Joyal

The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in High dimensional spaces that donot occur in lower dimensions like 3D physical space of every day life.
Dimensionally cursed phenomena occurs in sampling, numerical analysis, data mining , machine learning and databases. The common theme of these problem is when dimensionality increases, volume of space increases and available data are sparse.This becomes problem for any method that requires statistical significance.
In order to obtain a statistically sound and reliable results the amount of data needed to support the result often grows exponentially with the dimensionality. Also, organizing and searching data often relies on detecting areas where objects form a group with similar properties,  in high dimensional data, however all objects appear to be sparse and dissimilar in many ways, which prevent common data organization strategies from being efficient.
There are two things to consider regarding curse of dimensionality,  on one hand machine learning excels at analyzing data with many dimensions. Humans are not good at finding patterns that may spread across so many dimensions,  especially if those dimensions are interrelated in counter intuitive ways. On the other hand , as we add more dimensions we also increase the processing power we need to analyze the data,  and we also increase the amount of training data required to make meaningful models.
Hughes Phenomena 
Hughes phenomena shows that as number of features increases, classifiers performance increases as well until we reach the optimal number of features.  Adding more features based on the same size as the training set will then degrade the classifiers performance. 
Curse of dimensionality in distance function
An increase in the number of dimensions of a datasets means there are more entries in the vector of features that represent each observation in the corresponding Euclidean space. In other words as the number of features grows for a given number of observations,  the feature space becomes increasingly sparse; that is less dense or emptier. On the flip side, the lower data density requires more observations to keep average distance between the data points the same.
When the distance between observation grows supervised machine learning becomes more difficult because predictions for new samples are less likely to be based on learning from similar training features.
Over fitting and Under fitting
In curse of dimensionality even the closest neighbor can appear to being far away in a high dimensional space to give a good estimate. Regularization is one way to avoid over fitting. We can sometimes use feature selection and dimensionality reduction techniques to help us avoid the curse of dimensionality. Over fitting occurs when a model starts to memorize the aspects of the training set and in turn loses the ability to generalize.
Ex:-As our training data is not good enough we risk producing a model that could be very good at predicting the target class on the training datasets that may fail miserably when faced with new data. That is our model, doesn't have the generalization power.
To avoid overfitting is to preference  simple methods, hypothesis with fewest assumptions must be selected.
If we keep our model simple we must avoid overfitting but if we keep it simpler we may risk of suffering from undercutting. It arises when our model has such low representation power that it cannot model the data even if we had all the training data we want. A model undercuts when it fails to capture the pattern in the data. It suffers high bias.
Hence in order to avoid curse of dimensionality more data is needed.

Holy Trinity is also known as Project Management Triangle, Iron Triangle or Triple Constraint. It is an equilateral triangle with Cost, Time and Scope. It outlines the 3 major constraints that a project manager faces. It also dictate the scope of the product you deliver. Together, they outline a space in their center, which is project Quality. Out of all the 3 sides of the triangle in project -the client is allowed to control any two sides of the triangle, but the producer MUST be in control of the third, whichever that is. The amount of control you retain ultimately reflect in the quality of the project/outcome. 
The Cost, Time and Scope is interrelated.
Scenario #1
Client: Scope and Schedule
Producer: Budget
A demanding client isn't interested in slashing the scope of the project, nor are they interested in cherry picking items for prioritization, to get to market quickly. And they want it yesterday. This is the client that needs everything, and there is a hard deadline that just cannot be missed, no matter the cost. This is where the producer must stand firm on budget. If hitting a firm date is mission critical, and nothing can be left out of scope, then the only way this can be achieved is by allowing the producer the budget and resources they need to make this happen. It might mean additional contractors to be hired, putting in overtime, acceleration fees. The client won't be able to fault this logic, and must be open to the idea that things may cost more (variances), or the project might require re-estimation.
Scenario #2
Client: Schedule and Budget
Producer: Scope
The idea is to deliver on time and on budget. The funds are limited and for whatever reason, it's important to get to market quickly, perhaps for competitive advantage. In any situation where you have limited resources and also are limited in the timeframe that you have to work within, the only possible conclusion is that the producer needs to control the scope. There are only so many hours in a day, and if budget is also fixed, there is no chance of doing any additional overtime or hiring help. An open and frank discussion with the client about what is physically possible to achieve in the timeframe for the available budget. The client may insist that everything has to be done, but if they're not willing to pay extra or give you more time, then it's obvious that some requirements are going to have to give. 
Scenario #3
Client: Budget and Scope
Producer: Schedule
The client has a fixed budget, and they know exactly what they want - the requirements are set in stone. They probably also have an idea of when they would like the project to be completed, but unfortunately for them, that call lies with the producer. Of the three possible combinations, this one is the most unlikely. And nobody is saying that the budget doesn't matter - clearly you're never going to build a website for free simply because the client doesn't need it in any hurry. What it does mean is that while the client is set on holding you to your original quotation and they are not wanting to compromise on functionality or requirements, then they are going to need to work in with the producer and acknowledge that timeframes may need to shift here and there. Potentially another job has come in from sales, and it's super urgent. Think acceleration fees, or penalty clauses in the contract for missing delivery deadlines on milestones, etc. The production manager says the schedule has to shift, and the original client is being shunted down the priority queue. A little more time is needed here. It may not be a happy discussion, but at the end of the day, but by retaining at least one side of the triangle and you remain in control. A quality project is still ensured.
Scenario #4
Client: Scope, Schedule and Budget
Producer: None
If you find yourself in the situation where you are not in control of anything, project is not favorable. Don't hold on and fight your way through to the end. You'll end up stressed.
Where it all falls into a pit is when we have to let go of the triangle. Nobody is saying that we can't give the client everything they want, we just need to ensure we are still in control. Our best chance of delivering a quality project on time, on budget and in scope, is by ensuring that you get what you need from the triangle.
 

An interrelationship diagram can  depict relationship in a complex situation; the one which are not easily traceable.
It can be best used when 
1. Trying to understand links between ideas or cause and effect relationships; especially when trying to identify greatest impact of improvement 
2. When complex issue is analyzed for causes
3. When complex solution is being implemented 
4. In RCA, to understand how different aspects of problems are connected 
Seeing that relationship between problem and possible cause can be further analyzed 
5. After generating fish bone and tree diagram,  to more completely explore relations of ideas
Practical examples:-
1. A computer support group planning to replace mainframe computers; the interrelationship diagram can be drawn to sort out a confusing set of elements involved in project. The ideas that were brainstormed were a mixture of action steps, problem, desired results and less desirable effects handled. All these ideas went onto diagram together.
2.Decline in productivity at a workplace,  as resources hired is a cost to the company.