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What is low dimensional space?
Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to its intrinsic dimension.
What is low dimensional embedding?
Low dimensional embedding is a method which maps the vertices of a graph into a low dimension vector space under certain constraint. For each pair of vertices linked by an edge (u, v), the weight on that edge, wuv, indicates the firstorder proximity between u and v.
What is low dimensional dataset?
It generally refers to the number of features you have for each sample in the problem you are trying to classify. For example, the famous Iris flower dataset only includes 4 features (Sepal length, sepal width, petal width, petal length), and would be considered as a low dimensional dataset.
How do you avoid the curse of dimensionality?
To overcome the issue of the curse of dimensionality, Dimensionality Reduction is used to reduce the feature space with consideration by a set of principal features.
What do you mean by high dimensional sparse data?
So, high dimensional sparse data (let’s say that the dimension is N) refers to data that if arranged in a Nd-tensor would only occupy a very small percentage of the total number of cells in the tensor. Here in Quora there are already some questions/answers related with this kind of data, such as:
Which is an example of a dense dimension?
For example, in the Sample.Basic database, accounts data exists for almost all products in all markets, so Measures is chosen as a dense dimension. Year and Scenario are also chosen as dense dimensions. Year represents time in months, and Scenario represents whether the accounts values are budget or actual values.
Why are multidimensional databases chosen as sparse dimensions?
Because not every product is sold in every market, Market and Product are chosen as sparse dimensions. Multidimensional databases also contain dense dimensions. A dense dimension has a high probability that one or more cells is occupied in every combination of dimensions.
Which is better sparse or dense in data modeling?
Sparse and dense are a storage property of the values of an attribute. Sparse is better than Dense Logical Data Modeling – Attribute Linear Algebra – Vector