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One-hot
View on Wikipediafrom Wikipedia
| Decimal | Binary | Unary | One-hot |
|---|---|---|---|
| 0 | 000 | 00000000 | 00000001 |
| 1 | 001 | 00000001 | 00000010 |
| 2 | 010 | 00000011 | 00000100 |
| 3 | 011 | 00000111 | 00001000 |
| 4 | 100 | 00001111 | 00010000 |
| 5 | 101 | 00011111 | 00100000 |
| 6 | 110 | 00111111 | 01000000 |
| 7 | 111 | 01111111 | 10000000 |
In digital circuits and machine learning, a one-hot is a group of bits among which the legal combinations of values are only those with a single high (1) bit and all the others low (0).[1] A similar implementation in which all bits are '1' except one '0' is sometimes called one-cold.[2] In statistics, dummy variables represent a similar technique for representing categorical data.
Applications
[edit]Digital circuitry
[edit]One-hot encoding is often used for indicating the state of a state machine. When using binary, a decoder is needed to determine the state. A one-hot state machine, however, does not need a decoder as the state machine is in the nth state if, and only if, the nth bit is high.
A ring counter with 15 sequentially ordered states is an example of a state machine. A 'one-hot' implementation would have 15 flip-flops chained in series with the Q output of each flip-flop connected to the D input of the next and the D input of the first flip-flop connected to the Q output of the 15th flip-flop. The first flip-flop in the chain represents the first state, the second represents the second state, and so on to the 15th flip-flop, which represents the last state. Upon reset of the state machine all of the flip-flops are reset to '0' except the first in the chain, which is set to '1'. The next clock edge arriving at the flip-flops advances the one 'hot' bit to the second flip-flop. The 'hot' bit advances in this way until the 15th state, after which the state machine returns to the first state.
An address decoder converts from binary to one-hot representation. A priority encoder converts from one-hot representation to binary.
Comparison with other encoding methods
[edit]Advantages
[edit]- Determining the state has a low and constant cost of accessing one flip-flop
- Changing the state has the constant cost of accessing two flip-flops
- Easy to design and modify
- Easy to detect illegal states
- Takes advantage of an FPGA's abundant flip-flops
- Using a one-hot implementation typically allows a state machine to run at a faster clock rate than any other encoding of that state machine[3]
Disadvantages
[edit]- Requires more flip-flops than other encodings, making it impractical for PAL devices
- Many of the states are illegal[4]
Natural language processing
[edit]In natural language processing, a one-hot vector is a 1 × N matrix (vector) used to distinguish each word in a vocabulary from every other word in the vocabulary.[5] The vector consists of 0s in all cells with the exception of a single 1 in a cell used uniquely to identify the word. One-hot encoding ensures that machine learning does not assume that higher numbers are more important. For example, the value '8' is bigger than the value '1', but that does not make '8' more important than '1'. The same is true for words: the value 'laughter' is not more important than 'laugh'.
Machine learning and statistics
[edit]In machine learning, one-hot encoding is a frequently used method to deal with categorical data. Because many machine learning models need their input variables to be numeric, categorical variables need to be transformed in the pre-processing part. [6]
| Food Name | Categorical # | Calories |
|---|---|---|
| Apple | 1 | 95 |
| Chicken | 2 | 231 |
| Broccoli | 3 | 50 |
| Apple | Chicken | Broccoli | Calories |
|---|---|---|---|
| 1 | 0 | 0 | 95 |
| 0 | 1 | 0 | 231 |
| 0 | 0 | 1 | 50 |
Categorical data can be either nominal or ordinal.[7] Ordinal data has a ranked order for its values and can therefore be converted to numerical data through ordinal encoding.[8] An example of ordinal data would be the ratings on a test ranging from A to F, which could be ranked using numbers from 6 to 1. Since there is no quantitative relationship between nominal variables' individual values, using ordinal encoding can potentially create a fictional ordinal relationship in the data.[9] Therefore, one-hot encoding is often applied to nominal variables, in order to improve the performance of the algorithm.
For each unique value in the original categorical column, a new column is created in this method. These dummy variables are then filled up with zeros and ones (1 meaning TRUE, 0 meaning FALSE).[citation needed]
Because this process creates multiple new variables, it is prone to creating a 'big p' problem (too many predictors) if there are many unique values in the original column. Another downside of one-hot encoding is that it causes multicollinearity between the individual variables, which potentially reduces the model's accuracy.[citation needed]
Also, if the categorical variable is an output variable, you may want to convert the values back into a categorical form in order to present them in your application.[10]
In practical usage, this transformation is often directly performed by a function that takes categorical data as an input and outputs the corresponding dummy variables. An example would be the dummyVars function of the Caret library in R.[11]
See also
[edit]- Constant-weight code – Method for encoding data in communications, where a constant number of bits are set
- Two-out-of-five code – Error-detection code for decimal digits, widely used in barcoding and at one time in telephone exchanges
- Bi-quinary coded decimal – Numeral encoding scheme
- Gray code – Ordering of binary values, used for positioning and error correction
- Kronecker delta – Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
- Indicator vector
- Serial decimal
- Single-entry vector – Concept in mathematics
- Unary numeral system – Base-1 numeral system
- Uniqueness quantification – Logical quantifier
- XOR gate – Logic gate
References
[edit]- ^ Harris, David and Harris, Sarah (2012-08-07). Digital design and computer architecture (2nd ed.). San Francisco, Calif.: Morgan Kaufmann. p. 129. ISBN 978-0-12-394424-5.
{{cite book}}: CS1 maint: multiple names: authors list (link) - ^ Harrag, Fouzi; Gueliani, Selmene (2020-08-11). "Event Extraction Based on Deep Learning in Food Hazard Arabic Texts". arXiv:2008.05014 [cs.SI].
- ^ Xilinx. "HDL Synthesis for FPGAs Design Guide". section 3.13: "Encoding State Machines". Appendix A: "Accelerate FPGA Macros with One-Hot Approach". 1995.
- ^ Cohen, Ben (2002). Real Chip Design and Verification Using Verilog and VHDL. Palos Verdes Peninsula, CA, US: VhdlCohen Publishing. p. 48. ISBN 0-9705394-2-8.
- ^ Arnaud, Émilien; Elbattah, Mahmoud; Gignon, Maxime; Dequen, Gilles (August 2021). NLP-Based Prediction of Medical Specialties at Hospital Admission Using Triage Notes. 2021 IEEE 9th International Conference on Healthcare Informatics (ICHI). Victoria, British Columbia. pp. 548–553. doi:10.1109/ICHI52183.2021.00103.
- ^ Brownlee, Jason. (2017). "Why One-Hot Encode Data in Machine Learning?". Machinelearningmastery. https://machinelearningmastery.com/why-one-hot-encode-data-in-machine-learning/
- ^ Stevens, S. S. (1946). “On the Theory of Scales of Measurement”. Science, New Series, 103.2684, pp. 677–680. http://www.jstor.org/stable/1671815.
- ^ Brownlee, Jason. (2020). "Ordinal and One-Hot Encodings for Categorical Data". Machinelearningmastery. https://machinelearningmastery.com/one-hot-encoding-for-categorical-data//
- ^ Brownlee, Jason. (2020). "Ordinal and One-Hot Encodings for Categorical Data". Machinelearningmastery. https://machinelearningmastery.com/one-hot-encoding-for-categorical-data//
- ^ Brownlee, Jason. (2017). "Why One-Hot Encode Data in Machine Learning?". Machinelearningmastery. https://machinelearningmastery.com/why-one-hot-encode-data-in-machine-learning/
- ^ Kuhn, Max. “dummyVars”. RDocumentation. https://www.rdocumentation.org/packages/caret/versions/6.0-86/topics/dummyVars
One-hot
View on Grokipediafrom Grokipedia
One-hot encoding is a fundamental representation technique in computer science and machine learning, where categorical or discrete data is transformed into binary vectors of fixed length equal to the number of possible categories, with exactly one element set to 1 (indicating the active category or state) and all others set to 0.[1] This method produces sparse, high-dimensional vectors that are semantically independent, ensuring no implicit ordering or numerical relationships are assumed between categories.[1]
Originating from digital circuit design, one-hot encoding is commonly applied in finite state machines (FSMs) to assign states using dedicated flip-flops, where each state activates a unique bit to simplify next-state and output logic while minimizing combinational complexity.[2] In this context, it facilitates efficient implementation in hardware like field-programmable gate arrays (FPGAs), though it requires more storage than binary or Gray coding for large state spaces.[1] The approach's simplicity in logic design makes it advantageous for systems demanding clear state distinction, but its exponential growth in bit width can increase bandwidth demands.[1]
In machine learning, one-hot encoding serves as a key preprocessing step for handling nominal categorical variables, enabling algorithms such as neural networks, decision trees, and support vector machines to process non-numeric data without bias toward artificial hierarchies.[3] It is particularly prevalent in natural language processing for tokenizing words or characters within a vocabulary, where each unique item receives its own binary indicator vector.[1] Despite its ease of implementation and ability to preserve category distinctions, one-hot encoding can lead to the curse of dimensionality in datasets with many categories, resulting in sparse representations that may degrade model performance or increase computational costs.[1] Alternatives like label encoding or embeddings are often considered for high-cardinality features to mitigate these issues.[4]
This function assumes a pre-defined list of categories and produces a dense binary vector for a single input.[12]
For datasets with a large number of categories (high dimensionality), dense binary vectors can consume excessive memory due to the predominance of zeros; in such cases, sparse matrices are preferred, storing only the non-zero indices and values to optimize space and computation.[12]
Fundamentals
Definition
One-hot encoding is a representational scheme used to convert categorical variables into binary vectors of dimension , where denotes the number of distinct categories, such that exactly one element in the vector is set to 1 (indicating the active category) and all remaining elements are 0.[5] This approach ensures that each category is distinctly and equally represented without implying any numerical hierarchy or ordering among them.[5] The concept originated in digital electronics, where it was employed for state representation in finite state machines (FSMs) within sequential circuits, assigning a dedicated flip-flop to each possible state to simplify decoding and minimize combinational logic requirements.[1] In this context, the term "one-hot" derives from the single "hot" (active high) bit among otherwise "cold" (low) bits, facilitating unambiguous state identification in hardware designs.[2] It corresponds to the use of dummy variables or indicator variables in statistics and was later adapted under the name one-hot encoding for data representation in machine learning to handle nominal categorical data effectively.[6] A key distinction from binary encoding lies in one-hot's avoidance of positional weighting, where binary methods assign decimal values based on bit positions (e.g., treating categories as 00, 01, 10, implying ordinal progression), potentially introducing unintended assumptions of order or magnitude that are inappropriate for non-ordinal categories.[5] In contrast, one-hot treats categories as mutually exclusive without such implications, preserving their nominal nature.[2] This vector form, often denoted mathematically as a standard basis vector in , provides a sparse, interpretable encoding suitable for various computational paradigms.[5]Mathematical Representation
In one-hot encoding, a categorical variable taking one of distinct values is represented as a vector . For the category indexed by (using 1-based indexing), the one-hot vector has a 1 in the -th position and 0s elsewhere, corresponding to the -th standard basis vector in : with the 1 at the -th entry.[7][8] Given an input category index , the resulting one-hot vector is defined component-wise by if and otherwise. This can be compactly expressed using the Kronecker delta function , which equals 1 if and 0 otherwise, as .[9][10] For a dataset with samples, each associated with a category index for , the one-hot representations form an matrix whose -th column is the one-hot vector . This matrix consists of selected columns from the identity matrix , specifically those corresponding to the category indices .[8] The dimensionality of each one-hot vector is , equal to the number of unique categories, which results in a highly sparse representation since only one entry is nonzero.[10][11]Encoding Techniques
Construction Process
The construction of one-hot encoding begins with identifying the unique categories present in the categorical dataset, typically during a fitting phase where the encoder learns the distinct values from the training data.[12] Next, integer indices are assigned to these categories in an arbitrary but consistent order, forming a mapping that determines the position of the '1' in the output vector.[13] For each input sample, a binary vector is then generated with length equal to the number of unique categories, placing a 1 at the index corresponding to the sample's category and 0s in all other positions.[12] When encountering unknown categories not seen during the fitting phase—such as new values in test data—implementations handle them variably: strict modes raise an error to prevent invalid encodings, while more flexible approaches set the entire vector to zeros to ignore the input or map unknowns to a designated infrequent category if configured. A dedicated "unknown" category can be manually included in the category list during fitting to handle unseen values explicitly.[12] A simple pseudocode representation of the core encoding function, based on standard implementations, is as follows:function one_hot_encode(category, category_list):
if category not in category_list:
# Handle unknown: e.g., raise error or return zero vector
raise ValueError("Unknown category")
index = category_list.index(category)
vector = [0] * len(category_list)
vector[index] = 1
return vector
function one_hot_encode(category, category_list):
if category not in category_list:
# Handle unknown: e.g., raise error or return zero vector
raise ValueError("Unknown category")
index = category_list.index(category)
vector = [0] * len(category_list)
vector[index] = 1
return vector