Innovative Dimensionality Reduction with Topological Data Analysis

Innovative Research in Data Analysis

We specialize in topological data analysis and dimensionality reduction methods, enhancing data interpretation through theoretical and experimental approaches.

Layered abstract design featuring a series of curved and flowing shapes resembling a topographic map. Predominant use of blue hues with variations in shade creating a sense of depth.

Topological Analysis

Research on dimensionality reduction using topological data analysis methods.

An array of 3D geometric shapes, including cylinders and rectangular prisms, arranged in a dense pattern. The shapes are predominantly in shades of green, creating a harmonious and uniform visual appearance.

Data Methods

Evaluating methods on various benchmark datasets for accuracy.

A minimalist 3D abstract composition featuring layered, translucent geometric shapes with smooth surfaces. The elements are primarily spherical and elliptical, with subtle shading and gradients creating a sense of depth and dimension. The backdrop has a soft, diffused gradient of peach and teal colors, enhancing the ethereal quality.

Comparative Study

Comparing TDA methods against traditional dimensionality reduction techniques.

A geometric, isometric art piece composed of 3D cubes arranged in a pattern that mimics a topographical map. The colors transition from blue to green, suggesting water and land formations.

A geometric and abstract 3D shape with sharp, angular facets in a mix of light and dark tones, resembling a crystallized structure with a central convergence of points. The object is rendered in shades of red, white, and black, against a solid black background.

Experiment Design

Experimental validation of new dimensionality reduction approaches discussed.

API Support

Utilizing APIs for efficient data preprocessing in research.