Introduction
A matrix can be broken down into its component parts with the help of a mathematical technique called the SVD Singular Value Decomposition. It finds use in many different areas, such as signal processing, image compression, and machine learning, among others.
For the past few years, SVD has also been utilised in the process of analysing massive datasets, particularly data pertaining to the financial industry. The Pensions Authority is a government agency in Ireland that is responsible for regulating the pension industry there. Within the scope of this research, we will investigate the usage of SVD by that organisation in the analysis of financial data. In particular, we will examine a scenario in which the Pensions Authority utilised SVD to uncover potential fraud in pension funds and then submitted its results to the appropriate law enforcement officials.
SVD Background
Pension plans in Ireland are subject to regulation and oversight by the Pensions Authority, which was established for this purpose. The Authority, as part of its responsibility as a regulatory body, performs routine audits of pension funds to ensure that the funds are being administered in line with the applicable legal requirements.
In recent years, the Authority’s level of worry regarding the possibility of fraud in the pension industry has grown to an all-time high, particularly in connection to self-administered pension funds. These are pension funds that are handled not by an outside professional fund manager but rather by the members of the pension fund themselves.
An audit of a pension fund that was self-administered was carried out by the Authority in 2018, and during that audit, a number of inconsistencies were discovered in the fund’s financial records.
The Authority specifically observed that the fund’s assets had been greatly exaggerated, and that there had been a number of transactions that were dubious that took place within the fund. In addition, the Authority indicated that there had been a number of suspicious transactions. The Authority had a hunch that the trustees of the fund had been involved in fraudulent behaviour and made the decision to look into the matter further.
Analysis
The Authority made the decision to conduct an SVD analysis of the fund’s financial data in order to investigate the possibility of fraud. SVD is a strong technique that may be used for the analysis of huge datasets. It can be utilised to find patterns and abnormalities that might not be immediately obvious to the naked eye. In the case of the pension fund, the Authority utilised SVD to decompose the fund’s financial data into its constituent parts, and then evaluated those pieces in order to uncover any anomalies that may have occurred.
The gathering of financial information from the pension fund constituted the initial stage of the investigation. This featured information on any transactions that had taken place within the fund, as well as statistics on the fund’s assets, liabilities, income, and expenses.
Also, this included any and all transactions that had taken place. After then, the information was arranged in the form of a matrix, where each row was supposed to stand for a distinct financial account and each column was supposed to stand for a distinct time period.
The Authority employed singular value decomposition SVD to breakdown the matrix into three matrices once the data had been organised into a matrix. These matrices included a matrix of left singular vectors, a diagonal matrix of singular values, and a matrix of right singular vectors.
The singular vectors on the left reflect the directions in which the data exhibit the greatest variance, whereas the singular vectors on the right show the directions in which the data exhibit the greatest covariance. The solitary values each illustrate the significance of their respective directions.
The second stage of the investigation consisted of looking at the unique values to see if there were any recurring themes or peculiarities.
The Authority discovered that there were a handful of singular values that were significantly greater than the rest, which indicated that there were certain accounts or transactions that were significantly more important than others.
During more investigation, the Authority found a number of accounts that had been greatly inflated, including those that had been used to hide illicit transactions. Among these accounts was one that had been utilised to significantly inflate its revenue.
In addition, the Authority investigated the left singular vectors in search of any recurring patterns or peculiarities. Any unusual occurrences in the data will be mirrored in the left singular vectors since they indicate the directions in which the data show the most variation.
The Authorities came to the conclusion that the fake accounts were the cause of the variance in the data after discovering a number of left singular vectors that had a strong correlation with these accounts.
At the end, the Authority looked at the correct single vectors to see if there were any patterns or unusual occurrences. Any irregularities in the data will be reflected in the right singular vectors since these vectors represent the directions in which there is the greatest covariance in the data.
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