Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Most manifold learning methods consider only one similarity matrix to induce a low-dimensional manifold embedded in data space. In practice, hover,  often use multiple sensors at a time so that each sensory information yields different similarity matrix derived from the same objects. In such a case, manifold integration is a desirable task, combining these similarity matrices into a compromise matrix that faithfully reflects multiple sensory information. A small number of methods exists for manifold integration, including a method based on reproducing kernel Krein space (RKKS) or DISTATIS, where the former is restricted to the case of only two manifolds and the latter considers a linear combination of normalized similarity matrices as a compromise matrix.   present a new manifold integration method, Markov random walk on multiple manifolds (RAMS), which integrates transition probabilities defined on each manifold to compute a compromise matrix. Numerical experiments confirm that RAMS finds more informative manifolds with a desirable projection property.
['Heeyoul Choi', 'Seungjin Choi', 'Yoonsuck Choe']
I am writing a research paper on a idea Manifold integration with Markov random walks
[{"from": "human", "value": "I am writing a research paper on a idea Manifold integration with Markov random walks"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Most manifold learning methods consider only one similarity matrix to induce a low-dimensional manifold embedded in data space. In practice, hover,  often use multiple sensors at a time so that each sensory information yields different similarity matrix derived from the same objects. In such a case, manifold integration is a desirable task, combining these similarity matrices into a compromise matrix that faithfully reflects multiple sensory information. A small number of methods exists for manifold integration, including a method based on reproducing kernel Krein space (RKKS) or DISTATIS, where the former is restricted to the case of only two manifolds and the latter considers a linear combination of normalized similarity matrices as a compromise matrix.   present a new manifold integration method, Markov random walk on multiple manifolds (RAMS), which integrates transition probabilities defined on each manifold to compute a compromise matrix. Numerical experiments confirm that RAMS finds more informative manifolds with a desirable projection property."}]