Question at position 18 While creating a machine learning model on text data, you created a document term matrix of the input data of 100K documents. Which of the following remedies can be used to reduce the dimensions of data? 1. Latent Dirichlet Allocation2. Latent Semantic Indexing3. Keyword Normalization Select ALL correct answers. 312多项选择题
A
3
B
1
C
2

Question

Question at position 18 While creating a machine learning model on text data, you created a document term matrix of the input data of 100K documents. Which of the following remedies can be used to reduce the dimensions of data? 1. Latent Dirichlet Allocation2. Latent Semantic Indexing3. Keyword Normalization Select ALL correct answers. 312多项选择题

A

3

B

1

C

2

BlackTom AI · Accepted Answer

Latent Dirichlet Allocation (LDA) and Latent Semantic Indexing (LSI) are both established methods for reducing the dimensionality of a document-term matrix, so options 1 and 2 are correct.

1) Relevant knowledge points and concepts
- Document-term matrix (DTM): typically an N x V matrix (N = number of documents, V = vocabulary size) that is high-dimensional and sparse.
- Dimensionality reduction for text: map each document from V dimensions to a much smaller k dimensions (k << V) while preserving semantic structure.
- LSI: a linear algebra approach using truncated Singular Value Decomposition (SVD) to produce a low-rank approximation.
- LDA: a probabilistic topic model that represents each document as a distribution over k latent topics (topic proportions).

2) Step-by-step reasoning and mechanics
- Start with DTM X of shape N x V (here N = 100,000).
- LSI (SVD) procedure:
  - Compute SVD: X = U Σ V^T.
  - Truncate to k components: keep U_k (N x k), Σ_k (k x k), V_k (V x k).
  - Low-dimensional document vectors = U_k Σ_k (N x k). This reduces each document from V dims to k dims.
- LDA procedure:
  - Fit a generative model that finds k topics; estimate per-document topic proportions θ_d (k-dimensional vectors).
  - Each document is represented by θ_d (N x k), reducing dimensionality from V to k.

3) Intermediate steps / equations (illustrative)
- X: 100,000 x V
- SVD: X = U Σ V^T
- Truncate: X ≈ U_k Σ_k V_k^T
- Document embedding via LSI: d_i ≈ (U_k Σ_k)[i, :] ∈ R^k
- LDA embedding: θ_i ∈ R^k for each document i

4) Why the correct answers are correct
- Both LSI and LDA explicitly produce lower-dimensional representations (topic/component vectors) that reduce the feature space used for downstream models.

5) Why the other option is incorrect
- Keyword Normalization (option 3): refers to text preprocessing (lowercasing, stemming, lemmatization, removing punctuation). It may slightly reduce variant forms but does not systematically reduce the DTM dimensionality to a compact semantic k-dimensional space the way LSI/LDA do. It’s not a dimensionality-reduction algorithm.

6) Conclusion
Therefore, the correct remedies to reduce dimensions from the given options are 1 (LDA) and 2 (LSI), which matches the provided answer.

类似问题

The output of the Latent Dirichlet Allocation (LDA) topic model is:

The Latent Dirichlet Allocation (LDA) topic model is a generative model, that is it mimics (but in a simplified way) how humans write documents:

Who decides on the number of topics in the Latent Dirichlet Allocation (LDA) topic model?

The Latent Dirichlet Allocation (LDA) topic model needs an initial guess for the distribution of topics in documents and distribution of words in each topic:

The Latent Dirichlet Allocation (LDA) topic model accepts data in the following format (choose one best answer):

The topics are latent in the Latent Dirichlet Allocation topic model and therefore have to be inferred from the data:

The Latent Dirichlet Allocation (LDA) approach to topic modeling assumes that:

The Latent Dirichlet Allocation (LDA) estimates the distribution of topics in documents and the distribution of words in topics

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