Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$?
Understanding Inverse Document Frequency (IDF)
The Inverse Document Frequency (IDF) measures how important a term is in a collection of documents. It diminishes the weight of terms that occur very frequently across documents, such as common words ('the', 'is', 'a'), and increases the weight of terms that occur rarely.
IDF Formula Derivation
Let:
- $N$ be the total number of documents in the collection.
- $d$ be the number of documents where the specific term $t$ appears (document frequency, often denoted as $df_t$).
The core component of the IDF calculation involves the ratio of the total documents to the documents containing the term. While IDF is typically calculated using a logarithmic function (e.g., $\log(\frac{N}{d})$ or $\log(\frac{N}{d+1})$ to avoid division by zero if a term doesn't appear), the question asks for the specific fraction used in its definition, representing the inverse relationship between document frequency and importance.
This fraction represents how many documents are 'missed' by the term. A higher value indicates a rarer term.
Selecting the Correct Fraction
Based on the definition and common formulas for IDF, the fraction representing the relationship between total documents ($N$) and the documents containing the term ($d$) is:
$ \frac{N}{d} $
Comparing this with the given options:
- Option 1: $\frac{N}{d}$ - Matches the required fraction.
- Option 2: $\frac{1}{N+d}$ - Incorrect structure.
- Option 3: $\frac{1}{N-d}$ - Incorrect structure.
- Option 4: $\frac{1}{Nd}$ - Incorrect structure.
Therefore, the fraction used to define the inverse document frequency (idf) of the term $t$ is $\frac{N}{d}$.
Important Questions from Numerical Computation
$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - The total number of unique character bigrams in the string thoughtsoftheghosts (which contains 19 characters) is ______.
A bacterium can be approximated as a cylinder with a hemisphere at each end, as shown in the figure. The cylinder has a height of $1 \mu\text{m}$ and diameter of $1 \mu\text{m}$. Assuming that the density of the bacterium is equal to that of water, what is the approximate mass of this bacterium?
Given: density of water = $10^3 \text{ kg/m}^3$; $1 \mu\text{m} = 10^{-6}\text{ m}$
Volume of a cylinder = $\pi r^2 h$, where $r$ is the radius and $h$ is the height of the cylinder
Volume of a sphere = $\frac{4}{3} \pi r^3$, where $r$ is the radius of the sphere
