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An improved visual analytics framework for high-dimensional pareto-optimal front: a case for multi-objective portfolio optimization


Visual representation of a many-objective Pareto-optimal front in a high-dimensional (four or more) objective space requires a large number of data points. Choosing a single point from a large number of data points even with preference information is problematic, as it causes a large cognitive burden on the part of the decision-makers. Therefore, many-objective optimization and analytics practitioners have been interested in practical visualization methods that enable them to filter down a large set of data points to a few critical points for further analysis. Most existing visualization methods are borrowed from other data analytics domain and they are too generic to be effective for many-criteria decision making. In this paper, we propose a visualization method, following an earlier concept, using star-coordinate plots for effectively visualizing many-objective trade-off solutions (data points). We demonstrate the use of the proposed method to a couple of high-dimensional test problems and a 4-objective portfolio optimization problem. We also show a case of interactive exploratory data analytics where we use the ‘Pareto Race’ technique from the multi-criteria decision analysis (MCDA) literature to demonstrate the ease and advantage of the proposed visualization method.

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  1. In this paper, we denote each data point with \(\mathbf {f}\) instead of a more standard notation \(\mathbf {x}\). Since each data point \(\mathbf {f} = (f_1, f_2, \ldots , f_m)\) is a vector of objective function values in \({\mathbb {R}}^{m}\).

  2. Or \(\mathcal {D} \subset {\mathbb {R}}^{3}\) for the case of three-dimensional visualization.

  3. This might depend on the properties of the data set as well

  4. In our case the total number of stock is 12, i.e. \(n = 12\).

  5. Or, we can restart the entire procedure to explore other points in the vicinity of \(F_4\).


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Correspondence to AKM Khaled Talukder.

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Talukder, A., Deb, K. An improved visual analytics framework for high-dimensional pareto-optimal front: a case for multi-objective portfolio optimization. J BANK FINANC TECHNOL 5, 105–115 (2021).

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  • Pareto-optimal Front
  • Visualization
  • Multi-criterion Decision Making
  • Visual Analytics
  • Alpha-shape
  • Non-convex Hull
  • Pareto-race
  • PaletteViz