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Principal Component Analysis

Principal Component Analysis (PCA) is a common technique in statistical analysis, widely used for pattern recognition, data compression, image preprocessing, signal-noise analysis, and high resolution spectrum analysis.

Principal Component Analysis transforms a group of activites into a set of unique components, where each component has a numerical degree of distance and relatedness from an agreed on centered component. The first component has the largest possible variance (it accounts for most of the variability in the group). Each succeeding component has the highest variance that is orthogonal to the preceding components. The transformation of the group proceeds linearly from a group with a high degree of dimensionality to a group with a low degree of dimensionality of which the components of the group with a low degree of dimensionality are uncorrelated.

Principal Component Analysis is also used in the forecast of a most likely outcome through time-series analysis and regression analysis. Since Principal Component Analysis has two important characteristics valuable in the forecast of probable outcomes.

The first characteristic, notably the most well-known, of Principal Component Analysis that's valuable in the forecast of probable outcomes reduces the dimensionality of a complex group of possibly unrelated activities into a smaller group of principal components that accurately represent the entire group with minimum information loss and no loss of essential intrinsic information. The next characterisitic of Principal Component Analysis reveals the internal structure of a group of possibly unrelated activities, it leads to the discovery of meaningful relationships based on the commonalities the internal structure of the group shares with other activities that happened in the past.

So in forecasting through time-series analysis and regression analysis the approach taken with Principal Component Analysis is to focus the reconstruction of projected outcomes on the optimization or maximization of the variances of specific activities. In most cases the predictability of specific activities can be calculated with high percentages of certainity.

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