Conversely, agglomerative clustering starts by grouping all observations into one large cluster and then iteratively divides this larger cluster into smaller ones, based on some predefined criteria such as distance or density.

The key difference between these two approaches lies in the way they affect the dissimilarities among clusters. In hierarchical clustering, once two clusters have been merged together there is no changing back; any further changes must be based on the new composite cluster. This can sometimes lead to overly-simplified relationships among data points due to early merges that may not accurately reflect true differences between groups within the data set. On the other hand, agglomerative methods maximize granularity by allowing more opportunities for re-structuring clusters at each stage of analysis; this can help avoid issues caused by committing too soon to early-stage mergers when creating data partitions around potentially meaningful relationships in datasets with complex relational dynamics between groups of observations.