The Fundamentals of Functional Data Analysis

Introduction - Functional Data Analysis

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The digital revolution is responsible for improving machine learning and functional data analysis. In a global and fast-paced economy, businesses must take advantage of all of the analysis tools available in order to remain competitive. Data analysis experts such as Ramsay Silverman claim Organizations that invest in functional data analysis and other techniques can learn from their mistakes, optimize problem-solving, correct inefficiencies, and increase the bottom line.

Functional data analysis is one important technique used by many modern businesses in the digital era. FDA identifies patterns in data that would otherwise be unnoticeable, allowing business owners to make decisions based on statistics rather than guesswork. Read ahead for an overview of functional linear models, how they work, and their benefits.

The What, Where, and Why of Functional Data Analysis

Functional data analysis (FDA) is an offshoot of statistical analysis. It refers to surfaces, curves, or other patterns that operate on a spectrum. Businesses, researchers, and analysts are gathering this type of information to extract insights and predict future trends, reach new markets, and make better decisions.

In FDA, each data sample is considered a function. The spectrum that each function operates on is referred to as either time or probability. Businesses use different data samples to understand and forecast time series data, or data collected at different times. Time series data is collected to develop insight into cause and effect relationships and how historical data impacts future outcomes.

This assists in developing business strategies that increase operational effectiveness.
Viewing how functional data analysis works through specific examples can help to understand its advantages. Here is how using functional analysis helps an organization achieve operational effectiveness -

1. Functional Data Analysis Creates Better Strategies

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FDA helps to understand causal relationships between two variables or data sets. By identifying a variable that results in a good outcome, businesses will know to make similar choices in the future.

To illustrate, a retailer may want to study the relationship between coat sales and month to pinpoint which months sales are the highest. Months (time values) would be on the bottom of the chart, and coat sales (value) would be on the left-hand side of the chart.

Sales are slow in the summer months and then gradually increase through the remainder of the year, with a spike in December and a slow decrease back to baseline. A curve shape describes this time series causal relationship.

The retailer determines that sales are highest from November-February. The store uses these findings to generate new business strategies that increase the bottom line and decrease waste. Potential solutions include increasing coat advertisements during busy months, adding new promotions in November, or further decreasing the production of coats in slower months to save money.

2. Functional Data Analysis Improves Forecasting

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Forecasting is an essential modeling tool for growth-driven organizations that want to fine-tune decision-making and problem-solving. Executives can use historical information to identify patterns and predict future outcomes. This allows businesses to make decisions based on facts and evidence rather than guesswork, which optimizes problem-solving and saves money.

To illustrate, a new startup wants to see whether they received a return on investment for the 5 previous years. They generate a chart labeled Return on Assets, with Years placed on the bottom and Money Spent placed on the left-hand side of the graph.

After plotting their historical data, an analyst finds that the startup did not receive a return on investment until after the 4th year of operations. They also discover that they lost much more money during those first 4 years than they should have, which decreased the small return on investment they received in the 4th and 5th years. If business strategies don't change, the analyst predicts that the startup will continue to lose money the following year.

Even though it is typical for a startup to lose money in its first couple of years of operating, this startup does not want to waste any more money than necessary. After drilling down into spending data to find any areas of waste, the analyst discovers that there is way too much money spent on labor costs.

After generating a new strategy to decrease labor costs and improve the onboarding process, the business receives a much bigger return on investment the following year. By utilizing a discriminant analysis to gain insight into historical patterns and predicting future patterns, every company can make better decisions in the future.

Functional Data Analysis - Key Takeaways

In conclusion, here is what to know about functional data analysis

  • Functional data analysis is a branch of statistics that uses data to study curves, patterns, and trends. Utilizing this field of analysis to extract insights about historical information can help to make better business decisions in the future.
  • Functional linear models helps interpret patterns in data sets and find relationships between variables. If an organization wants to find the relationship between coat sales and month, it can use multivariate analysis displaying a curve to do so.
  • Once interpretations are gathered in a functional regression analysis, the business can generate new strategies to optimize future coat sales and decrease waste et al.
  • A functional principal component analysis also optimizes forecasting by pinpointing patterns in historical information. Companies can use these principal components to cut back on spending, increase sales, and optimize workflows in the future.