Research And Application Of Multidimensional Scaling Analysis Method For Interval Data

In real life,there are plenty of series data and panel data measured with daily data.If you want to perform multivariate statistical analysis on them,roll the original data into a quarterly or annual interval data and then develop multivariate statistical analysis based on it.Multidimensional Scaling(MDS)is a classic method of reducing dimensions of multidimensional research objects in multivariate statistics and visualizing the relationship between sample points in a low-dimensional space.When calculating the distance matrix,the commonly used Hausdorff distance for interval data assumes that the original data is uniformly distributed in the interval,and it is difficult to effectively use the information of the original data in the interval,especially when the point data in the interval obey a skewed distribution.Therefore,based on the basic idea of Hausdorff distance,this paper proposes the median-quartile-deviation distance measurement.The traditional multi-dimensional scaling method is mainly suitable for crosssectional data.When it is time series data or panel data,it cannot reflect the dynamic similarity between the objects,so it is no longer applicable.This article attempts to extend the existing self-weighting Multiview Multidimensional scaling(MVMDS)to time series data and panel data,thereby visually show the dynamic similarity between objects in low-dimensional space.Self-weighting MVMDS treats data from different sources as different views,calculates a distance matrix for each view,and uses a single parameter γ to control the weight of each view.When MVMDS model is applied to time series data or panel data,each time point corresponds to a view.However,it is often impossible to follow rule of the time series forecasting model.So this article will also adjust the MVMDS method with artificially given weight parameters.The air quality index and the stock index are respectively typical time series daily data and panel daily data.From an annual or quarterly perspective,the data within the interval obey a skewed distribution.Therefore,this paper selects air quality index data and stock index data to carry out empirical analysis and draw conclusions.