classification - Whats the meaning of dimensionality and what is it . . . Dimensionality is the number of columns of data which is basically the attributes of data like name, age, sex and so on While classification or clustering the data, we need to decide what all dimensionalities columns we want to use to get meaning information
Why is dimensionality reduction always done before clustering? Reducing dimensions helps against curse-of-dimensionality problem of which euclidean distance, for example, suffers On the other hand, important cluster separation might sometimes take place in dimensions with weak variance, so things like PCA may be somewhat dangerous to do
What is the curse of dimensionality? - Cross Validated Specifically, I'm looking for references (papers, books) which will rigorously show and explain the curse of dimensionality This question arose after I began reading this white paper by Lafferty and
Explain Curse of dimensionality to a child - Cross Validated The curse of dimensionality is somewhat fuzzy in definition as it describes different but related things in different disciplines The following illustrates machine learning’s curse of dimensionality: Suppose a girl has ten toys, of which she likes only those in italics: a brown teddy bear; a blue car; a red train; a yellow excavator; a green
Dimensionality reduction with least distance distortion Cosine similarity is directly related to euclidean distance for normalized vectors called then chord distance So, if you are using cosine or chord distance, you may use an iterative MDS, even its metric version MDS is expected to "distort" your distances less than any dimensionality reduction methods $\endgroup$ –
clustering - PCA, dimensionality, and k-means results: reaction to . . . As the dimensionality of the data increases, if the data are uniformly distributed throughout the space, then the distribution of the distances between all points converges towards a single value So to check this, we can look at the distribution of pairwise distances, as illustrated in @hdx1011's answer
What is embedding? (in the context of dimensionality reduction) In the context of dimensionality reduction one often uses word embedding, which seems to me a rather technical mathematical term, which rather stands out compared to the rest of the discussion, which in case of PCA, MDS and similar methods is just the basic linear algebra Yet, I would rather avoid using interpreting this term too loosely
dimensionality reduction - How to reverse PCA and reconstruct original . . . The centered data can then be projected onto these principal axes to yield principal components ("scores") For the purposes of dimensionality reduction, one can keep only a subset of principal components and discard the rest (See here for a layman's introduction to PCA )
Reduce or Increase Dimensionality? Machine Learning In many machine learning methods, we try to reduce the dimensionality and find a latent space manifold in which the data can be represented, i e neural networks taking in images In other methods like SVM kernels, we try and find a higher dimensional space so we can separate classify our data