Dimensionality Reduction

Evaluating TDA methods against traditional dimensionality reduction techniques.

A three-dimensional abstract geometric shape with a smooth, wavy surface featuring blue and gray hues. The shape is set against a blurred background with gradients of gray and black.
A three-dimensional abstract geometric shape with a smooth, wavy surface featuring blue and gray hues. The shape is set against a blurred background with gradients of gray and black.
Topological Analysis

Extracting features from high-dimensional datasets for evaluation.

A geometric, paper-crafted object with a complex, polyhedral shape is suspended against a beige background. The object appears to be made from pieces of paper with map-like details, featuring lines and small symbols.
A geometric, paper-crafted object with a complex, polyhedral shape is suspended against a beige background. The object appears to be made from pieces of paper with map-like details, featuring lines and small symbols.
An abstract 3D structure composed of geometrical shapes, including interconnected rectangular prisms and cylindrical objects. The surfaces are covered with a polka dot pattern. The background features a dark gradient, adding contrast to the shapes.
An abstract 3D structure composed of geometrical shapes, including interconnected rectangular prisms and cylindrical objects. The surfaces are covered with a polka dot pattern. The background features a dark gradient, adding contrast to the shapes.
Three-dimensional geometric shapes are arranged in a vertical sequence surrounded by an abstract background. An orange structure resembling a block with openings is positioned on top, followed by a green circular object with a textured pattern on its edge. At the bottom, a blue block with cutouts is placed. All these objects rest on red elliptical platforms, creating a futuristic and abstract composition.
Three-dimensional geometric shapes are arranged in a vertical sequence surrounded by an abstract background. An orange structure resembling a block with openings is positioned on top, followed by a green circular object with a textured pattern on its edge. At the bottom, a blue block with cutouts is placed. All these objects rest on red elliptical platforms, creating a futuristic and abstract composition.
Comparative Experiments

Testing performance on public datasets like MNIST and CIFAR-10.

An array of three-dimensional geometric shapes featuring triangular pyramids arranged in a symmetrical pattern. The shapes have a glowing cyan outline, creating a futuristic and dynamic visual effect against a dark background.
An array of three-dimensional geometric shapes featuring triangular pyramids arranged in a symmetrical pattern. The shapes have a glowing cyan outline, creating a futuristic and dynamic visual effect against a dark background.

Experiments

Evaluating TDA methods against traditional dimensionality reduction techniques.

A complex, abstract 3D shape with smooth, intertwined curves featuring a gradient of colors on a black background. The structure appears dynamic, with seamless blending of hues creating a visually striking pattern.
A complex, abstract 3D shape with smooth, intertwined curves featuring a gradient of colors on a black background. The structure appears dynamic, with seamless blending of hues creating a visually striking pattern.
A pattern of densely packed, vertically aligned cylindrical shapes creating an abstract, geometric landscape. The arrangement forms a textured surface with varying heights, reminiscent of a futuristic cityscape or digital terrain.
A pattern of densely packed, vertically aligned cylindrical shapes creating an abstract, geometric landscape. The arrangement forms a textured surface with varying heights, reminiscent of a futuristic cityscape or digital terrain.
Research

Innovative dimensionality reduction through topological data analysis.

© 2025. All rights reserved.