Principal component analysis assignment help
Principal component analysis, commonly denoted as PCA, is a dimensionality reduction technique that is generally used to “reduce the dimensionality” or rather, reduce the number of variables in a large set of data. What this method does is that it transforms large sets of variables into smaller ones that contain as much information as possible as the larger ones. Though reducing dimensionality of a data set makes it easier to manipulate and analyze data, it can make it less accurate.
Principal component analysis trades a little part of data accuracy for simplicity. Since smaller sets of data are easier to visualize and explore, data analysis becomes much faster and easier for machine learning algorithms because there are no extraneous variables to process. The purpose of principal component analysis is simple; to reduce the number of variables in a data set without losing much information of the initial data set.
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Understanding principal component analysis
To fully understand the concept ofprincipal component analysis, let’s consider an example where you want to forecast the GDP (gross domestic product) of a certain country for the year 2021. You have plenty of information available:
- The country’s GDP for the entire 2020, 2019, 2018, and so forth
- Several publicly available economic indicators such as the inflation rate, unemployment rate, and so on
- The country’s latest census data indicating how many people work in each sector
- The stock prices in different industries
- The number of Initial Public Offerings (IPOs) occurring every year
Despite having large sets of data from this information, you also have plenty of variables to work with. Now, working with numerous variables can sometimes present problems, hence, when dealing with large datasets like what we have above, there are a few questions you should ask yourself:
- Do I understand how the variables in this data related to each other?
- Is the number of variables extremely high that I might risk overfitting my data model or violating the assumptions of my modeling technique?
You may also ask yourself, “How can I reduce the number of variables in this data and concentrate only on a few of them? Simply what you mean here is that you want to reduce the dimensionality of your feature space, and by doing so, you will end up with fewer associations between variables and the likelihood of overfitting your model will be much less. Of course, this doesn’t mean that you are completely not likely to over fit your data model; but you sure are on the right track! So, what’s next? Implement the two techniques of dimensionality reduction as explained below by our principal component analysis project help experts.
The feature elimination method is just what the name suggests – reducing the feature space by removing features. In our example of predicting the GDP above, instead of working with all the variables we have in our data, we might do away with all the variables except the ones we feel are likely to give us the best GDP prediction.
The upside of feature elimination is that it is simple to use and makes variables easier to interpret. The downside? You will not gain any information from the variables you have eliminated. For instance, if we only use the GDP of the year 2020, one economic indicator like the inflation rate, and the current census data, we will be missing out on whatever information the eliminated variables could have contributed to our data model. In simple terms, when we remove features, we also remove any benefits we could have reaped from those features.
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Unlike feature elimination, feature extraction does not get you losing the information that was contained in the variables you dropped. Let’s say you have fifteen independent variables. When using this technique, you will create fifteen “new” independent variables, whereby each “new” independent variable will be a combination of the fifteen “old” independent variables. Nevertheless, you will create these new variables in a particular way and arrange them in order of how accurately they predict your dependent variable.
At this point you may want to know, “Where exactly does reduction of dimensions come in?” Well, you will retain as many new independent variables as you wish, but you will get rid of the ones that seem the least important. Since you had arranged the new independent variables in the order of how accurately they predict your dependent variable, you can easily identify the variables that are the most important and those that are less important. Here is the best part; since you formed the new independent variables by combining the old ones, you will still be retaining the most important parts of your old independent variables, even when you remove one or multiple new variables.
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What dimensionality reduction technique does principal component analysis work with?
Principal component analysis uses feature extraction for dimensionality reduction. So technically, it puts together your input variables and organizes them in a particular way. From there, you can be able to select the most important variables and eliminate the least important, while still keeping the most important information of all your variables. Here is an added advantage: every new variable formed after a principal component analysis is independent of each other. This benefit is a great deal because the assumptions of linear regression models require that variables be independent of each other. So if you were to fit these new variables into a linear model, then this assumption will perfectly be satisfied.
The principal component analysis is a great technique to use when you want to get rid of some variables but are not quite sure about which variables you should completely get rid of. It is also an excellent way to make sure that the variables you are working with are completely independent of each other and easily interpretable.
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Advantages of principal component analysis
Principal component analysis has several advantages over other dimensionality reduction techniques. Here are a few:
- Removes correlated features: It is very common to get thousands of variables and features in a dataset you are working with. And since running your algorithm with numerous features can reduce its performance, you must find a way to get rid of some of these features. Principal component analysis will do this for you efficiently.
- Improves the performance of your algorithm: Running your algorithm with so many features will degrade its performance. By using principal component analysis you are able to eliminate correlated features that do not add value to decision making, which speeds up your algorithm.
- Minimizes overfitting: Overfitting occurs when there are plenty of variables in a data set. Principal component analysis overcomes the issue of overfitting by eliminating some of the variables.
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